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Darts

Darts is a fabulous sport. You can play it with your friends in local pubs or you can invite the neighbours to a darts-evening. You will never get bored with darts.

Darts is no longer just a pub sport. Millions of darts-fans all over the world have already hung a dart-board on their wall. There is no other play-ground where you can play so many different games as on the Clock-board.

In the following pages you can see some quotations of The Dart Book.

Kari Kaitanen 1996


The Dart Book

In this book you can find dozens of different interesting dart-games. Numerous examples with clear pictures welcome all new players to this great sport. You also learn how to throw more accurately.

For experts this book offers a deep and scientific study of darts. For the first time all the finishes of 01-games have been optimised with a computer from every point of the game five turns ahead. Just by knowing the absolute best finish for your level you will greatly improve your chances of winning.

THE DART BOOK, first edition 1994, Kari Kaitanen, 270 pages, ISBN 951-96680-1-2

 

Please note that I can't handle delivering any copies myself ! (Please order your copy for example through Darts World -Magazine: Darts World Book Shop, 9 Kelsey Park Road, Beckenham, Kent BR3 2LH, England, tel: 0181-650 6580, fax: 0181-650 2534. Order number (A81) and e.g. credit card number acquired, price about 10 ~ 13.Sold out !!! Please help us find a publisher in your country!)

 

DARTS PELIT ('Darts Games'), first edition 1992, Kari Kaitanen, 144 pages, ISBN 951-96680-0-4, sold out in 1992.
The new generation of dart-games is rapidly increasing in popularity in Finland. The first real strategy game in darts, Mawari, is an excellent choice from beginners to experts. As Snooker is called billiard's chess, Mawari is the chess of darts.



Different levels of players

In every sport there are those who win championships. Then there are those who are in it as a hobby. There are many different levels and many ways to throw darts. There are those who make a living with it and those who just enjoy the social life that darts provides - and usually spend their salary in places where they meet. Both players - in my opinion - live a very full life and probably die with a big smile on their face.

For the lesser players, as in every sport, it's almost impossible to beat a master. This is also true in darts. However, it's typical of darts that the game is interesting even if the players are of different levels. With a little luck a beginner can beat an average player. But what's also typical of darts is that there are not many sports where players of different levels can and should do so much so differently from each other. The right choices depend on the level you are playing at. This is if you want to win the game.

It's very useful to watch the decisions masters make and learn from them. But when for example speaking about finishes in 501 (or 301), all the masters have their own favourite finishes. Preferences speak more loudly when you try to find the best 'out', and there is not one objective player in the world to say which 'out' is the best. So this is not the way you can find the best finishes for your level. There is only one way to solve the problem. You must programme the computer to throw with the different - but exact - sprays of darts.

At first we must learn the figure of the dispersion. There is one old dart-player (there is no historical basis for this), Carl Friedrich Gauss (1777-1855), who helped us in this enormous task. Without his discovery of normally diversed phenomenon, it would be hard to calculate the probabilities exactly. Gauss's dispersion proved to depict the most natural symptoms in life. So we chose it to depict the distribution of dart shots.

Levels of players in The Dart Book

After solving how the darts are spread around the aiming point you must decide which kind of players you want to take into your calculations. I decided to use four different levels of players. Just to make it easier for you to know what level I am talking about, I have named these levels: professional, expert, average and beginner.

Since the dispersions of darts should be exact for finding the exact percentages for these levels, there must be something that makes them exact. I have chosen the probability of hitting the treble-bed. The 'professional's' probability of hitting the treble is hereby always 46.42% in the book. An expert can hit the treble with the probability of 21.54%. For an average player the same figure is 10.00% and for the beginner only 4.64%.

I have not chosen these numbers randomly: the percentage of a professional raised to the third power makes exactly 10%. You can thus say that a 'pro' can get 180 points - three darts to treble-bed - every tenth time he tries. As you may already have guessed an expert can score 180p every 100th time and so on.

                   probability of    probability of
                     hitting the       scoring 180
                       treble            points
------------------------------------------------------
professional (pro)     46.42%           1 to 10
expert (exp)           21.54%           1 to 100
average (ave)          10.00%           1 to 1000
beginner (beg)          4.64%           1 to 10000
------------------------------------------------------
You must, however, notice that the probability of getting 180 points is only theoretical: (46.4%^3 = 10%). After the first two darts there is already considerably less space on the treble-bed for the third dart. Therefore you often have to change your aiming point. Thus the 'right' probability of scoring the maximum score may be one-to-twenty or even less.

Then there is the mental pressure, which may be enormous. If you have never reached 180 points before, your hands may start to tremble. If you have practiced darts for many years already and have never scored 180, it is probably the biggest reason for this. It doesn't mean that you must now rank yourself in the 'beginners' group. In fact, even if you try to test the level of your play to find it out, there is no reason to start calling yourself 'an expert' or 'an average player'. As mentioned earlier, the names are used only because it's much easier to understand what kind of sprays I'm talking about. However, the test can help you to see what level you should be interested in.

On the other hand, after the first dart the beginner e.g. might have a good 'sighter' for his next shots, and the probability of throwing the remaining darts into the target can be much bigger than before. So, it's very hard to tell the exact level of scoring 180 points.

It would be more correct to say that an expert can hit three different trebles, for example T20, T15 and T16, every hundredth time. Since the theoretical probability is approximately right, it's easier to say that an expert can get 180 points every tenth time.


The exact dispersions of darts

The next task is to iterate the dispersions to receive the exact required percentage. Compared to the first book (published in Finnish) there are many minor improvements. First, the probabilities are calculated much more accurately; instead of using circles of four millimetres, the areas around the aiming point are divided into parts smaller than 0.05 mm. The difference is significant for example in the bull's-eye, the smallest target on the board.

The computer is programmed to imitate the real world as closely as possible. For example, the wires hamper the players. The critical wire width is programmed to be 0.2 mm. This means that an expert aiming at the centre of a treble-bed loses 1.7% of his shots as 'wire-darts'. In the bull's-eye the probability of wire-darts is already 3.1% for the expert.

Note that the wires are, of course, wider than the given 0.2 mm, but if the dart hits a bit on the side of a wire it still goes in. It is not possible to know the exact percentage of wire-darts, but it is important to tell the computer that it's more probable in some areas - like in the bull's-eye - than in the centre of singles. Nowadays technology makes darts more flexible and the percentage of wire-darts is getting smaller.

 


Professional (pro)

When the term 'professional player' (pro) is used in the book it means a player who can throw (theoretically) 180 points every 10th time. The dispersion of darts is thus very small. You can hear the great 'one-hundred-and-eightyyy...' shouted at the biggest tournaments often enough to know that this level is not just theoretical. However, there aren't many players in the world who represent this honourable level of play.

As you can see in the picture, the area of possible hits is small, when a 'pro' aims at the centre of a treble-bed. The dispersion of this level is programmed to the computer, and it uses exactly the same spray of darts when aiming at any point on the board. When the dispersion is estimated to be normally divided, you can calculate the exact probabilities for this level.

 


Expert player (exp)

The spray of darts is still quite small. If an 'expert player' (exp) aims at the middle of triple-20, no darts are missed over sectors 1 and 5. The possibility of throwing 180 points is one in a hundred (1:100). The player of this level most certainly plays in a darts-league. Since this level is already represented by a much greater amount of players - and is still a very high level - I have tried to mention the 'expert' player often.

The spray of darts around treble-20 already looks more human and possible to reach than the one of a 'professional player'. Already 16% of his darts fly to the adjacent sectors. The average scoring is still very high: 74.7 points with three darts (without doubling). This level can be the result of a great deal of practice and years of social life in local pubs.

 


Average player (ave)

The level of an average player can be very near the next one. The spray of hits is already quite large. Only one tenth of the darts hit triple-20 when aiming at the middle of it. Theoretically an average player (ave) is projected to throw 180 points every 1000th time. A few darts already miss over one sector and when for example trying the heart of treble-20, one dart in every thirteenth turn hits sector 18 or sector 12.

Only one tenth of the shots at a treble are successful. Note that the aiming point often has to be on the other side of a treble, when the bed is already crowded. Move the same spray of darts only one centimetre to the right and already every 26th dart (3.8%) hits sector 18 - meaning one dart every ninth turn. Does this look more like your play?

 


Beginner (beg)

Beginners are the group of players where levels vary the most. But when using the word 'beginner' (beg) in the book, it means that the spray of darts draws quite a large pancake around the aiming point. The 'beginner' finds it difficult to hit the same sector that he aims at and thus the average score is not much different in any area of the dart-board. 180 points is almost never achieved (1:10000).

A beginner finds it very frustrating to aim at a double-band. At first only one shot in fourteen will score. And then there is the baby in the next room who starts to cry every time you hit the enclosure cabinet. And these total misses are not few at the beginning of your road to the championship tournaments. Just a little practice and you will improve your play a great deal.


Theory

Note that in the 'real world' the dispersion of darts isn't usually exactly a circle, but an ellipse. This due to the way one throws darts at the dart-board. It's often more difficult to release the darts at the same point every time than to keep the same vertical line. This means the spray is more often high than wide. Of course there are players who do the opposite - they are the ones who are more likely to hit the single of sector six (and double-top) than the single-20.

