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Computing where the doubling window opens -- WITH gammons

Posted By: John O'Hagan
Date: Saturday, 3 January 2009, at 5:14 p.m.

In Response To: Computing where the doubling window opens -- WITH gammons (Jason Lee)

First compute the min dbling point ignoring gammons which is risk/risk + gain. Ex, 0-1 to 5. Don't double and lose makes the score 0-2 with about 35% match equity(ME), do double and lose makes it 0-3 with about 25%ME. The risk from doubling is therefore 10%ME. Don't double and win makes the score 1-1 with 50%ME, do double and win makes it 2-1 with about 57.5%ME. The gain from doubling is therefore 7.5%ME. This makes the gammonless min dbling point 10%/10% + 7.5%, about 57%.

Next compute the 2-cube gammon prices for both players: The 2-cube single game swings are from 25% ME to 57.5% ME. A gammon win makes it 4-1 Crawford with about 82%ME, a gammon loss loses the match with 0%ME. The gammon price when you win a gammon is therefore 24.5%/32.5% (about 75%) vs. 25%/32.5%(about 77%) when you lose one.

The min dbling point including gammons is then: 57% - 75%*gammon wins + 77% * gammon losses. So if you win/lose 20%/10% g's your min dbling point becomes 49.7%.

The absolute lowest your gammon-included minimum doubling point could be at this score occurs where all of your wins are gammons and none of your losses are. The risk from doubling in this situation is still 10% but the gain from doubling is 24.5%, making your min dbling point 10%/34.5%, about 29%. At a moneylike score (say 0-0 to 25), the lowest possible gammon-cncluded min dbling point is 1/3.

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