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BGonline.org Forums
Do you remember this position?
Posted By: Daniel Murphy In Response To: Do you remember this position? (rambiz)
Date: Saturday, 17 March 2012, at 10:11 p.m.
since far over half of White's wins are on two or four.
Well, 56.2% of White's wins are on 2 or 4, according to your stats.
Apparently the ~0.9 gammon value is not all we should be concerned with
Ignore the 4-cube games. In your rollout White only won a 4-cube game 0.274% of the time. And Blue probably won a 4-cube game perhaps 0.8% of the time, since Blue will only be giving White a live 2-cube near the top of Blue's doubling window (TP = White wins 23.3% / Blue wins 76.7%).
What about the 2-cube games? For Blue's decision to play on in the original position, do they matter much? And if they did, how would you consider them over the board?
Recall that 0a 5a = 100%, 1a 5a = 84.2%, 2a 4a = 66.9%, and 2a 3a = 59.9%%.
If all games result in a gammon win or a single win or loss on a 1-cube, playing on risks 17.3% to gain 15.8%, for a gammon price of ~0.9.
If instead all games of Blue's losses but none of his wins are on a 2-cube, then playing on risks 24.3 to gain 15.8%, for a gammon price of ~0.65.
But that can't be the real price, for two reasons: (1) not all of Blue's losses are 2-cubes and (2) White doesn't win all the 2-cubes (or the 4-cubes).
If White doubles, Blue's take point is ~18%.
If Blue doubles in a nonlast roll position, White's take point is ~23%.
If Blue doubles in a last roll position, White's take point is ~40%.
So we might estimate that White wins, say, 70% of the 2- and 4-cubes.
And then, what's Blue's play-on risk if (1) all his losses are 2-cubes and he wins 30% of the 2-cubes? Or (2) about half of his losses are 2-cubes and he wins 30% of the 2-cubes?
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