To be more exact the ellipse may not be exactly vertical. For the right-handed players the figure usually leans a bit to the left. This comes from the motion of the hand when throwing. It also gives one more reason to use double-16 (and double-8) in doubling out.

For master players, however, the dispersion is closer to a circle and for them every area on the dart-board is quite as good.

Probabilities

As you have noticed, everything in darts has something to do with probabilities. When you choose the way of finishing you just try to find the best probability to win the game. The probability of the opponent finishing the next turn is also important. You can estimate these probabilities in your head or you can even calculate them mathematically, as you have seen done in the book first time ever.

At first you must find out the dispersions of darts for the player. You can do that with a test, but that would require a lot of throws to be reliable. Or you can do it purely mathematically when you know the theory of normal dispersion. Since we want to make the results of optimal play as general as possible, we must use a circle as the form of the dispersion. One way or another you have to know what the player's probability of hitting for example a double is, how many darts then fly to a single, which percentage to the sector beside and so on. These probabilities have to be known for every aiming point you want to calculate.

When you have found a suitable spray of darts, you simply move it around the dart-board. When you place exactly the same dispersion to the centre of a double you get the percentage of hitting the double. Note that for the computer there are three aiming points in every bed of treble, double and single.

Naturally, you must also use the same spray of darts for the bull's-eye.


Finding finishes with the computer

There are many variations for finishing 501. When placing only one aiming point in the middle of each bed: single, double and treble, there are exactly 82407 different ways to end the game! From 58 points you can finish in 1404 different ways! So, if you try to calculate the exact probabilities by hand, you will probably lose a good hand for playing darts.

To be a bit more exact, I chose to use three different aiming points in each bed: one in the middle, and two on both sides of the bed. As there still are 21 points in the bull, the computer uses 201 different aiming points when searching for the optimal play.

Different aiming points are marked a bit differently in the book than you may have seen before. For example 'T16(8)' means the point in treble-16 but closer to sector 8. Marking the aiming points like this also helps you to realise to which sector it is better to miss your dart - if you should miss it.

With the computer we can check every possible way to finish the game. Since the calculating model is quite simple, the programmes are also easy to make. A simple carefully made programme guarantees correct results. All you have to do is to make the computer try every possible aiming point on the dart-board, and search all possible - and sensible - areas the dart might hit. The computer must then try to finish the game from each different point. If it's not programmed to be selective, it has to again try every possible aiming point available. Note that a beginner can very easily hit one side of the board when trying for the other, but this shouldn't affect his choices.

The computer now plays with 201 different aiming points. Then it considers at least 15 different places (treble, double and single - in five sectors) around the aiming points where the dart may land. This makes already 3015 different variations, but for example around the bull's-eye there are 22 beds which the dart may hit. So I now simplify things a bit.

From every possible point it tries to continue the game again - with 201 different ways - and so on. For three darts the computer must thus check at least 27.407.000.000 (3015^3) different variations of play. And after this it has solved an optimised way to finish from only one point. In the game of 501 there are 162 different points where the player can finish the game. This means calculating the probabilities for 4.440.000.000.000 times!

All this requires powerful computers to get results in a reasonable time. Note that in the book I decided to go a bit further. Like in chess the computer thinks ahead five turns, i.e. 15 darts! And the variations above were calculated for three darts only. There were also more points than 162 to check this time. The computer searched for the best play from every point under 501! This of course means that you need to make a bit more complicated programmes to solve the problems.


Opponent's situation

There is more. As you have noticed solving the probability of finishing is only one part of the game. But there are always two players in darts and the opponent can finish the game before you. Winning the game means that you must finish first. To find the best way to play the computer must also consider the opponent's moves. When figuring out the optimal finishes, the computer checks the best finishes for every possible situation where the opponent can be. Note that it's assumes that both players play the game with similar skills.

Since the subject is quite interesting, let me show you the way the computer does the calculating. Let's take an example where a professional player has 90 points and three darts in hand. The opponent has 123 points. By playing T20-D15 a pro would still get to the bull with singles (20-20-B50). That is why T20-D15 is easier (47.8%) to finish with three darts than for example T18-D18 (46.5%):

An opponent of the same level is at 123 points and finishes the game in the next turn with the probability of 24.3%. This means that the player can still have a chance to win the game on the second turn with the probability of 75.7% (100%-24.3%). This means that the player will win the game (on the next two turns) with the probability of 78.5% (0.478+0.7570.405) when trying the path T20-D15. Because the probability for the path T18-D18 is better, 79.7% (0.465+0.7570.438), in this situation it's better to aim at treble-18.

Simple, isn't it!


Searching for the optimal play in 501

Finishing the game of 501 (301) is the most interesting part of the game. As in every sport you can learn a lot by watching how the masters play.

But the problem is that all players have their favourite doubles and finishes from each point. On the other hand, the level of play may be quite different from yours. There is no sense in trying to end the game when it would require a miracle and leads to a worse situation than in normal play.

The difference between several great endings is often small. This gives room for variations of different throws and only the worst ones can be claimed to be wrong. As a conclusion you may say that it's impossible for anyone to give exact rules for how you should finish your game.

It would, however, be interesting to know the exact and best way to play the game. This is not only for memorising - which of course gives you a big advantage - but analysing the game is also a very useful way to improve your own game.

Computer throws darts

This was the reason to make a computer throw darts. You can programme different dispersions of darts to a computer and thus find the very best finishes for each level of players.

Since the best throw means the best aiming points to win this game - and not finishing on the next turn - you can also see when a player should go for it and when to play it safe. With a more complicated programme you can also include the opponent's situation in the game and find the best throw for every 'real' situation of the game.

There are only a few differences from the real world. For example, due to a lot of practice you may find triple-20 a bit easier target than triple-19. If the difference in probabilities in table is very small, you should choose T20 to play. Better players, like professionals, should be able to hit any part of the board with almost the same success. Since the computer has never 'practiced' darts, it recommends triple-19, even when it is only a little better throw than e.g. triple-20.

At first for a beginner and an average player triple-19 is the best choice for scoring, but it is assumed that this will pass with a lot of practice. Therefore the theoretical notation of the computer - that at bigger points a beginner should use T19 to get points - is removed from the table.


How to read the table of optimised play

In the following table you will see some results of optimised play in 501. (This table and lots of others are enclosed into The Dart Book. There you can find the optimised play for each point - up to 501pts - also for the second and the last dart in your hand.)

The best paths have been selected by a computer for four different levels of players. Since the area of hits is very large for a beginner, the optimised aiming point might sometimes be in a peculiar place. If for example the sectors 17 and 19 are the right areas to play, the computer may recommend aiming at triple-3. This is no doubt the best place to aim at if the dispersion of darts is big, but since this is in controversy with the basics of darts, I have usually removed these paths from the table. In these cases it's better to practice your throwing - and not start throwing into awkward places on the board. There is a lot of other information hidden in the table.

For every level an exact dispersion is chosen so that exact percentages can be calculated. So please remember that the name of the level only describes the level of players. It doesn't mean that e.g. every 'pro' scores 180 points every tenth time. It only makes the table more understandable.

As mentioned in the book getting to small points doesn't always mean that you have better possibilities to finish the game. The local tops of the winning probabilities (when the opponent has those 32 points) are marked with exlamation marks (in the book it's a small dot).

For maximum accuracy the computer may recommend that you don't use the middle of the bed but one side of it. "T19(7)" means that the best aiming point is in triple-19 but closer to sector 7. With the help of the computer it is possible to find an even more exact point, but it would be more difficult to mark it.

Marking the finishes this way also helps the player to understand the game. You can see that if you miss sector 19, it will be better to avoid sector three and hit sector seven. Moving the aiming point, however, means that you don't hit the best target as often. Since the exact side point is programmed to be 6 (from the centre) to the other side in every bed, the computer may recommend another side for the average player and the centre of the bed for experts. This doesn't mean that the optimal target for an expert is in the centre - but closer to it than to the side point. So, if you read carefully, you also receive information between the lines.

The order of the rows is not random. For each level of player the first path is the best when the exp-level opponent has 32 points (D16). This means the most critical - and perhaps most important - situation. The second path is better than the third one and so on.

Note that there are some points where the outer bull (25p) is the best way to continue the game. But, as proved in the book, the best chance for all levels to hit the outer bull is when you aim at the centre of the bull. (This is when the inner bull doesn't lead you to a bad situation, like busting.) Only if you are better than the 'professional' mentioned in the book, do you start to get an advantage from moving your aiming point to the outer bull. Therefore, if 25 points is the best way to continue the game, the best aiming point is given in parenthesis "B50(25)".

The probabilities of finishing are also listed. There you can find the finishing percentages for the turn (3 darts). The computer optimises your play five turns ahead, so it "plays" the game 15 darts ahead - this means it optimises the game from the very beginning of 501! There are no limits for planning the game even further ahead, but the following turns have little impact on this turn.

Note that the probability of finishing doesn't mean the probability of exactly throwing the mentioned path! That is not important. The probability means the chances of finishing the game when you start the turn by aiming at the given point. All the possible mistakes and the different variations they cause are taken into account in the percentage.

