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Player on roll is 4 pips behind 

In this section we take a look at positions where the player on roll is behind 4 pips. Listed are positions from 10-6, 11-7, 12-8, 13-9, 14-10 and 15-11 pips.

Pip counts: gnubg 6, ace 10
Position ID: FQAAIAMAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.553
	0.776 0.000 0.000 – 0.224 0.000 0.000
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.085	+0.085
3.	No double	+0.663	-0.337
Proper cube action:		Redouble, pass

 

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Pip counts: gnubg 7, ace 11
Position ID: FgAAEAYAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.305
	0.652 0.000 0.000 – 0.348 0.000 0.000
Cubeful equities:
1.	Double, take	+0.496
2.	Double, pass	+1.000	+0.504
3.	No double	+0.372	-0.124
Proper cube action:		Redouble, take

 

Pip counts: gnubg 7, ace 11
Position ID: GQAAIAUAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.505
	0.753 0.000 0.000 – 0.247 0.000 0.000
Cubeful equities:
1.	Double, take	+0.975
2.	Double, pass	+1.000	+0.025
3.	No double	+0.621	-0.354
Proper cube action:		Redouble, take

 

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Pip counts: gnubg 8, ace 12
Position ID: KQAAIAkAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.373
	0.686 0.000 0.000 – 0.314 0.000 0.000
Cubeful equities:
1.	Double, take	+0.615
2.	Double, pass	+1.000	+0.385
3.	No double	+0.496	-0.119
Proper cube action:		Redouble, take

 

Pip counts: gnubg 8, ace 12
Position ID: GgAAIAYAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.252
	0.626 0.000 0.000 – 0.374 0.000 0.000
Cubeful equities:
1.	No double	+0.367
2.	Double, pass	+1.000	+0.633
3.	Double, take	+0.356	-0.011
Proper cube action:		No redouble, take (1.7%)

 

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Pip counts: gnubg 9, ace 13
Position ID: SQAAQAkAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.239
	0.620 0.000 0.000 – 0.380 0.000 0.000
Cubeful equities:
1.	No double	+0.333
2.	Double, pass	+1.000	+0.667
3.	Double, take	+0.246	-0.087
Proper cube action:		No redouble, take (11.5%)

 

Pip counts: gnubg 9, ace 13
Position ID: MQAAQAkAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.305
	0.652 0.000 0.000 – 0.348 0.000 0.000
Cubeful equities:
1.	Double, take	+0.450
2.	Double, pass	+1.000	+0.550
3.	No double	+0.402	-0.049
Proper cube action:		Redouble, take

 

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Pip counts: gnubg 10, ace 14
Position ID: MgAAQAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.174
	0.587 0.000 0.000 – 0.413 0.000 0.000
Cubeful equities:
1.	No double	+0.266
2.	Double, pass	+1.000	+0.734
3.	Double, take	+0.102	-0.164
Proper cube action:		No redouble, take (18.2%)

 

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Pip counts: gnubg 11, ace 15
Position ID: YQAAgAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.179
	0.590 0.000 0.000 – 0.410 0.000 0.000
Cubeful equities:
1.	No double	+0.280
2.	Double, pass	+1.000	+0.720
3.	Double, take	+0.222	-0.058
Proper cube action:		No redouble, take (7.4%)

 

Some conclusions:

• It looks like all positions with 10 or less pips at the rollers side are a redouble/pass.
• All positions with 11-7 pips are a redouble/take.
• With a pipcount of 12-8 I found only one position (552-332) which is no double/take. All others are a redouble/take.
• Most positions with a pipcount of 13-9 are a no double/take. Only 643-441 and 643-333 are a redouble/take  because of the opponents bd (bad distribution).
• Most positions with a pipcount of 14-10 are a no double/take. If the opponent has a gd (good checker distribution, i.e. 631) it’s yet a no double/beaver.  
• Nearly all positions with 15-11 pips are a no double/beaver. Only 654-551 (bd for opponent!) is a no double take.

Mirrored positions

In this part we’ll only cover positions where green and white have a mirrored position.

Pip counts: gnubg 10, ace 10
Position ID: hgAAYAgAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.535
	0.767 0.000 0.000 – 0.233 0.000 0.000
Cubeful equities:
1.	Double, take	+0.966
2.	Double, pass	+1.000	+0.034
3.	No double	+0.621	-0.345
Proper cube action:		Redouble, take

Position 622 looks like the only one with 10 pips which is a moneygame take. All other mirror positions (433, 442, 532, 541, 631) are a redouble/pass.

Pip counts: gnubg 11, ace 11
Position ID: TAAAwAQAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.509
	0.755 0.000 0.000 – 0.245 0.000 0.000
Cubeful equities:
1.	Double, take	+0.974
2.	Double, pass	+1.000	+0.026
3.	No double	+0.601	-0.373
Proper cube action:		Redouble, take

Pip counts: gnubg 11, ace 11
Position ID: igAAoAgAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.536
	0.768 0.000 0.000 – 0.232 0.000 0.000
Cubeful equities:
1.	Double, take	+1.000
2.	Double, pass	+1.000	+0.000
3.	No double	+0.627	-0.373
Proper cube action:		Redouble, take

533 is the only redouble/take position at a pipcount of 11. 632 is a borderline take/pass. All other mirror positions (443, 542, 551, 641) are redouble/pass.

