Doubling in backgammon and Match Equity
Starting from a given score, it is possible to know your chances of winning the match. Consider a simple example: You are trailing 2-0 in a 3-point match. You need to win two games to win the match, period. (If you win the first game without a gammon, you will of course double on the first roll of the next game.) Since you are 50% to win each game, you are 50% times 50% or 25% to win the match.
Suppose instead you are trailing 2-1 in the Crawford game. Now your chances are a little better. You can win a gammon in this game to win the tavla match, and on average you'll do that about 10% of the time. The other 40% of the time that you win (but don't win a gammon) you'll win the match 50% of those times. 10% plus 40% times 50% makes you 30% to win the match.
It is possible to know all the tavla match-winning odds for all the scores. That discussion is very complex, but let's try:
So, suppose you are leading 1-0 in a match to 5. When should you double? When should you take?
Start with the take decision. The odds are:
Leading 2-0, 66% to win the match
Leading 3-0, 75% to win
Tied 1-1, 50% to win
Trailing 2-1, 41% to win
If you drop the double, you will be 34% to win (trailing 2-0). If you take, you will be 25% when you lose the game (trailing 3-0) and 59% when you win (leading 2-1). You are risking 9% (34%-25%) to gain 25% (59% - 34%). So you need 9 wins for every 25 losses to break even, or about 26%. So you should take if you are 26% to win, and you should double if you think there's a good chance that by your next roll you will be at least 74% to win, or if you're already over that.
There are some complexities, of course. You can take a little more aggressively than this, because you own the cube and have the sole right to redouble. But if you are going to get gammoned more often than you win a gammon, you have to adjust for this.
Is this issue complex? Yes. Is it important? Only if you want to be a good player. Huge numbers of matches are lost by incorrect doubling decisions.
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