The limits show you at what points the opponent may be when the path is recommended. The level of the opponent should now be the same as the player's - as in most cases it is.


The table of optimised play with the first dart

The following table and lots of others are enclosed into The Dart Book. There you can find the optimised play for each point (up to 501pts) - also for the second and the last dart in your hand.

----------------------------------------------------------------------------------
PTS FINISH                pro         expert      average     R rec. finish lost
                          player,     player,     player,       lvl  with 3 prob.
                          use when    use when    use when           darts  op32p
                          oppon. at   oppon. at   oppon. at          (exp)  (exp)
----------------------------------------------------------------------------------
170 T20-T20-B50           Always      Always      Always      R pro   0.5%      !

169 T20-T20-9...40p       (c)         (c)32..140p               exp    -         
    T20-T20-17...32p      2..501p                               pro    -    -0.1%
    T19-T20-12...40p                  141..501p   (c)32..146p   ave    -    -0.1%
    T19-T16-T16(8)...16p                          147..501p     ave    -    -1.1%

168 T20-T20-8(16)...40p               (c)32..109p (c)           exp    -        !
    T20-T19-11...40p      (c)         110..120p                 exp    -    -0.0%
    T20-T19-19...32p      32..375p                              pro    -    -0.1%
    T19-T19-14...40p                  121..501p   2..501p       ave    -    -0.2%

167 T20-T19-B50           (c)32..160p (c)32..65p              R pro   0.5%      !
    T19-T20-B50                                               R pro   0.5%  -0.1%

166 T20-T20-14...32p      36..270p    2..501p                   exp    -         
    T20-T17-15...40p      (c)32..82p                            pro    -    -0.1%

165 T20-T16-17...40p                  (c)32..174p (c)           exp    -        !
    T19-T20-8(16)...40p                           32..140p      ave    -    -0.5%
    T19-T19-11...40p                  170..501p                 beg    -    -0.5%
    B50-T19-18...40p      (c)32..270p                           pro    -    -2.1%

164 T19-T19-B50           32..135p    32..65p                   pro   0.5%      !
    T20-T18-B50           (c)         (c)                     R exp   0.5%  -0.7%
    T19-T19-10...40p                  62..348p    2..501p       exp   0.0%  -1.3%
    T20-T16-16...40p                              (c)           ave   0.0%  -1.5%
    B50-T20-14...40p      131..400p                             pro    -    -3.7%

163 T20-T19-14...32p      259..300p   2..501p                   exp    -         
    T20-T19-6(10)...40p               (c)         (c)           exp    -    -0.0%
    T20-B50-13...40p      (c)32..260p                           pro    -    -0.4%
    T19-T14-T16(8)...16p                          32..501p      ave    -    -0.9%

162 T20-T20-10(6)...32p               (c)32..93p  (c)           exp    -        !
    T20-T20-10...32p      Always      83..501p                  exp    -    -0.0%
    T19-T16-17...40p                              2..501p       ave    -    -0.7%

161 T20-T17-B50           (c)32..130p (c)32..40p              R pro   0.5%      !
    T20-T19-12...32p      132..135p   33..185p                  exp   0.0%  -0.5%
    T20-T19-8(16)...36p                           (c)           ave   0.0%  -0.8%
    T19-T16-16...40p                              2..501p       ave   0.0%  -1.2%
    T19-T19-15...32p                  186..501p                 exp   0.0%  -1.2%
    B50-T20-19...32p      131..501p                             pro    -    -3.7%

160 T20-T20-D20           Always      Always      Always      R exp   1.2%      !
    T20-B50-B50                                               R ave   0.3%  -5.2%

159 T20-T19-10(6)...32p               (c)32..93p  (c)           exp    -         
    T20-T19-10...32p      (c)32..300p 81..501p                  exp    -    -0.0%
    T19-T14-20...40p                              32..501p      beg    -    -0.6%
    T20-T17-16...32p      299..501p                             pro    -    -1.2%

158 T20-T20-D19           (c)32..410p (c)32..180p (c)         R exp   1.2%      !
    T20-T20-6...32p                   181..213p                 exp   0.0%  -4.1%
    T19-T19-12...32p                              2..501p       ave   0.0%  -5.3%

157 T20-T19-D20           (c)32..380p Always      (c)         R exp   1.2%      !
    T19-T20-D20                                   2..501p     R ave   1.2%  -0.7%

156 T20-T20-D18           (c)32..450p (c)32..205p (c)         R exp   1.2%      !
    T19-T19-10(6)...32p                           2..501p       ave    -    -4.3%
    T19-T19-10...32p                  206..338p                 exp    -    -4.3%

155 T20-T19-D19           (c)32..350p 32..180p    (c)         R exp   1.2%      !
    T19-T20-D19                       (c)         32..109p      ave   1.2%  -0.2%
    T20-T19-6...32p       339..440p   181..240p                 exp   0.0%  -4.1%
    T19-T14-16...40p                              110..501p     ave   0.0%  -5.3%

154 T19-T19-D20           32..52p     2..501p     2..501p       exp   1.2%      !
    T20-T18-D20           34..341p                            R pro   1.2%  -0.2%
    T20-T20-D17           (c)         (c)         (c)           exp   1.2%  -0.4%
    T18-T20-D20                                               R pro   1.2%  -1.4%

153 T20-T19-D18           (c)32..450p Always      Always      R exp   1.2%      !

152 T20-T20-D16           (c)32..370p Always      Always      R exp   1.2%      !

151 T20-T17-D20           2..501p     Always                  R exp   1.2%      !
    T19-T18-D20                                   2..501p     R ave   1.2%  -0.2%
    T20-T19-D17           (c)                     (c)           ave   1.2%  -0.4%
    T17-T20-D20                                               R pro   1.2%  -2.0%

150 T19-T19-D18           84..450p    2..501p     2..501p       exp   1.2%      !
    T20-T18-D18           32..140p                            R pro   1.2%  -0.3%
    T20-T20-D15           (c)         (c)         (c)         R exp   1.2%  -0.7%
    T20-B50-D20                                               R exp   0.6%  -2.6%

149 T20-T19-D16           (c)32..310p 32..93p     (c)         R pro   1.2%      !
    T19-T20-D16                       (c)81..501p 2..501p     R exp   1.2%  -0.1%

148 T20-T16-D20           32..270p    32..220p                R exp   1.2%      !
    T19-T17-D20                       (c)                       exp   1.2%  -0.2%
    T20-T20-D14           (c)                                 R exp   1.2%  -0.6%
    T16-T20-D20                       219..501p               R exp   1.2%  -0.8%
    T19-T19-D17(2)                                (c)32..160p   ave   1.0%  -1.5%
    T18-T18-D20                                               R exp   1.2%  -1.9%

147 T19-T18-D18           32..275p    32..160p    32..501p    R exp   1.2%      !
    T20-T17-D18                                               R pro   1.2%  -0.2%
    T20-T19-D15           (c)         (c)         (c)           exp   1.2%  -0.3%
    T19-T16-10...32p      273..310p   199..327p                 exp   0.0%  -3.9%

146 T19-T19-D16           2..501p     Always      Always      R exp   1.2%      !
    T20-T18-D16           (c)                                 R pro   1.2%  -0.7%

145 T20-T15-D20           32..170p    2..501p                 R exp   1.2%      !
    T20-T19-D14           (c)                                 R exp   1.2%  -0.1%
    T19-T16-D20                                   2..501p       ave   1.2%  -0.2%
    T20-T15(10)-D20                   99..246p                  exp   1.0%  -0.6%
    T18-T17-D20           448..501p                           R exp   1.2%  -1.9%
    T17-T20-D17                       (c)         (c)           exp   1.2%  -2.9%
    B50-T19-D19           159..450p                             pro   0.6%  -3.1%

144 T20-T20-D12           (c)         32..207p                R exp   1.2%      !
    T20-T16-D18                       208..501p               R exp   1.2%  -0.1%
    T19-T17-D18           32..260p                              pro   1.2%  -0.4%
    T19-T19-D15                       (c)         (c)32..48p    ave   1.2%  -0.4%
    T20-T18-D15                                               R exp   1.2%  -0.9%
    T19-T19(7)-D15                                37..85p       ave   1.0%  -1.2%
    T18-T18-D18                                               R exp   1.2%  -1.9%
    B50-T18-D20           261..341p                             pro   0.6%  -3.6%

143 T19-T18-D16                       2..501p                 R exp   1.2%      !
    T20-T17-D16                       (c)                     R exp   1.2%  -0.1%
    T20-T19-D13           (c)                                 R exp   1.2%  -0.3%
    T19-T16-D19                                   32..64p       ave   1.2%  -0.3%
    T18-T19-D16           32..310p                              pro   1.2%  -1.2%
    T17-T20-D16                                   (c)           ave   1.2%  -2.1%
    T19-T14-12...32p                              63..501p      ave   0.0%  -3.9%

