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BGonline.org Forums
All-in?
Posted By: Daniel Murphy In Response To: All-in? (higonefive)
Date: Friday, 26 August 2011, at 6:51 p.m.
I learned, that 2a-2a is a subclass of DMP, and someone said, that you should double, when there is the slightest possibility to lost your market.
That someone might be Kit Woolsey. In How to Play Tournament Backgammon you can find this:
"... at two-away versus two-away you should always double if there is any chance that after the next exchange you will lose your market...."That's an optimal strategy at 2-away all. It's a twist on another optimal strategy, which is to simply double on your first turn. But it's not applicable to the original position in this thread.
Notice that both optimal strategies imply, correctly, that you don't have to be a favorite to double. In practice, Woolsey's strategy is better, assuming you will make no cube errors and your opponent will. If you, having no market losers, do not double, your opponent in turn will either cube optimally or make a cube error. Not doubling now costs you nothing (since you have no market losers), but you gain whenever opponent errs. The general case is that 100% of the time, either you or your opponent will make a takable double. In that case, the only way you can lose equity is to fail to double when you have market losers.
The original position is quite different.
The main difference is that when you miss (16/36), your opponent will not be doubling you. He will play on for gammon. He overshot the doubling window a long ago. You may get another shot or even two, but now your hits are even less likely to be winners. Whenever your hits save the gammon but don't win the game, doubling now costs you 32.3% match equity. Whenever your hits win the game, doubling now gains much less -- the difference between 67.7% and whatever your GWC is after a hit.
Likewise, if Blue doubles now and hits, Blue gains the difference between GWC and 67.7% whenever Blue wins the game. But doubling now costs 32.3% match equity whenever Blue hits and loses the game but would have saved the gammon.
Finally, consider the possibility that although Blue obviously have market losing sequences (hitting twice, or a single hit followed by a fan) there may not be many market losers, or most of them are very small. Perhaps after you hit White should double from the bar! White will have some market losers after a single checker is hit (White can enter with 6-2 or 6-1) and White's gammon chances have dropped a lot. What are White's game winning chances after being hit once on the 5 point or on the 2 point?
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