Two Trice bearoff cubes from the chouette

At the chouette this week we had both (a) Stack & Straggler and (b) Rolls versus Pips cube actions. I find these happen every so often, but just infrequently enough that my memory is hazy as to all the details.

Take a look at my earlier post for reference on EPC basics.

http://bigmoneybill.blogspot.com/2011/12/racingepc-and-prop-57-practice.html

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Rolls versus Pips. Cube Action?

is Player 2 score: 0 pip: 23

Unlimited Game Jacoby Beaver

pip: 30 score: 0 is Player 1

XGID=--AB-BB--------------cbac-:1:1:1:00:0:0:3:0:10

on roll, cube action?

Analyzed in XG Roller++	No redouble	Redouble/Take
Player Winning Chances:	69.45% (G:0.00% B:0.00%)	69.44% (G:0.00% B:0.00%)
Opponent Winning Chances:	30.55% (G:0.00% B:0.00%)	30.56% (G:0.00% B:0.00%)
Cubeless Equities	+0.389	+0.778
Cubeful Equities
No redouble:	+0.661
Redouble/Take:	+0.651 (-0.010)
Redouble/Pass:	+1.000 (+0.339)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 2.8%

eXtreme Gammon Version: 2.10

You can see it is borderline No Redouble / Take. Let's try the Trice formula.

EPC: (Pips) = 30 pips + about 7 for wastage or 37

Point of Last Take = (# Rolls to go) - 3
= approx (37 pips / 7) - 3
= about 2 pips

So point of last take = 39 pips for this position

EPC (Rolls) = 7N+1 plus adjustment for nearmiss

= (7*5 + 1) + near miss adjustment
= 36 + near miss adjustment

near-miss: Avg Pip is 23 pips / 9 checkers or 2.5
2.5 translates to 1 pip adjustment.

So EPC (rolls) = 36 + 1 = 37 pips

Application:

Double w/in 2 pips of last take
Redouble w/in 1 pip of last take

Implies that this position would be an initial double but not a redouble.

Appears to be right on target! Pretty neat.


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Stack & Straggler vs. Stack & Straggler:  Cube Action?

is Player 2 score: 0 pip: 20

Unlimited Game Jacoby Beaver

pip: 32 score: 0 is Player 1

XGID=-CBBB------A-a----------h-:2:-1:-1:00:0:0:3:0:10

on roll, cube action?

Analyzed in Rollout	No redouble	Redouble/Take
Player Winning Chances:	77.69% (G:0.00% B:0.00%)	77.68% (G:0.00% B:0.00%)
Opponent Winning Chances:	22.31% (G:0.00% B:0.00%)	22.32% (G:0.00% B:0.00%)
Cubeless Equities	+0.554	+1.107
Cubeful Equities
No redouble:	+0.813 (-0.161)	±0.002 (+0.811..+0.816)
Redouble/Take:	+0.974	±0.005 (+0.969..+0.979)
Redouble/Pass:	+1.000 (+0.026)
Best Cube action: Redouble / Take
Rollout details
1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:		100.0%
Take Decision confidence:		100.0%
Duration: 1.1 seconds

eXtreme Gammon Version: 2.10

Computer shows it as Redouble / Take. Let's try Trice's Stack & Straggler method and see how it does.

Recall for Stack + 1 straggler: EPC = (3.5 x # of checkers) + the outside man


EPC (doubler) = (3.5 x 9) + 12
                        = 43.5

Point of Last take =   (43.5 / 7) or about 6 rolls to go less 3
    =  3 pips  or 46.5 pips for taker is point of last take

EPC (taker) =(3.5 x 10) + 11
                    = 46


Application:
Taker is just barely within the point-of last take implies this is a Redouble / Close Take

Once again the method was correct.  Very impressive!