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Daily Quiz 2/14
Posted By: Daniel Murphy
Date: Sunday, 19 February 2012, at 3:03 a.m.
In Response To: Daily Quiz 2/14 (kruidenbuiltje)
Position 2:
The score is: White 0, Blue 4 (match to 11 points). Blue on roll
gnubg 61
Blue 52 Position ID: 23YnAAC7tQcAAA Match ID: UQlgAQAAIAAE I noticed your GWC estimates and match equity calculations were pretty good, according to Tim's results, but I also noticed something missing.
(let’s look it up : a score of 5a/11a gives 20% chance, 3/11 gives 11% chance, so this is a risk of 9%, winning gives 50% chance (7a/7a), TP = 9/39, about 20%, so white can take until 80%)
The match equities are good, rounded, and your R/(R+G) = 9/39 is right, but 9/39 is actually 23%, not 20%! So, cubeless, this is a slightly larger pass than your estimate, since White wins 18% cubeless, or 5% short of a take (you had estimated 16% wins and a 20% takepoint).
What's missing is the value of holding a 4cube in a notcubeless race trailing 11a7a. Holding a 4cube, White can (1) force Blue to drop an 8cube or (2) give Blue a takable 8cube. Hard to estimate, easier to see that it must be important.
Recall that in a money game, the doubling window is 5075% in a last roll position, or typically up to ~78% if the cube is live. White must get to at least 50% GWC to consider doubling, and more than 75% or ~78% to force Blue to pass. But at the score, White only needs to get to 66% GWC to force Blue to drop an 8cube, and only 30% GWC to be able to give Blue a takable 8cube.
The top of White's redoubling window:
Pass > 7a7a = 50% MWC
Take/win > 0a11a= 100% MWC
Gain from taking = 50%
Take/lose > trail 7a3a = 24% MWC
Risk of taking = 26%
Blue's takepoint = R/(R+G) = 26/(26+50) = 26/76 = 34%
Top of White's redoubling window is 10034 = 66%.The bottom of White's redoubling window:
No double and win 4 points > 7a7a = 50% MWC
Double and win 8 points > 3a7a = 76% MWC
Doubling gains 26% MWC
No double and lose 4 point > 11a3a = 11% MWC
Double and lose 8 points > 0% MWC
Doubling risks 11%.
Bottom of White's redoubling window is R/(R+G) = 11/(11+26) = 11/37 = 30%.It must be more likely that White will improve from 18% to 30% (possible redouble/take) or to 66% (redouble/pass) than from 18% to 50% (possible money game redouble/take) or to 7578% (money game redouble/pass). I verified this with Gnubg's "show statistics" rollout feature.
Here are the actual results of a rollout at the score after double/take:
Cube level All games White wins Blue wins 4 83.41% 11.34% 72.07% 8 16.59% 8.64% 7.95% Any 100.00% 19.98% 80.02%
8cubes Taken 16.59% Passed 9.33% Given 25.92% With those results, White's MWC after taking the 4cube is:
Result freq. * ME MWC Wins 8 points 0.0864 * 0.76 = 6.56% Wins 4 points 0.1134 * 0.50 = 5.67% Loses 4 points 0.7207 * 0.11 = 7.92% Loses 8 points 0.0795 * 0 = 0.00% Total 20.16% ... a little better than White's 20% MWC  precisely, 19.72%  from passing.
In the ATS rollout, White went from 18% GWC to at least 66% GWC, forcing a pass, in 9.33% of all games. Unfortunately we do not know how often White would have won those games if he had not been able to redouble Blue out. White went from 18% GWC to at least 30% GWC, allowing a takable 8cube, in only 16.59% of all games. But these games were worth 3.25% match equity to White, compared to passing the 4cube:
White's MWC gained in games where there was an 8cube taken Result Frequency * MWC over/under Pass MWC = MWC Win .0864 * (7620 = 56%) = 4.84% Lose .0795 * (200 = 20%) = 1.59% Total = 3.25% For comparison, here are the actual results in a money game rollout:
Cube level All games White wins Blue wins 4 96.66% 14.35% 77.31% 8 7.94% 5.47% 2.47% 16 0.38% 0.08% 0.30% Any 100.00% 19.91% 80.09% In only 3.34% of money games did the cube reach 8 or higher, compared to 16.59% in the ATS rollout.
8cubes Taken 8.33% (instead of 16.59% ATS) Passed 11.11% (instead of 9.33% ATS) Given 19.44% (instead of 25.92% ATS)

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