Pip counts: gnubg 12, ace 12
Position ID: oQAAEAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.539
	0.770 0.000 0.000 – 0.230 0.000 0.000
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.024	+0.024
3.	No double	+0.640	-0.360
Proper cube action:		Redouble, pass

At a pipcount of 12
Position 651 is the only mirror position which is a redouble/pass. All others (444, 543, 552, 633, 642) are a redouble/take.

Non mirrored positions

For non-mirrored positions I get the following results:

10 433 442 532 541 622 631 433 P P P P P P 442 P P P P P P 532 P P P P P P 541 P P P P P P 622 T T T T T T 631 P P P P P P

11 443 533 542 551 632 641 443 P P P P T P 533 P T T P T T/P 542 P P P P P P 551 T T T P T T 632 P P P P T/P P 641 P P P P P P

12 444 543 552 633 642 651 444 T T T T T T 543 P T P T T T 552 T T T T T T 633 T T T T T T 642 P T P T T T 651 P T P T T P

Some conclusions:

• All positions with a pipcount of 9 or less are a redouble/drop.
• All positions with a pipcount of 13 or more are a redouble and a take.
• Besides 622 on the rollers side all positions with 10 pips are a redouble/pass.
• Most positions with 11 pips are a redouble/pass.
• Most positions with 12 pips are a redouble/take.

Three opponent checkers on the acepoint

We start with three similar positions and a bad distribution for the roller (441, 551, 661):

Pip counts: gnubg 3, ace 9

Position ID: BwAAEAMAAAAAAA Match ID: UQngAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.541	(Money: +0.541)
	0.771 0.000 0.000 – 0.229 0.000 0.000
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.095	+0.095
3.	No double	+0.598	-0.402
Proper cube action:		Redouble, pass

Pip counts: gnubg 3, ace 11

Position ID: BwAAEAYAAAAAAA Match ID: UQngAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.265	(Money: +0.265)
	0.632 0.000 0.000 – 0.368 0.000 0.000
Cubeful equities:
1.	Double, take	+0.422
2.	Double, pass	+1.000	+0.578
3.	No double	+0.333	-0.089
Proper cube action:		Redouble, take

Pip counts: gnubg 3, ace 13

Position ID: BwAAEAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		-0.118
	0.441 0.000 0.000 – 0.559 0.000 0.000
Cubeful equities:
1.	No double	-0.062
2.	Double, pass	+1.000	+1.062
3.	Double, take	-0.594	-0.532
Proper cube action:		No redouble, beaver (33.4%)

In the next three positions there is no checker on greens acepoint (632, 552, 652):

Pip counts: gnubg 3, ace 11

Position ID: BwAAoAgAAAAAAA Match ID: UQngAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.386	(Money: +0.386)
	0.693 0.000 0.000 – 0.307 0.000 0.000
Cubeful equities:
1.	Double, take	+0.723
2.	Double, pass	+1.000	+0.277
3.	No double	+0.485	-0.238
Proper cube action:		Redouble, take

Pip counts: gnubg 3, ace 12

Position ID: BwAAIAYAAAAAAA Match ID: UQngAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.163	(Money: +0.163)
	0.582 0.000 0.000 – 0.418 0.000 0.000
Cubeful equities:
1.	No double	+0.283
2.	Double, pass	+1.000	+0.717
3.	Double, take	+0.190	-0.093
Proper cube action:		No redouble, take (11.5%)

Pip counts: gnubg 3, ace 13

Position ID: BwAAIAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.059
	0.529 0.000 0.000 – 0.471 0.000 0.000
Cubeful equities:
1.	No double	+0.178
2.	Double, pass	+1.000	+0.822
3.	Double, take	-0.085	-0.263
Proper cube action:		No redouble, beaver (24.3%)

Another three positions where the lowest checker is on the 3-point (333, 346, 355)

Pip counts: gnubg 3, ace 9

Position ID: BwAAwAEAAAAAAA Match ID: UQngAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.507	(Money: +0.507)
	0.753 0.000 0.000 – 0.247 0.000 0.000
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.034	+0.034
3.	No double	+0.615	-0.385
Proper cube action:		Redouble, pass

Pip counts: gnubg 3, ace 13

Position ID: BwAAQAkAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.148
	0.574 0.000 0.000 – 0.426 0.000 0.000
Cubeful equities:
1.	No double	+0.239
2.	Double, pass	+1.000	+0.761
3.	Double, take	+0.023	-0.216
Proper cube action:		No redouble, take (22.1%)

Pip counts: gnubg 3, ace 13

Position ID: BwAAQAYAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.049
	0.524 0.000 0.000 – 0.476 0.000 0.000
Cubeful equities:
1.	No double	+0.128
2.	Double, pass	+1.000	+0.872
3.	Double, take	-0.129	-0.257
Proper cube action:		No redouble, beaver (22.8%)

