In this article, I will not try to give you all of the formula for adjusting pip counts based on gaps and distribution in this article…I simply want you to know that this is something that must be taken into account, and something you will have to learn if you want to become a pro backgammon player. But I do want to give you what I consider to be the “best” approach to determining whether to take or drop cubes in race situations, and that is the Trice Formula (developed by Walter Trice). I believe this is the best formula to apply over the board in most race situations, and I encourage you to learn it and use it.
The Trice Formula states that if the leader’s total pip count is under 62, you subtract 5, divide by 7, and round up. That gives you the number of pips (or less) needed to take the cube in a money game or 25 percent take situation. Once you have calculated that number, you can make adjustments for distribution and for the possibility of getting or leaving a shot.
For example, let’s say that White has a pip count of 58 and you have 63. Using the Trice Formula, you subtract 5 from 58, and that is 53. You divide 53 by 7, which is 7 and 4/7, and you round up to 8. You add 8 to 58 and that is 66. So you can take this cube if your pip count is 66 or less. Since you have 63, it is a clear take.
If you take a look at Position 7 below, which has a pip count of 58 for White and 63 for Black, you will see how this position looks over the board with no contact, and if you look at Figure 8, you will see Snowie’s evaluation agrees with the Trice Formula…it is a clear take.
If Black had 66, the Trice Formula says it is a drop, and so does Snowie.
It is important to remember that the Trice Formula does not take distribution into account. Once you have done the math, you must adjust for distribution factors. In the above example, Black was losing 63 to 58 and it is a clear take, but with the same pip count and poor distribution, as in Position 9 below, it is a clear drop.
What if the leader’s pip count is over 62. Then, according to the Trice Formula, you divide by 10 and round down. For example, if the pip count is 85 to 95, you take 85, divide by 10, and that 8.5, and you round down to 8, Add 8 to 85 and that’s 93. So at 93 you are at the exact 25 percent take point. You would drop if you are over 93, unless there are other factors such as distribution or recube potential to allow you to take even with a few more pips than 93.
The Trice Formula may sound a little confusing, but once you memorize it and get used to using it, it is extremely accurate and useful. Again, the Trice Formula, and all racing formula, are most efficient when there is no contact. When there is any chance of either party leaving a shot, those odds must be figured into the equation.
Just to give you an idea of how important the contact factor is, take a look at Position 10 below.
In this situation, with White on Roll and leading by 25 pips, applying the Trice Formula, it is a huge drop. With Black’s checkers only 1-away from White’s checkers, the odds of getting and hitting a shot are not very high.
But if you move Black’s two checkers from the 13 point to the 15 or 16 point, it is a huge take because of the odds of getting and hitting a shot. If you move those checkers to the 17 point, it’s not even a double, and if you were to put them on the 18 point, it would be a Beaver if White made the mistake of doubling. Keep in mind that each of those changes actually gives White an even bigger lead in the race, but the odds of winning go way down because of the odds of leaving a shot, and of course, there are even possibilities of a double shot when the checkers get moved farther back.
There is another situation where you should discount, or totally discard the Trice Formula--when you are at the end game where the key is the number of possible rolls, not the pip count. To give you an extreme example to illustrate the point, in Position 11 below, the pip count is even, but White only wins 1 out of 100 games here even when White is on roll.
In summary, when I am in a pure race, or “almost” a pure race, I always count the pips, apply the Trice Formula, adjust for distribution, pray to the Dice Gods, and then make my cube and checker play decisions accordingly.