142 T20-T14-D20           32..130p    2..501p                 R exp   1.2%      !
    T20-T18-D14                                               R exp   1.2%  -0.4%
    T19-T15-D20                                               R beg   1.2%  -0.4%
    T20-T20-D11           (c)                                 R exp   1.2%  -1.0%
    T19-T15(10)-D20                               2..501p       ave   1.0%  -1.0%
    T19-T17-D17                       (c)                       exp   1.2%  -1.1%
    T20-B50-D16           128..129p   90..221p                R exp   0.6%  -1.5%
    T18-T16-D20                                               R exp   1.2%  -1.8%
    B50-T20-D16           131..370p                             pro   0.6%  -3.0%

141 T20-T19-D12           (c)         32..183p                R exp   1.2%      !
    T19-T20-D12           32..130p    (c)                       pro   1.2%  -0.2%
    T20-T15-D18                                               R exp   1.2%  -0.3%
    T19-T16-D18                                   2..501p     R ave   1.2%  -0.4%
    T20-T17-D15                                               R exp   1.2%  -0.6%
    T20-T15(10)-D18                   184..501p                 exp   1.0%  -0.9%
    T17-T18-D18                                               R exp   1.2%  -3.0%
    T17-T20-D15                                   (c)           ave   1.2%  -3.3%
    B50-T17-D20           131..501p                             pro   0.6%  -3.5%

140 T20-D20-D20           (c)32..89p  (c)32..60p                exp   1.5%      !
    T20-T20-D10           90..270p    61..130p                R exp   1.2%  -0.5%
    T20-T16-D16           265..501p   145..317p   32..102p    R ave   1.2%  -0.9%
    T20-20-20...40p                   128..144p                 exp   0.2%  -3.4%
    T19-T17-D16                       318..501p   (c)           ave   1.2%  -4.6%
    T18-T18-D16                                               R exp   1.2%  -6.1%
    T19-19-T16(8)...16p                           103..501p     ave   0.1%  -8.4%

139 T19-T14-D20           32..130p    2..501p     2..501p     R exp   1.2%       
    T20-T19-D11           (c)                                 R exp   1.2%  -0.3%
    T19-T18-D14                                   (c)         R exp   1.2%  -0.4%
    T20-T13-D20                                               R exp   1.2%  -1.2%
    T19-B50-D16           128..501p   90..221p                R exp   0.6%  -1.4%
    T20-T17-D14                                               R exp   1.2%  -1.5%
    T18-T17-D17                       (c)                       exp   1.2%  -5.3%

138 T20-D19-D20           32..60p     32..60p                   exp   1.5%      !
    T20-T18-D12           61..334p    33..120p                R exp   1.2%  -0.4%
    T20-D20-D19           (c)         (c)                       exp   1.5%  -0.6%
    T20-T20-D9                                                R exp   1.2%  -0.8%
    T20-T14-D18           335..450p                           R exp   1.2%  -1.3%
    T19-T19-D12                                   2..501p     R ave   1.2%  -1.6%
    T18-T20-D12           131..170p                             pro   1.2%  -1.7%
    T19-T17-D15                                   (c)           ave   1.2%  -2.1%
    T20-20-18...40p                   121..501p                 exp   0.2%  -3.3%
    T18-B50-D17           159..221p                             pro   0.6%  -3.4%

137 T20-T19-D10           33..270p    32..143p                R exp   1.2%      !
    T19-D20-D20           (c)32..40p  (c)                       exp   1.5%  -0.5%
    T20-T15-D16           262..315p                           R exp   1.2%  -1.1%
    T19-T16-D16                                   2..501p     R ave   1.2%  -1.4%
    T17-T18-D16           311..501p                           R pro   1.2%  -2.9%
    T20-19-18...40p                   144..501p                 exp   0.1%  -3.2%
    T18-T17-D16                                   (c)           ave   1.2%  -3.3%

136 T20-D18-D20           32..60p     32..40p                   exp   1.5%      !
    T20-D20-D18           (c)         (c)                       exp   1.5%  -0.2%
    T20-T20-D8            61..334p    33..130p                R exp   1.2%  -0.3%
    T20-T16-D14                                               R exp   1.2%  -0.4%
    T19-T19-D11                       82..97p     32..48p       ave   1.2%  -0.6%
    T19-T17-D14                                   (c)           ave   1.2%  -1.8%
    T20-20-16...40p                   141..501p   55..88p       ave   0.2%  -3.2%
    T19-20-19...40p                   91..140p    33..501p      ave   0.0%  -3.6%

135 T19-D19-D20                       32..60p                 R exp   1.5%      !
    T19-T18-D12           265..334p   33..52p                 R exp   1.2%  -0.4%
    T20-T17-D12           95..270p    61..160p                R exp   1.2%  -0.5%
    T20-T15-D15                                               R exp   1.2%  -1.0%
    T19-T14-D18           335..450p               36..501p      ave   1.2%  -1.3%
    T20-T13-D18                                               R exp   1.2%  -2.0%
    T18-T17-D15                                   (c)           ave   1.2%  -3.0%
    T19-19-19...40p                   159..501p   32..139p      ave   0.1%  -3.4%
    B50-T15-D20           32..100p                            R pro   1.6%  -5.5%
    B50-T19-D14           (c)         (c)                     R pro   1.6%  -5.6%

134 T20-D17-D20           32..60p     32..40p                   exp   1.5%      !
    T20-T14-D16           61..310p    33..501p                R exp   1.2%  -0.0%
    T20-D19-D18           (c)                                   pro   1.5%  -0.2%
    T19-T19-D10                                   32..74p     R ave   1.2%  -0.3%
    T20-T18-D10                                               R exp   1.2%  -0.5%
    T18-D20-D20                       (c)                       exp   1.5%  -0.9%
    T19-T19-D10(6)                                75..92p       ave   1.0%  -1.1%
    T19-T15-D16                                               R ave   1.2%  -1.4%
    T17-T17-D16           302..410p               (c)           pro   1.2%  -2.8%
    T19-19-18...40p                               91..501p      beg   0.1%  -3.4%

133 T19-D18-D20           32..60p     32..40p                   exp   1.5%      !
    T20-T19-D8            61..354p    33..198p                R exp   1.2%  -0.1%
    T19-D20-D18           (c)                                   beg   1.5%  -0.2%
    T19-T20-D8                                                R pro   1.2%  -0.3%
    T20-T11-D20           355..501p                           R exp   1.2%  -1.1%
    T14(11)-T17-D20                   (c)                       exp   1.6%  -2.8%
    T14(11)-T19-D17                               (c)           ave   1.6%  -3.1%
    T19-20-16...40p                               2..501p       ave   0.2%  -3.1%
    T20-17-16...40p                   199..501p                 exp   0.1%  -3.4%

132 T20-D20-D16           261..501p   2..501p                   exp   1.5%      !
    T20-T16-D12           211..260p   33..260p                R exp   1.2%  -0.1%
    T20-T12-D18                                               R exp   1.2%  -0.5%
    T19-T17-D12           95..210p    82..99p                   exp   1.2%  -0.6%
    T20-T20-D6                                                R exp   1.2%  -0.8%
    T19-T19-D9                                    32..40p       ave   1.2%  -1.0%
    T18-T18-D12                                               R exp   1.2%  -1.5%
    T17-T17-D15                                   (c)           ave   1.2%  -3.7%
    T19-19-16...40p                               33..501p      ave   0.1%  -3.7%
    B50-T14-D20           32..100p                            R pro   1.6%  -4.2%
    B50-T18-D14           (c)                                 R pro   1.6%  -4.4%
    B50-T20-D11                       (c)                       exp   1.6%  -4.7%
    B50-B50-D16                                               R pro   1.3%  -4.9%

131 T19-D17-D20           32..60p     32..40p                   exp   1.6%      !
    T19-T14-D16                       33..501p                R exp   1.3%  -0.0%
    T19-D19-D18           (c)                                   pro   1.6%  -0.2%
    T20-T13-D16           61..501p                            R exp   1.2%  -0.2%
    T20-T17-D10                                               R exp   1.2%  -0.8%
    T14(11)-T19-D16                   (c)         (c)           exp   1.6%  -0.9%
    T20-T19-D7                                                R exp   1.3%  -1.2%
    T19-18-16...40p                               2..501p       ave              

130 T20-T20-D5            (c)32..130p (c)32..40p              R pro   3.8%      !
    T20-20-B50                                                R exp   3.4%  -0.9%
    T20-T14-D14                       35..48p                   exp   2.5%  -1.3%
    T20-T10-D20                                               R exp   2.5%  -1.3%
    T20-T18-D8            125..129p                           R exp   2.5%  -1.6%
    T19-T19-D8            131..354p   33..197p    32..77p     R exp   1.2%  -3.1%
    T14(11)-T20-D14                               (c)           ave   1.6%  -4.1%
    T19-17-16...40p                   198..501p                 exp   0.1%  -6.3%
    T19-14-19...40p                               78..501p      ave   0.0%  -6.5%

