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Bearoff Cube Formulas
Posted By: Albert Steg
Date: Tuesday, 20 December 2016, at 1:29 a.m.
Anyone who plays with me regularly knows that I'm one of the less numerate overtheboard types. I'm not great with mental math (I can't hold a 7digit phone number in my head between the yellow pages and the keypad)  and I'm just plain lazy. But after patching up a lot of gaps in my game over the past year I thought maybe I should learn and start to apply the Keith Count, at least in sketchy positions with stacks on various points. Heretofore, I've relied on the basic 8% Double/ 9% Redouble/ 12% Pass rule of thumb.
So, I pulled up some positions I'd saved from past sessions involving a race, and try to show myself how much I'd been missing, and the very first one I try out is this:
White is Player 1
score: 0
pip: 53Unlimited Game
Jacoby Beaverpip: 48
score: 0
Blue is Player 2XGID=ABDDdda:1:1:1:00:0:0:3:0:10 Blue on roll, cube action?
eXtreme Gammon Version: 2.10
I look at it with my 'dumb' formula and it comes out between 1011% Double/Take hohum, and then I work out the Keith Count and it's 54/53 Pass  though 1/7 of 48 is dang near 7, which means borderline Take if you fudge the formula just a tiny tad. Then, checking XG's "Race Formulas" I see that Trice and Thorp formulas also get Pass.
Okay, well, it's probably just real close . . . except it's not! It's a big .083 Take!
Analyzed in Rollout No redouble Redouble/Take Player Winning Chances: 76.27% (G:0.00% B:0.00%) 76.19% (G:0.00% B:0.00%) Opponent Winning Chances: 23.73% (G:0.00% B:0.00%) 23.81% (G:0.00% B:0.00%) Cubeless Equities +0.525 +1.048 Cubeful Equities No redouble: +0.815 (0.102) ±0.002 (+0.813..+0.817) Redouble/Take: +0.917 ±0.003 (+0.914..+0.921) Redouble/Pass: +1.000 (+0.083) Best Cube action: Redouble / Take Rollout details 1296 Games rolled with Variance Reduction.
Moves: 3ply, cube decisions: XG RollerDouble Decision confidence: 100.0% Take Decision confidence: 100.0% Duration: 10.1 seconds eXtreme Gammon Version: 2.10
This is not what I was hoping to discover to spur me out of my slothful habits! I'm sure as I look at more positions I'm going to find plenty that encourage me to be more quantitative in my approach, but for the meantime, I'm just really puzzled by this particular result. I'd be real interested to hear explanations about why the more sophisticated metrics fall down so hard on this one  and whether there are any general principles that would allow me to be wary of them in other positions "like this" (whatever this position is like?)
Also, it wouldn't surprise me if I just set up or interpreted something wrong. So sorry for wasting everybody's time in advance if that's the case!

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