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BGonline.org Forums
Computing where the doubling window opens -- WITH gammons
Posted By: John O'Hagan In Response To: Computing where the doubling window opens -- WITH gammons (John O'Hagan)
Date: Saturday, 3 January 2009, at 5:44 p.m.
Another way to figure this out would be to Kit Woolsey's blended average approach. The idea here is to include the gammon wins/losses into the risk/reward ratio.
Here's how it works (using the same 0-1 score to 5). You need to first estimate 2 figures: your gammon wins/your total wins and your gammon losses/your total losses. Let's use 40% and 20% for these two figures.
If you don't double and lose this game, 80% of the time you'll be down 0-2 with 35%ME and 20% of the time you'll be down 0-3 with 25%ME. 80%*35% + 20%*25% = 33%. Do double and lose, 80% of the time you're down 0-3 with 25%ME and 20% of the time you lose the match with 0%ME. 80%*25% = 20%. The risk from doubling is then 13%.
Now the reward side. Don't double and win, 60% of the time you're tied 1-1 with 50%ME and 40% of the time you're up 2-1 with 57.5%ME. 60%*50% + 40%*57.5% = 53%. Do double and win, 60% of the time you're up 2-1 with 57.5%ME and 40% you're up 4-1 Crawford with 82%ME. 60%*57.5% + 40%*82% = 67.3%. This makes the gain from doubling 14.3%.
The min dbling point is therefore 13%/27.3%, about 47.6%.
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