Quote:
Originally Posted by Andrew B.
I don't know if I'm understanding this discussion correctly. But if I am a weaker player than the bot, then there would be close situations where a bot should double and I should not. The reason is that the bot is making a decision based on how likely it is to win from that position. It is not looking at how likely I am to win from that position, and being that I am a weaker player, it might not be best for me to risk playing a doubled game. . Well, unless is is factoring in my playing history I have with the bot, and I don't know if they apply that to doubles.
I think we are discussing match play here mainly (and the idea is simpler to understand vs money play). Assume you are playing a 3 point match against a top-level pro or a bot. In one match we can play normal backgammon rules; cube in play, gammons etc. in another.there are no cubes or gammons; each game counts as 1 point. Which match gives us a better chance to win?
Well, it should be obvious but the normal rules give us a much better chance (especially against a bot who will use optimal cube strategy and not adjust for skill difference). Say you are bad enough that you will only win 30% of the time on average. If you must win 3 out of 5 games, you have about a 16% chance of winning. Under normal rules, though, you can double at first opportunity and win 2 points when you win. This effectively changes things from needing to win 3 out of 5 to a match where you need to win 2 out of 3. You would have a 21.6% chance in that case.
You could do even better with a more optimal cube strategy, and in this example you could almost guarantee at least a 25% chance of winning almost all the time. If you play a bot, it will double when it has a 75% chance of winning the current game (give or take a bit). If you get doubled you could simply redouble immediately and play for the match with your 25% chance of winning.
In general the principle holds that in any unfavorable gamble, you have a better chance of coming out ahead by increasing the variance. You will never beat a top pro poker player, for example, by playing 100K hands using a normal strategy— the variance gets washed out over that sample size. You can give yourself a pretty decent chance to beat him in a heads up tournament type game by playing an all in pre flop or fold strategy. At worst, even if he knows what you are doing and only calls with premium hands you can give yourself at least a 20% chance of winning — the variance is high.
Getting the cube to high levels increases variance. You want to increase variance. Your best chance of winning is not to play safer, but to play riskier, especially if you do manage to put yourself in a favorable position