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March 27, 2013

Something basic I learned in Cleveland!!

is Player 2

score: 0
pip: 4
Unlimited Game
Jacoby Beaver
                          pip: 4
score: 0

is Player 1
on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
  Player Winning Chances: 79.94% (G:0.00% B:0.00%) 79.94% (G:0.00% B:0.00%)
  Opponent Winning Chances: 20.06% (G:0.00% B:0.00%) 20.06% (G:0.00% B:0.00%)
  Cubeless Equities +0.599 +1.198
Cubeful Equities
No redouble:+0.599 (-0.352)
Redouble/Pass:+1.000 (+0.049)
Best Cube action: Redouble / Take

eXtreme Gammon Version: 2.02

We all know this is a double and a take.

But why? Yellow (the weaker side) only wins 20%. Why take? Because of the recube.

OK, that makes some sense. But how do you know? How do you measure that?

This is what I learned in Cleveland. Last roll position.

Win chances = [(# rolls opponent misses) x (# rolls you hit)] / 1296.

You need 25% of 324 to take.

(10) * (26) = 260 implies drop.

What gives? OK, so this is the trick. The recube doubles your equity to the extent you are a favorite.

So, when we get to roll we have 26 rolls to get off, or 8 more than half of 18. We add the 8 rolls into the calculation.

It's as if we get off 34 times (rather than 26) since we win those games with a recube.

So, the corrected calculation is:
(10) * (26 + 8) = 340 or take.
We get double the value on those wins.
Pretty neat. Thanks Dima. dfd