129 T19-D20-D16           (c)32..65p  (c)32..40p                pro   2.8%       
    T19-T16-D12           62..89p     33..60p     32..501p    R pro   2.5%  -0.1%
    T20-T19-D6            79..135p                            R pro   2.5%  -0.4%
    T19-T12-D18                                               R pro   2.5%  -0.5%
    T19-T20-D6                                                R pro   2.5%  -0.8%
    T20-19-B50                                                R exp   2.1%  -2.0%
    T20-T15-D12                       61..67p                   exp   1.2%  -2.1%
    T20-T11-D18                                               R exp   1.2%  -2.1%
    T20-T15(10)-D12                   68..80p                   exp   1.0%  -2.6%
    T20-T13-D15                                               R exp   1.2%  -2.7%
    T18-T17-D12           131..310p   81..160p                  exp   1.2%  -3.1%
    T14(11)-T19-D15                               (c)           ave   1.6%  -3.4%

128 T20-D18-D16                       32..56p                   exp   2.3%       
    T18-D17-D20           32..60p                               pro   2.8%  -0.6%
    T18-T14-D16           61..130p                            R pro   2.5%  -0.6%
    T18-D19-D18           (c)                                   pro   2.8%  -0.8%
    T18-T18-D10                                               R pro   2.5%  -1.1%
    T18-D20-D17                       (c)                       exp   2.8%  -1.2%
    T20-18-B50                                                R exp   2.2%  -1.2%
    T19-T13-D16           125..501p   61..501p    85..501p    R ave   1.3%  -1.3%
    T20-T12-D16                       33..60p                   exp   1.2%  -1.3%
    T20-T16-D10                                               R exp   1.2%  -1.8%
    T20-T12(9)-D16                                32..84p       ave   1.0%  -1.8%
    T20-T20-D4                                                R exp   1.2%  -1.8%
    T15(10)-T17-D16                               (c)           ave   1.6%  -2.8%

127 T20-T17-D8            (c)32..160p (c)32..60p              R pro   3.8%      !
    T20-T9-D20                        61..67p                   exp   2.5%  -1.7%
    T20-17-B50                                                R exp   3.3%  -1.9%
    T19-20-B50                                                R exp   2.2%  -3.3%
    T19-T14-D14                                   32..501p      ave   1.2%  -3.7%
    T19-T10-D20                                               R exp   1.2%  -3.7%
    T19-T18-D8                                                R exp   1.2%  -4.0%
    T16-T19-D11                       63..97p                   exp   1.2%  -4.7%
    T15(10)-T14-D20                   221..501p                 exp   1.6%  -4.7%
    T18-T19-D8            159..354p                             pro   1.2%  -5.3%
    T15(10)-B50-D16                   201..220p                 exp   1.1%  -5.7%
    T9-T20-D20                                    (c)           ave   1.6%  -7.2%
    T16-20-19...40p                   91..200p                  exp   0.0%  -7.4%

126 T19-T19-D6            (c)32..135p (c)32..60p              R pro   3.8%      !
    T19-19-B50                                                R exp   3.3%  -1.6%
    T19-T15-D12                       61..67p                 R exp   2.5%  -1.7%
    T19-T11-D18                                   2..501p     R ave   2.5%  -1.7%
    T19-T15(10)-D12                   68..92p                   exp   2.3%  -2.1%
    T19-T11(14)-D18                               33..134p      ave   2.3%  -2.2%
    T16-T18-D12                                               R exp   2.5%  -3.1%
    T16-T14-D18                                               R beg   2.5%  -3.9%
    T20-16-B50                                                R exp   2.2%  -4.4%
    T20-D15-D18                                               R exp   1.5%  -5.0%
    T18-D20-D16           261..501p                             pro   1.5%  -5.1%
    T14-T20-D12                       91..205p                  exp   1.4%  -5.1%
    T18-T16-D12           256..260p                             pro   1.2%  -5.1%
    T14-T16-D18                       206..501p                 exp   1.4%  -5.2%
    T20-T12-D15                                               R exp   1.2%  -5.3%
    T20-T18-D6                                                R exp   1.2%  -5.4%
    T15(10)-T17-D15                               (c)           ave   1.6%  -5.5%
    T17-T17-D12           131..255p                             pro   1.2%  -5.8%

125 B50-T17-D12           (c)32..310p (c)32..61p  (c)         R pro   3.0%      !
    T20-B50(25)-D20                   62..89p                 R exp   2.4%  -1.0%
    B50-B50(25)-B50                                           R exp   2.9%  -1.2%
    T20-T15-D10                                               R exp   2.6%  -1.8%
    T18-T13-D16                                               R exp   2.5%  -2.9%
    T20-T11-D16                       88..200p                R exp   1.3%  -3.4%
    T20-15-B50                                                R exp   2.1%  -3.6%
    T20-T19-D4                                                R exp   1.3%  -3.8%
    T15-T16-D16                                               R exp   2.7%  -4.0%
    T19-T12(9)-D16                    204..501p   2..501p       ave   1.1%  -4.6%

124 T20-T14-D11           (c)32..130p (c)32..40p              R pro   3.8%       
    T20-T8(16)-D20                                32..82p       ave   2.8%  -0.6%
    T19-T17-D8            125..160p   33..60p                 R exp   2.5%  -0.9%
    T20-T16-D8                                                R ave   2.7%  -1.0%
    T20-14-B50                                                R ave   3.4%  -1.4%
    T20-T12-D14                                               R ave   2.5%  -1.9%
    T20-T20-D2                                                R exp   2.5%  -2.4%
    T19-T9-D20            159..227p   61..100p                  exp   1.2%  -2.6%
    T16-T20-D8            228..350p   91..136p                  exp   1.4%  -2.8%
    T14(11)-T18-D14                               (c)           ave   2.6%  -3.0%
    T18-T18-D8                                                R exp   1.2%  -4.7%
    T16-20-16...40p                   134..501p   180..501p     ave   0.3%  -5.5%
    T20-16(8)-8(16)...40p                         83..97p       ave              
    T19-11-16...40p                               98..179p      ave              

123 T19-T16-D9            (c)32..100p (c)32..40p              R pro   3.8%      !
    B50-T19-D8            95..354p    33..60p                   exp   3.1%  -0.2%
    B50-T17-D11                                   (c)           ave   3.1%  -0.5%
    T20-T13-D12                       61..77p                 R exp   2.5%  -1.0%
    T19-16-B50                                                R beg   3.4%  -1.3%
    T19-T14-D12                                   32..133p    R ave   2.5%  -1.7%
    T19-T10-D18                                               R ave   2.5%  -1.8%
    T20-T9-D18                        75..263p                  exp   1.2%  -3.4%
    T17-D20-D16           378..400p   264..501p                 exp   1.5%  -5.1%
    T19-10-16...40p                               134..501p     ave              

122 B50-D20-D16           261..380p   32..40p     (c)           exp   3.2%      !
    B50-T16-D12           90..260p    33..60p                 R exp   3.1%  -0.0%
    T19-B50(25)-D20                   61..89p     32..40p       exp   2.4%  -1.0%
    T18-D18-D16                                               R exp   3.6%  -2.5%
    T18-T18-D7            (c)32..89p  (c)                     R pro   3.8%  -2.8%
    T19-T11-D16                       88..240p    33..211p      ave   1.3%  -3.3%
    T18-18-B50                                                R exp   3.5%  -3.7%
    T18-T12-D16                                               R exp   2.6%  -3.7%
    T20-D15-D16                                               R exp   1.6%  -3.8%
    T20-T10-D16           381..501p                           R exp   1.3%  -3.9%
    T18-T20-D4                                                R exp   2.6%  -4.2%
    T16-T14-D16                       239..501p                 exp   1.5%  -4.7%
    T14-T16-D16                                   212..501p     ave   1.6%  -5.0%
    T12-T18-D16                                               R exp   2.8%  -5.9%

121 T20-B50(25)-D18                   32..40p                 R exp   3.6%      !
    B50-T13-D16           95..501p    33..103p                  exp   3.1%  -0.4%
    T20-T11-D14           (c)32..100p                         R pro   3.8%  -0.6%
    B50-T17-D10                                   (c)           ave   3.1%  -0.7%
    T20-T7-D20                                                R exp   2.7%  -2.1%
    T19-T8(16)-D20                    201..237p   32..501p      ave   1.7%  -2.1%
    T20-11-B50                                                R exp   3.3%  -2.4%
    T20-T15-D8                                                R exp   2.5%  -2.4%
    T19-T16-D8                                                R exp   1.6%  -2.5%
    T19-D16-D16                       238..501p                 exp   1.7%  -2.8%
    T17-T20-D5                        (c)                     R pro   3.8%  -2.9%
    T17-20-B50                                                R exp   3.4%  -3.8%
    T16-T19-D8                        102..200p                 exp   1.6%  -3.9%
    T17-T10-D20                                               R exp   2.5%  -4.1%
    T17-T18-D8                                                R exp   2.5%  -4.4%

120 T20-20-D20            Always      (c)32..248p Always      R exp   8.1%      !
    T20-D14-D16                       249..501p                 exp   4.7%  -8.0%

119 T19-T12-D13           (c)32..130p (c)32..40p              R pro   5.9%       
    T20-19-D20            125..501p   33..501p                R exp   5.0%  -0.2%
    T19-12-B50                                                R beg   5.5%  -1.3%
    T19-T10-D16                                               R ave   4.6%  -1.5%
    T19-T10(6)-D16                                32..154p      ave   4.4%  -2.0%
    19-T20-D20                                    (c)           ave   5.1%  -2.6%

