Here's a question for the Backgammon players out there: When is it appropriate to double "on spec" -- e.g., early in the game when there's nothing in your position to suggest you have an advantage.
There's one obvious case, I'll just get it out of the way: If your opponent will win the match if they win the current game and you won't, and you have control of the cube, you should double immediately regardless of your position. For instance, if you've just survived the Crawford round in a five-point match and the score is 4-1, you should double immediately, because if your opponent wins, he wins the match anyway with a 5-1 victory, but if you win you'll be at 4-3 instead of 4-2 (and of course if you did win and get to 4-3, you'd double again so you're playing for the match). Another case where this happens is if your opponent doubles, and the new cube value puts them within reach of victory but doesn't put you there. So if someone doubles you when the score is 3-2 to them (five-point match), you should immediately double back because otherwise they can win the match on that game but you can't. So that's the simple case.
But are there any other valid cases?
Here's a scenario which came up for me fairly recently. In the end, I decided not to double on spec, and I think I was right, but I'll bring it up: I was up 7-4 in a nine-point match. Should I double on spec, so I can take the match on that game? As I said, my answer is no, and here's part of why: Applying the rule above, my opponent would immediately double back so we were playing for four points. That means if I won, I'd win the match, but if he won, he'd take the lead 8-7 and I'd have to win two more games to win the match (since the first would be the Crawford Round). Anyone disagree and think I should have doubled on-spec?
Certainly agree with the most simple case -- i.e., immediate double after surviving crawford round; any waiting simply gives the opponent an option to decline and start over with no impact on the match.
Agree with the other simple case, adding the (perhaps obvious) proviso that it be correct to accept this double in the first place.
I don't think I agree with "doubling on spec" as I understand it from the comment. In general, I await the "normally appropriate time" to make a double, and think people usually do more harm to their results than help by altering typical play because of the present score.
In a recent 5-pt match, my opponent led 3-0 and then doubled when ahead in the next game. This presents a neat case for discussing probabilities. Let us assume that we are of equal backgammon skill -- and translate that to a 50% probability of winning any game before it begins. Let us also assume that my chance of winning the game in progress is 30%.
Now, if I decline the double, it will be 4-0 and I must win the next three games. That yields a 12.5% chance of winning the match: 50%x50%x50%.
If I accept, I will redouble on my next turn. Then, if I win (a 30% chance), I will lead 4-3, and need only win 1 of the next two games (a 75% chance (1 - 50%x50%), which yields a 22.5% chance of winning the match.
Though my chance of winning the match was not great in either case, I could nearly double my chances of winning the match by accepting the double.
I will leave for others to factor in considerations of differing chances of winning the game in progress, differing skill levels, or the opportunity afforded by the one-turn change in probability of winning between the double and the redouble. ;-)
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