by Joe Sylvester
(This article originally appeared in the Flint Backgammon News January, 1989)
Editor’s Note: When reading the article below, keep in mind that while a number of computer programs can give you the correct answer to the question posed, those programs will not be available to you over the board in a live tournament situation. And so, it is important that you be able to form accurate estimates of wins, losses and gammons over the board. For the overall match equity, you can refer to any number of tables, one of which can be found here: http://www.pion.ch/backgammon/mem-met.php
When gammons are a possibility in a game, determining take points becomes much more complex. The ability to evaluate positions becomes of the utmost importance.
Let’s assume the score is 4-3 in a match to 9 points. The following position occurs, and we, the leader, are doubled…
At this point, we must evaluate the following probabilities:
• % of Games Taken & Won
• % of Games Taken & Lost
• % of Games Taken & Gammon Won
• % of Games Taken and Gammon Lost
If we take, our match equity is the sum of these percentages times the resulting score’s match equity. This figure compared to our match equity if we pass determines our action.
Let’s assume we evaluate example 1 as follows:
• 30% Wins = Score of 6-3 or 73% (50+9+8+6)
• 40% Losses = Score of 4-5 of 41% (50-9)
• 5% Wins Gammon = Score of 8-3 Crawford of 90%
• 25% Loses Gammon = Score of 4-7 or 27% (50-9-8-6)
If we take, our equity is:
.30 X .73 = a21.9
.40 X .41 = a16.4
.05 X .90 = a4.5
.25 X .27 = a6.8
If we pass, the score is 4-4 or 50%. The decision is borderline. At this point, we may wish to reevaluate the position and/or our opponent’s relative strengths and weaknesses. For example, how does he handle this type of blitz position? How will my opponent’s play be affected by a win? A loss? A gammon?
IMPORTANT! Clearly the final evaluation is arbitrary. The number of wins, losses and gammons is absolutely the most important, crucial evaluation in all of tournament backgammon. One person using a different evaluation than the next may find this position an absolute drop, while the next person might question whether he should have been doubled or not.
I strongly urge you to evaluate this position on your own, and use whichever equity chart or sequence you wish. Try out your evaluation at different scores.
Remember, no answer is absolute. In middle game situations we can only estimate. However, your estimations can help you form a much more accurate cube decision.