118 T20-18-D20            Always      Always      (c)32..80p  R exp   8.2%      !
    T18-T16-D8                                                R ave   4.5%  -8.5%
    T18-14-B50                                                R ave   5.3%  -8.8%
    T19-19-10(6)...32p                            79..501p      ave              

117 T20-17-D20            33..501p    2..501p     2..501p     R exp   8.1%      !
    T19-20-D20            (c)32..40p  (c)         (c)         R beg   8.5%  -0.4%

116 T19-19-D20            (c)32..315p Always      2..501p     R exp   8.3%      !
    T20-16-D20            311..501p               (c)         R exp   8.3%  -0.7%
    T20-20-D18                                                R exp   8.2%  -1.8%

115 T19-18-D20            33..501p    2..501p     Always      R exp   8.4%       
    T20-15-D20            32..40p                             R exp   8.4%  -0.4%
    T20-17-D19            (c)         (c)                       exp   8.4%  -1.9%
    T15-20-B50                                                R exp   5.5%  -9.4%

114 T19-17-D20            32..40p     32..40p     2..501p       ave   8.4%       
    T20-14-D20            33..501p    33..501p                R exp   8.2%  -0.0%
    T20-18-D18                                                R exp   8.2%  -0.9%
    T20-16-D19                                    (c)           ave   8.2%  -1.5%
    T19-19-D19            (c)         (c)                       exp   8.5%  -1.7%

113 T19-16-D20            32..310p    (c)32..60p  (c)32..154p R pro   8.6%      !
    T20-13-D20            302..501p   61..501p                R exp   8.3%  -0.4%
    T20-17-D18                                                R exp   8.5%  -0.9%
    T19-18-D19            (c)                                   pro   8.6%  -1.6%
    T19-16(8)-D20                                 155..501p     beg   7.6%  -2.4%

112 T20-12-D20                        2..501p     32..40p     R exp   8.5%      !
    T20-20-D16            2..501p     170..254p               R pro   8.5%  -0.2%
    T20-16-D18            (c)         (c)         (c)           ave   8.6%  -0.5%
    T19-15-D20                                    33..501p      ave   8.3%  -0.9%

111 T19-14-D20                        2..501p     2..501p     R exp   8.5%      !
    T20-11-D20                                                R exp   8.4%  -0.6%
    T20-19-D16            2..501p                             R pro   8.4%  -0.8%
    T19-18-D18            (c)         (c)                     R exp   8.6%  -0.9%
    T19-16-D19                                    (c)           ave   8.6%  -1.4%
    T17-20-D20                                                R pro   8.1%  -2.2%

110 T19-13-D20            2..501p     2..501p     32..138p      exp   8.6%       
    T18-16-D20            90..270p                            R pro   8.5%  -0.2%
    T20-10-D20                                                R exp   8.5%  -0.4%
    T19-17-D18            (c)         (c)                       exp   8.7%  -0.5%
    T20-18-D16            271..415p                           R pro   8.4%  -0.7%
    T20-16-D17                                    (c)           ave   8.5%  -2.1%
    T14-T12(9)-D16                                139..501p     ave   4.7%  -9.1%
    T20-B50                                                   R ave    (2 darts)

109 T20-9-D20                         2..501p                 R exp   8.4%      !
    T19-12-D20                                    2..501p     R ave   8.5%  -0.2%
    T20-17-D16            2..501p                             R pro   8.4%  -0.2%
    T19-20-D16                                                R exp   8.5%  -0.4%
    T17-18-D20                        (c)                       exp   8.5%  -0.5%
    T19-16-D18            (c)                     (c)           ave   8.5%  -0.7%
    T14-T9-D20                                    75..99p       ave   5.7%  -7.3%

108 T20-8(16)-D20                     32..140p    Always        exp   9.1%      !
    T20-16(8)-D16                     141..152p                 exp   9.1%  -0.1%
    T16-20-D20            (c)32..90p  (c)                       pro   9.1%  -0.4%
    T20-8-D20                                                 R exp   8.9%  -0.6%
    T20-16-D16                                                R pro   8.8%  -0.7%
    T19-11-D20                        153..501p                 exp   8.4%  -1.4%
    T19-19-D16            91..501p    161..240p               R pro   8.4%  -1.6%
    T18-18-D18                                                R pro   8.8%  -3.4%

107 T19-10-D20                        32..283p    85..160p    R exp   9.3%      !
    T19-18-D16            32..347p                            R pro   9.2%  -0.2%
    T19-14-D18            (c)                                   pro   9.2%  -0.6%
    T19(7)-10-D20                                 32..84p       ave   8.8%  -1.3%
    T19-16-D17                        (c)                       exp   9.3%  -1.6%
    T19-10(6)-D20                                 161..501p     ave   8.2%  -2.3%
    T20-7-D20                                                 R pro   8.7%  -2.6%
    T19(7)-16-D17                                 (c)           ave   8.8%  -2.6%
    T18-13-D20                        284..501p                 exp   8.4%  -2.6%
    T20-15-D16            339..501p                           R pro   8.4%  -3.0%
    T17-16-D20                                                R pro   8.7%  -3.2%
    T19-B50                                                   R beg    (2 darts)

106 T20-6(10)-D20                     32..77p     (c)           exp   9.1%       
    T16-18-D20            (c)         63..99p     32..40p       exp   9.0%  -0.2%
    T20-10(6)-D18                     (c)                       exp   9.1%  -0.2%
    T20-6-D20                                                 R exp   8.9%  -0.5%
    T20-14-D16            61..501p    81..501p                R pro   8.5%  -0.9%
    T20-10-D18                                                R exp   8.9%  -1.0%
    T17-15-D20            32..60p                               pro   8.6%  -1.1%
    T18-12-D20                        119..141p                 exp   8.4%  -1.3%
    T14-T16(8)-D8                                 48..72p       ave   6.0%  -6.2%
    T14-T8(16)-D20                                33..84p       ave   6.0%  -6.3%

105 T19-8(16)-D20                     (c)2..501p                exp   9.6%      !
    T19-16(8)-D16                     130..348p                 exp   9.5%  -0.1%
    T16-17-D20            32..60p     61..137p    2..501p       ave   9.4%  -0.3%
    T19-8-D20                                                 R exp   9.3%  -0.6%
    T19-16-D16            61..501p                            R pro   9.2%  -0.7%
    T19(7)-8(16)-D20                              (c)           ave   9.1%  -1.6%
    T20-13-D16                                                R pro   8.9%  -1.7%
    T16-19-D19            (c)                                   pro   9.4%  -1.9%
    T20-5-D20                                                 R pro   8.9%  -2.0%
    T15-20-D20                                                R pro   8.7%  -3.1%

104 T16-16-D20            32..40p     32..220p    (c)32..156p   exp   9.5%      !
    T19-7(19)-D20                     (c)                       exp   9.7%  -0.6%
    T19-15-D16            33..100p                              pro   9.1%  -1.3%
    T16-18-D19            (c)                                   pro   9.5%  -1.5%
    T20-4-D20                                                 R exp   8.8%  -1.9%
    T18-10-D20                        221..501p               R pro   9.0%  -2.1%
    T20-12-D16                                                R pro   8.5%  -2.2%
    T16-16(8)-D20                                 157..501p     ave   8.5%  -2.3%
    T18-18-D16            99..501p                            R pro   8.9%  -2.3%
    T18-B50                                                   R ave    (2 darts)

103 T19-6(10)-D20                     32..80p     Always        exp  10.1%      !
    T19-10(6)-D18                     (c)                       exp  10.1%  -0.2%
    T19-6-D20             40..40p                             R exp   9.8%  -0.5%
    T19-14-D16            32..89p     81..224p                R pro   9.5%  -0.9%
    T19-10-D18            (c)                                 R exp   9.8%  -1.0%
    T20-3-D20                                                 R pro   9.5%  -1.6%
    T20-11-D16                        225..501p               R pro   8.9%  -2.7%
    T17-12-D20                                                R pro   9.2%  -2.9%
    T17-20-D16            90..501p                            R pro   9.1%  -3.1%

102 T20-10(6)-D16                     (c)32..100p               exp   9.6%       
    T14-20-D20            (c)32..65p              2..501p     R ave   9.6%  -0.3%
    T20-10-D16                        95..104p                R exp   9.3%  -0.5%
    T19-13-D16            62..501p    105..501p               R pro   8.9%  -1.2%
    T20(5)-10(6)-D16                              (c)           ave   9.2%  -1.4%
    T20-2-D20                                                 R pro   9.0%  -1.4%

