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BGonline.org Forums
Position Classique, Coup Classique, or Whatever the Correct Name Is
Posted By: Steve Mellen In Response To: Position Classique, Coup Classique, or Whatever the Correct Name Is (Bill Riles)
Date: Monday, 3 May 2010, at 10:04 p.m.
I'm sure someone will be posting bot analysis but here's something to think about in the meantime.
At a score of 8-8, running and conceding the gammon leaves you down 12-8 Crawford, with match equity of roughly 15%. On the other hand, if you turn the game around and win, you'll be ahead 10-8, with about a 66% chance to win the match. I'm drastically oversimplifying to make this point, but at the most basic level you're risking 15% match-winning chances (the difference between 15% and zero) for a chance to gain 51% (the difference between 15% and 66%).
Jason mentioned an example where he was ahead -2 -6 and holding a 2-cube. In that scenario, if he concedes the gammon the score goes to -2 -2, which is obviously 50/50. If he stays and ends up winning then he wins the match. So by staying he risks 50% match-winning chances for a chance to gain 50%.
Whether it's right to stay in a given position depends on a lot of other factors, like the number of times you'll win if you hit, the number of times you'll save the gammon by hitting even if you lose, etc. But setting all that to the side for a moment, there's obviously a huge difference between risking 15% for a chance to gain 51% and risking 50% for a chance to gain 50%. So it's unlikely that at the end of the process, we'll end up with a rule of thumb like "never stay if a backgammon costs you the match." The amount of equity you put at risk by chancing a backgammon varies tremendously based upon the actual score of the match.
Just to make one final point, let's imagine that the score is 0-0 in a 15-point match and you hold a 2-cube. If you run and concede the gammon, you're behind 0-4 (33% MWC). If you stay and lose a backgammon, you're behind 0-6 (24% MWC). If you stay and win, you're ahead 2-0 (58% MWC). So in this garden-variety case, you're risking 9% for a chance to gain 25%. What's striking about these numbers is that the risk-reward ratio is actually HIGHER than in the 8-8/13 case you presented. In other words, if it would be right to stay for the chance at a coup classique at a score of 0-0/15, it's even more right to stay in the position you watched!
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