FIBS Board backgammon forum

0-0
correct answer: double, take

The surprising thing in this position is that white wins here about 33% of the games. Because of the anchor black wins only 25 % gammons. This makes it very clear money take. In 5-away 5-away gammons value more because doubled gammons lead to crawford-game. However it's still not enough to make it a pass.

1-1
correct answer: double, pass
Now doubled gammons win the whole match which changes everything. It's a huge pass.

2-2
correct answer:double, pass

Let's work with the numbers a bit. First lets make simple and an unrealistic assumption that white will be able to redouble perfectly. I mean white will always redouble when he wins and never redouble when black wins single. So the match winning chance would be: white wins + black single wins x white wins from 3-away-1-away. 0,33 + 0,42x0,25=0,435. This is bigger then match winning chance if white drops which is at 2-away-3-away about 0,40. So it comes to how well white can redouble here. If I assume that white will never miss markets but 10 % of games he redoubles after which the games turns for black that would give 0,33 + 0,32x0,25= 0,41. Still higher then pass equity. The actual difference in pass and take according to gnu is well under 0,5 % and it's a borderline pass. This is surprising because normally you drop easily in this score. But high winning chances and redouble possibility in this score can sometimes make correct takes which might look desperate.

2-1
correct answer: no double, take

White can take in this score with very low winning chances because he will have monster redouble for match. And white should never ever miss his markets for redouble by doubling too late. Black can however lose the markets here. If he hits, rolls big doubles or white rolls something horrible like 5-4. Then again white could also improve his position with important points. Because white's low take point black should still hold his horses and wait just a move or two. Because white has an anchor black is likely to get almost perfect double later and risk of losing markets isn't just big enough compared to white's powerful cube ownership. I doubled here in this score. And you can justify it if there is a chance that white will drop.

1-2
correct answer: double, pass

This is enourmous pass. Doubled gammon would take black from the losing side to straight winner. It's even close to too good. But black's 25 % gammon chances is not enough to compensate for white's superjokers 1-1, 3-3, and 6-6.

Roll-outs are in the text-file. These are 2-ply but very short. Though the differences are big enough and standard error small enough (at least for me) to call it a result.

And as a side note now you could also add the possibility that opponent makes wrong takes/passes and asymmetric match equity tables and things would get really messy.