101 T19-4(18)-D20                     32..40p                   exp  10.1%      !
    T19-4-D20                         34..48p     32..32p       exp   9.9%  -0.1%
    T19-12-D16                        33..190p    33..80p     R exp   9.5%  -0.3%
    T19-16(8)-D14                                             R beg  10.1%  -0.4%
    T19-8-D18                                                 R ave   9.9%  -0.5%
    T19-6(10)-D19                                 (c)           ave  10.1%  -0.9%
    T19-10(6)-D17                     (c)                       exp  10.1%  -0.9%
    T20-9-D16                                                 R pro   9.4%  -1.0%
    T18-7-D20             40..40p                               pro   9.7%  -1.1%
    T19-16-D14                                                R exp   9.8%  -1.2%
    T20-1-D20                                                 R pro   9.4%  -1.3%
    T16-13-D20                                    81..501p      ave   9.4%  -1.3%
    T18-15-D16            2..501p                               pro   9.4%  -1.5%
    T14-19-D20            (c)                                   beg   9.6%  -2.0%
    T17-10-D20                                                R pro   9.1%  -2.3%
    T17-18-D16                                                R pro   9.0%  -2.5%
    T15(10)-16-D20                    191..501p                 exp   8.7%  -3.1%
    T17-B50                                                   R ave    (2 darts)

100 T20-D20               Always      Always      Always      R exp  14.6%      !

99  T19-10(6)-D16                     (c)32..100p Always        exp  10.8%       
    T19-10-D16            (c)32..270p 95..230p                R pro  10.5%  -0.4%
    T19-2-D20                                                 R pro  10.2%  -1.4%
    T16-11-D20                        264..501p                 exp   9.4%  -3.9%
    T16-19-D16            268..501p   231..263p                 pro   9.3%  -4.0%

98  T20-D19               (c)32..255p (c)32..120p (c)32..83p  R exp  13.2%       
    T20-6-D16             254..315p   119..197p                 exp  10.7%  -4.2%
    T18-12-D16                                                R ave  10.3%  -5.3%
    T14-16-D20                                    84..157p      ave   9.7%  -7.0%
    T16-10-D20                        198..501p                 exp   9.6%  -7.1%
    T16-18-D16            311..501p   199..207p                 exp   9.5%  -7.3%
    T14-16(8)-D20                                 158..501p     ave   8.7%  -9.1%
    T16-B50                                                   R beg              

97  T19-D20               Always      Always      Always      R exp  15.1%      !

96  T20-D18               (c)32..376p (c)32..286p (c)32..104p R exp  15.1%       
    T16-8(16)-D20                                 105..501p     ave  10.9%  -7.2%
    T20-4-D16             377..501p   287..501p                 exp  10.7%  -8.0%
    T19-7-D16                         131..180p                 exp   9.8%  -8.3%

95  T19-D19               (c)32..170p (c)32..100p (c)32..120p R exp  13.2%       
    T19-6(10)-D16                                 119..127p     ave  10.9%  -3.8%
    T20-3-D16             159..315p   99..501p                R exp  10.1%  -4.8%
    B50-13-D16                                                R beg  10.1%  -8.5%
    T15-B50                                                   R ave              

94  T18-D20               (c)32..450p (c)2..501p  (c)2..501p  R exp  15.1%       
    T20-D17                           101..105p                 exp  12.6%  -3.7%
    T14-12-D20                                    156..183p     ave  10.6%  -8.1%
    T20-2-D16                         106..175p                 exp   9.6%  -8.2%
    B50-12-D16                                                R beg  10.1% -11.0%

93  T19-D18               (c)32..376p (c)32..287p Always      R exp  14.4%      !
    T19-4-D16             377..501p   288..501p                 exp  10.0%  -7.9%
    T20-1-D16             159..260p                             pro   9.5%  -9.1%
    B50-3-D20                                                 R beg   9.9% -11.0%
    B50-11-D16                                                R beg   9.6% -11.5%

92  T20-D16               Always      Always      Always      R exp  15.1%      !
    B50-10-D16                                                R beg  10.3% -11.0%

91  T17-D20               (c)32..272p Always      (c)         R exp  14.3%       
    T19-D17                                       32..59p       ave  13.5%  -3.5%
    T19-D17(2)                                    37..80p       ave  13.0%  -4.3%
    T14(11)-13-D18                                81..173p      ave  10.8%  -7.0%
    T18-5-D16             271..350p                             pro   9.5%  -9.6%
    B50-9-D16                                                 R beg  10.1% -10.7%

90  T18-D18               79..375p    32..103p    (c)32..48p  R exp  15.2%       
    T20-D15               (c)32..88p  (c)                     R pro  15.8%  -1.9%
    B50-D20                                                   R beg  12.4%  -4.5%
    T14(11)-8(16)-D20                             44..56p       ave  11.6%  -5.6%
    T14-8(16)-D20                                 33..501p      ave  11.6%  -5.9%
    T16-10-D16                        102..301p                 exp  10.2%  -7.3%
    T17-7-D16             159..260p                             pro   9.8%  -8.8%

89  T19-D16               (c)32..170p (c)32..89p  Always      R exp  17.8%      !
    T15(10)-12-D16                    84..134p                  exp  10.5%  -9.3%
    T18-3-D16                         130..501p                 exp  10.1% -10.7%
    T16-9-D16             159..310p                             pro   9.8% -11.1%

88  T20-D14               (c)32..130p (c)32..40p              R pro  16.9%       
    T16-D20               125..450p   33..501p    Always      R exp  15.5%  -0.3%
    T14(11)-14-D16                    121..177p                 exp  10.5%  -7.6%

87  T17-D18               (c)32..170p (c)32..65p  (c)32..40p  R exp  17.6%       
    T15(10)-10(6)-D16                             33..501p      ave  11.6%  -7.0%
    T15(10)-10-D16                    259..501p                 exp  11.4%  -7.3%
    T14-13-D16                        62..258p                  exp  10.8%  -7.7%
    T20-11-D8             159..220p                             pro  12.6%  -8.3%
    D20-15-D16            221..501p                             pro  12.2%  -8.9%

86  T18-D16               (c)32..250p (c)2..501p  (c)2..501p  R exp  17.0%      !
    T14-12-D16                                    55..135p      ave  11.4%  -8.1%
    D19-16-D16            251..501p                             pro  12.7%  -8.7%
    T12(9)-10-D20                     99..160p                  exp  10.6%  -9.0%
    T12(9)-18-D16                     161..207p                 exp  10.5%  -9.2%

85  T15-D20               (c)32..130p (c)32..40p  (c)         R pro  18.1%      !
    T19-D14                                                   R pro  17.9%  -0.4%
    T15(10)-D20                                   2..501p       ave  17.0%  -0.9%
    B50-3-D16             128..501p   33..130p                  exp  15.8%  -1.0%
    B25(Left)-20-D20                                          R exp  15.0%  -3.7%
    T14(11)-11-D16                    128..501p                 exp  10.6%  -9.1%

84  B50-D17               99..220p    32..108p                  exp  17.1%      !
    T16-D18               (c)32..40p  (c)         2..501p     R ave  17.8%  -0.5%
    T20-D12               33..100p                (c)         R pro  17.7%  -1.3%
    B50-2-D16             221..501p   109..205p                 exp  15.7%  -2.2%
    T18-D15                                                   R exp  16.0%  -5.2%
    T12(9)-16(8)-D16                  206..501p                 exp  11.6%  -9.6%

83  T17-D16               (c)32..372p (c)32..48p  (c)         R pro  17.7%       
    B50(25)-18-D20                    33..143p                  exp  16.2%  -1.1%
    T19-D13                                       32..60p       ave  16.2%  -3.8%
    T9(12)-16-D20                     144..257p                 exp  11.0%  -9.2%
    T12(9)-15-D16                     258..501p                 exp  10.5%  -9.7%
    B50-1-D16             131..323p                             pro              

82  B50-D16               2..501p     (c)32..260p             R exp  18.3%      !
    T14-D20               (c)                     Always      R ave  18.0%  -1.9%
    B25(Down)-17-D20                                          R exp  17.3%  -3.0%
    T18-D14                                                   R pro  17.8%  -4.3%
    T11(14)-9-D20                     281..501p                 exp  13.8%  -7.8%
    T11(14)-17-D16                    259..280p                 exp  13.8%  -7.9%

81  T19-D12               (c)32..130p (c)32..47p  32..103p    R pro  18.2%       
    T15-D18                                       (c)         R ave  18.1%  -0.4%
    B50-7(19)-D12                     33..60p                   exp  16.4%  -1.2%
    B50-7-D12                         61..195p                  exp  16.3%  -1.3%
    T15(10)-D18                                   115..501p     ave  17.1%  -1.4%
    T17-D15                                                   R ave  16.0%  -5.1%
    T10(15)-11-D20                    286..501p                 exp  14.0%  -5.6%
    T10(15)-19-D16        268..501p   196..285p                 exp  14.0%  -5.7%
    T14(11)-7-D16                                 102..121p     ave  15.1%  -5.9%
    B50(25)-16-D20        131..270p                             pro              

80  T20-D10               (c)32..310p (c)32..89p              R exp  24.0%      !
    20-20-D20                         90..260p    (c)32..64p    ave  21.7%  -2.7%
    T16-D16                                       63..501p    R ave  18.8%  -9.9%
    20-D14-D16                        261..501p                 exp   8.2% -23.9%

