This article originally appeared in the June 1999 (Demo) issue of GammOnLine. Thank you to Kit Woolsey for his kind permission to reproduce it here. |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
1 | 50 | 70 | 75 | 83 | 85 | 90 | 91 | 94 | 95 | 97 | 97 | 98 | 98 | 99 | 99 |
2 | 30 | 50 | 60 | 68 | 75 | 81 | 85 | 88 | 91 | 93 | 94 | 95 | 96 | 97 | 98 |
3 | 25 | 40 | 50 | 59 | 66 | 71 | 76 | 80 | 84 | 87 | 90 | 92 | 94 | 95 | 96 |
4 | 17 | 32 | 41 | 50 | 58 | 64 | 70 | 75 | 79 | 83 | 86 | 88 | 90 | 92 | 93 |
5 | 15 | 25 | 34 | 42 | 50 | 57 | 63 | 68 | 73 | 77 | 81 | 84 | 87 | 89 | 90 |
6 | 10 | 19 | 29 | 36 | 43 | 50 | 56 | 62 | 67 | 72 | 76 | 79 | 82 | 85 | 87 |
7 | 9 | 15 | 24 | 30 | 37 | 44 | 50 | 56 | 61 | 66 | 70 | 74 | 78 | 81 | 84 |
8 | 6 | 12 | 20 | 25 | 32 | 38 | 44 | 50 | 55 | 60 | 65 | 69 | 73 | 77 | 80 |
9 | 5 | 9 | 16 | 21 | 27 | 33 | 39 | 45 | 50 | 55 | 60 | 64 | 68 | 72 | 76 |
10 | 3 | 7 | 13 | 17 | 23 | 28 | 34 | 40 | 45 | 50 | 55 | 60 | 64 | 68 | 71 |
11 | 3 | 6 | 10 | 14 | 19 | 24 | 30 | 35 | 40 | 45 | 50 | 55 | 59 | 63 | 67 |
12 | 2 | 5 | 8 | 12 | 16 | 21 | 26 | 31 | 36 | 40 | 45 | 50 | 54 | 58 | 62 |
13 | 2 | 4 | 6 | 10 | 13 | 18 | 22 | 27 | 32 | 36 | 41 | 46 | 50 | 54 | 58 |
14 | 1 | 3 | 5 | 8 | 11 | 15 | 19 | 23 | 28 | 32 | 37 | 42 | 46 | 50 | 54 |
15 | 1 | 2 | 4 | 7 | 10 | 13 | 16 | 20 | 24 | 29 | 33 | 38 | 42 | 46 | 50 |
The above table gives the match equity, in percent, for each score in a match of 15 points or less. The numbers on top and down the left hand side represent number of points to go. For example, suppose you are ahead 8 to 5 in an 11 point match. You have 3 points to go, and your opponent has 6 points to go. Look at the intersection of the third row and the sixth column, and you find the number 71. This means that your probability of winning the match is 71%.
This table was derived from a combination of empirical data and various assumptions about gammon probability and the value of doubling potential. All the figures may not be accurate, but they are likely to be correct to within a percent or two. The table has proven to be of practical value, and is used by most experts today.
Memorizing the entire table can be difficult. Neil Kazoross developed a simple way to calculate most of the figures without a lot of memorization, called "Neil's Numbers". The method is based on the following table:
3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
10 | 9 | 8 | 7 | 6 | 5 | 4 |
The numbers on top represent the number of points the trailer in the match has to go. The numbers on the bottom represent the value in percent that each point is worth to the leader. For example, suppose you are ahead 5 away 8 away. The trailer has 8 points to go, and Neil's number for 8 is 6 (the number below the 8 in the table). The difference in the scores is 3. So, multiply 3 X 6 = 18, add to 50%, and you come up with 68%. If you check the match equity table, you will see that the equity for being ahead 8 away, 5 away is 68%.
If there is no number in the table, do the appropriate interpolation. For example, suppose you are ahead 8 away 12 away. There is no number for 12, but it is 1/4 of the way between 11 and 15, and the numbers for these are 5 and 4. Therefore we can interpolate and use 4 3/4. The difference in the scores is 4, so we multiply 4 X 4 3/4 = 19, add to 50%, and get 69%. This matches the 8 away 12 away entry in the match equity table.
Remembering Neil's numbers is easy. The first four entries are trivial. After that, all you need to remember is the phrase "8 is 6, 11 is 5, 15 is 4", and you've got it.
For most scores, using Neil's numbers will either match or come within one percent of the entry in the match equity table. However if the leader has one or two points to go, Neil's numbers do not give accurate results. It is recommended that you memorize the equities when the leader has one or two points to go, and use Neil's numbers for other scores.
If you happen to be playing a very long match, the table can be extended. Neil's numbers are: 19 is 3 1/2, and 25 is 3.
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