79  T19-D11               32..300p    (c)32..60p  (c)         R pro  23.0%       
    19-20-D20                                     32..189p      ave  21.4%  -1.4%
    20-19-D20             299..501p   61..501p                  exp  21.1%  -1.6%
    T13-D20               (c)                                 R pro  17.9% -10.2%
    T17-D14                                                   R pro  17.8% -11.2%
    T11-6(10)-D20                                 190..501p     ave              

78  T18-D12               (c)32..315p (c)32..103p             R exp  24.0%      !
    20-18-D20                         102..501p   (c)32..130p   ave  21.8%  -2.9%
    T14-D18                                       131..501p   R ave  19.6% -10.3%
    T16-D15                                                   R pro              

77  T19-D10               (c)32..310p (c)32..100p (c)32..40p  R exp  25.2%      !
    19-18-D20                         101..501p   33..501p      ave  22.0%  -3.9%
    T15-D16                                                   R ave  18.7% -12.0%

76  T16-D14               (c)32..60p  (c)32..60p                pro  25.8%      !
    T20-D8                61..400p    61..121p                R exp  24.1%  -1.3%
    20-16-D20                         122..501p   (c)32..164p   ave  22.0%  -4.1%
    20-16(8)-D20                                  165..501p     beg  17.9% -10.4%

75  T17-D12               (c)32..270p (c)32..116p             R exp  24.4%       
    T19-D9                                        (c)           ave  23.4%  -2.2%
    T15-D15                                                   R exp  23.2%  -2.3%
    19-16-D20                         117..501p   32..164p      ave  21.9%  -3.3%
    19-16(8)-D20                                  165..501p     beg  17.8%  -9.7%
    B50(25)-18-D16        271..501p                             pro  18.6%  -9.7%
    T13-D18                                                   R pro              

74  T14-D16               Always      (c)32..260p (c)32..59p  R exp  26.0%      !
    18-16-D20                         261..501p   33..164p      ave  22.2%  -5.7%
    18-16(8)-D20                                  165..501p     ave  18.1% -11.9%

73  T19-D8                (c)32..360p (c)32..120p (c)32..40p  R exp  25.6%       
    19-14-D20                                     33..140p      ave  22.3%  -4.3%
    17-16-D20                         119..501p   141..164p     ave  21.9%  -4.7%
    T11(14)-D20                                               R ave  21.7%  -7.5%
    17-16(8)-D20                                  165..501p     ave  17.8% -11.0%
    T11-D20                                                   R beg              

72  T16-D12               (c)32..220p (c)32..130p (c)         R exp  26.1%      !
    T12-D18                                                   R pro  25.9%  -1.0%
    T20-D6                                                    R pro  25.0%  -2.7%
    16-16-D20                                     32..165p      ave  22.7%  -4.8%
    20-20-D16             262..501p   131..501p                 exp  22.1%  -5.4%
    D20-D16               221..270p                             pro  22.6%  -5.5%
    16-16(8)-D20                                  166..501p     beg  18.6% -11.0%

71  T13-D16               (c)32..310p Always      2..501p     R exp  26.0%      !
    T11(14)-D19                                   (c)           ave  25.1%  -1.8%
    T17-D10                                                   R pro  25.2%  -2.7%

70  T14-D14               (c)         (c)32..58p                exp  27.1%      !
    T14(11)-D14                       49..160p    (c)32..40p    exp  26.8%  -0.2%
    T10-D20               32..40p                             R exp  26.9%  -0.3%
    T18-D8                33..501p                            R pro  25.5%  -2.6%
    14(11)-16-D20                     161..200p   33..165p      ave  23.4%  -4.7%
    T20-D5                                                    R exp  23.7%  -6.2%
    18-20-D16                         199..501p                 exp  22.3%  -6.7%
    14(11)-16(8)-D20                              166..501p     beg  20.2%  -9.5%
    20-B50                                                    R ave              

69  T11(14)-D18                       (c)32..180p (c)32..167p   ave  27.1%      !
    T15(10)-D12                       33..169p                  exp  27.0%  -0.0%
    T11-D18               (c)40..40p  181..290p   168..501p   R exp  27.1%  -0.1%
    T15-D12               32..230p                            R pro  26.8%  -0.8%
    T19-D6                                                    R pro  26.1%  -2.9%
    T13-D15                                                   R exp  24.3%  -4.8%
    T11-4-D16                         291..320p                 exp  22.6%  -6.3%
    17-20-D16             228..501p                             pro              

68  T12-D16               Always      (c)2..501p  151..501p     exp  27.2%      !
    T12(9)-D16                        33..122p    32..150p      ave  27.1%  -0.0%
    T16-D10                                                   R pro  27.0%  -0.8%
    T20-D4                                                    R pro  27.0%  -1.3%
    T14-D13                                       (c)           ave  26.4%  -1.8%
    T18-D7                                                    R pro              
    D18-D16                                                   R pro              

67  T9-D20                (c)32..60p  (c)32..161p 32..80p       exp  28.1%      !
    T19(7)-D5                                     (c)           ave  26.7%  -2.8%
    T17-D8                61..340p                            R pro  25.5%  -4.2%
    19-16(8)-D16                      162..501p                 exp  25.0%  -4.2%
    11-16-D20                                     81..165p      ave  23.5%  -6.4%
    11-16(8)-D20                                  166..501p     beg  19.4% -12.4%

66  T14-D12               32..241p    32..174p    (c)         R exp  27.9%       
    T10-D18               (c)         (c)         32..60p     R ave  28.1%  -0.1%
    T10(6)-D18                                    61..100p      ave  27.4%  -1.1%
    T18-D6                                                    R pro  27.1%  -2.8%
    T16-D9                                                    R exp  26.2%  -3.1%
    T12-D15                                                   R exp  25.3%  -4.6%
    B50-D8                242..501p                           R exp  25.0%  -5.7%
    14-20-D16                         175..501p                 exp  23.5%  -6.0%
    D17-D16                                                   R pro              
    D15-D18                                                   R pro              
    10-16(8)-D20                                  166..501p     beg              
    10-16-D20                                     101..165p     ave              

65  B50(25)-D20           (c)32..160p (c)32..80p  32..40p     R exp  30.8%      !
    T11-D16               159..310p   81..501p    33..501p    R ave  28.1%  -2.8%
    T19(7)-D4                                     (c)           ave  28.4%  -3.5%
    T19-D4                                                    R ave  28.6%  -3.5%
    T15(10)-D10                                               R ave  27.0%  -4.9%
    T15-D10                                                   R exp  27.0%  -5.2%

64  T16(8)-D8             (c)         (c)32..185p (c)32..64p    exp  30.3%      !
    T16-D8                2..501p                             R pro  30.1%  -0.4%
    16-8(16)-D20                                  61..70p       ave  26.3%  -5.5%
    16-16(8)-D16                      186..501p                 exp  26.1%  -5.6%
    16(8)-8(16)-D20                               71..501p      beg  25.7%  -6.3%
    T14-D11                                                   R exp  26.1%  -6.7%
    D16-D16                                                   R ave              

63  T13-D12               (c)32..357p 32..192p    2..501p     R exp  27.8%       
    T17-D6                            (c)                     R pro  28.5%  -0.6%
    B50(25)-D19                                               R beg  28.1%  -1.3%
    T11-D15                                                   R exp  26.1%  -3.1%
    T19(7)-D3                                     (c)           ave  27.0%  -3.7%
    15-16(8)-D16                      193..320p                 exp  25.0%  -3.8%
    13-B50                                                    R beg              

62  T14-D10               (c)         (c)32..76p              R exp  29.4%       
    T10-D16               2..501p     75..226p                R pro  28.2%  -1.2%
    T10(6)-D16                        227..241p                 exp  27.4%  -2.4%
    T16(8)-D7                                     (c)           ave  28.1%  -2.9%
    14-8(16)-D20                                  2..501p       ave  26.1%  -4.0%
    14-16(8)-D16                      242..501p                 exp  26.0%  -4.2%
    T12-D13                                                   R exp  26.3%  -4.7%
    D15-D16                                                   R pro              

61  B50(25)-D18           (c)32..120p (c)32..100p (c)         R exp  32.3%      !
    T19(7)-D2                                     32..64p       ave  30.4%  -2.6%
    T7(19)-D20                                                R beg  29.9%  -2.8%
    T15-D8                121..392p   99..120p                R ave  29.4%  -3.2%
    T7-D20                                                    R exp  28.9%  -3.9%
    T11-D14                                                   R exp  28.1%  -5.2%
    13-8(16)-D20                                  63..501p      ave  25.8%  -7.5%
    13-16(8)-D16                      119..275p                 exp  25.7%  -7.6%
    19-10-D16                         276..501p                 exp  24.9%  -8.6%

copyright (c) kari kaitanen 1995

As you see some of these results are quite amazing. Please note that these figures are the "mathematical facts" of the sport and there is nothing I can do to change them - even if I wanted to! In most cases you can however quite easily comprehend the computer's way of thinking and find out why the specific path was recommended.

Please send me your opinion of these pages: kari.kaitanen@vtt.fi.

Yours, Kari


Updated 10.2.1996 by kari.kaitanen@vtt.fi
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