Last but not least two even worse positions (444, 445):

Pip counts: gnubg 3, ace 12

Position ID: BwAAgAMAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.117
	0.559 0.000 0.000 – 0.441 0.000 0.000
Cubeful equities:
1.	No double	+0.228
2.	Double, pass	+1.000	+0.772
3.	Double, take	+0.035	-0.193
Proper cube action:		No redouble, take (20.0%)

Pip counts: gnubg 3, ace 13

Position ID: BwAAgAUAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.091
	0.546 0.000 0.000 – 0.454 0.000 0.000
Cubeful equities:
1.	No double	+0.190
2.	Double, pass	+1.000	+0.810
3.	Double, take	-0.059	-0.249
Proper cube action:		No redouble, beaver (23.5%)

10 CL ND NR D/R 433 0.486 0.581 0.593 0.949 442 0.508 0.603 0.615 0.992 532 0.553 0.617 0.621 1.103 541 0.554 0.618 0.622 1.105 622 0.383 0.448 0.477 0.712 631 0.558 0.633 0.645 1.093

11 CL ND NR D/RD 443 0.354 0.429 0.475 0.617 533 0.340 0.351 0.408 0.573 542 0.420 0.504 0.530 0.797 551 0.265 0.268 0.330 0.413 632 0.386 0.441 0.480 0.703 641 0.392 0.437 0.486 0.689

12 CL ND NRD D/RD 444 0.117 0.128 0.228 0.035 543 0.293 0.335 0.399 0.470 552 0.163 0.276 0.207 0.197 633 0.202 0.141 0.256 0.174 642 0.291 0.335 0.409 0.439 651 0.256 0.249 0.338 0.338

Legend
CL:	cubeless
ND:	no double
NR:	no redouble
D:	double
RD:	redouble
Green:	redouble/take
Orange:	initial double/take
Red:	redouble/pass

Some conclusions

• All positions with 9 or less pips (6 behind) are a redouble/pass.
• Three positions with 10 pips (7 behind) are a redouble/pass (433, 442 and 622 are redouble/take).
• All positions with 11 pips (8 behind) are a redouble/take.
• Most positions with 12 pip (9 behind) are a redouble/take (552 and 633 are initial doubles, 444 is no double).
• Most positions with 13 or more pips (10 behind) are a no double/beaver (643 is no double/take).

Two vs. two checkers

The usage of this table is pretty easy. Search for the position of your checkers at very left column and for your opponents checkers at the top. The cell number itself will give you the cubeless winning probablity. For the colors take a look at the caption below.

	11 21	31	41	22	32	51 42	52	33 43*	61	53	62	44	63 54	64	55 65	66
11/21	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
31	94,4	94,8	95,5	96,0	96,1	96,4	97,1	97,4	97,7	97,8	98,0	98,3	98,5	98,8	99,1	99,4
41	80,6	81,6	84,3	86,0	86,5	87,6	89,7	90,8	91,9	92,4	93,0	94,1	94,6	95,7	96,8	97,8
22	72,2	73,8	77,6	79,9	80,7	82,3	85,3	86,9	88,4	89,2	90,0	91,5	92,3	93,8	95,4	96,9
32	69,4	71,1	75,4	77,9	78,8	80.5	83,9	85,6	87,3	88,1	89,0	90,7	91,5	93,2	94,9	96,6
51/42	63,9	65,9	70,9	73,9	74,9	76,9	80,9	82,9	85,0	86,0	87,0	89,0	90,0	92,0	94,0	96,0
52	52,8	55,4	61,9	65,8	67,1	69,7	74,9	77,5	80,1	81,4	82,8	85,4	86,7	89,3	91,9	94,5
33/43*	47,2	50,2	57,5	61,9	63,3	66,3	72,1	75,1	78,0	79,5	80,9	83,9	85,3	88,3	91,2	94,1
61	41,7	44,9	52,9	57,8	59,4	62,6	69,1	72,3	75,5	77,1	78,7	82,0	83,6	86,8	90,1	93,3
53	38,9	42,2	50,5	55,5	57,2	60,5	67,2	70,5	73,8	75,5	77,2	80,5	82,2	85,5	88,9	92,4
62	36,1	39,6	48,3	53,5	55,3	58,7	65,7	69,2	72,7	74,4	76,2	79,6	81,4	84,9	88,5	92,1
44	30,6	34,3	43,8	49,4	51,3	55,1	62,6	66,4	70,2	72,1	79,6	77,7	79,7	83,5	87,3	91,2
63/54	27,8	31,6	41,2	46,8	48,7	52,7	60,4	64,2	68,1	70,0	71,9	75,8	77,8	81,7	85,7	89,8
64	22,2	26,1	36,0	41,8	43,8	47,7	55,6	59,5	63,4	65,5	67,4	71,4	73,4	77,6	82,0	86,5
55/65	16,7	20,8	31,3	36,3	39,7	43,8	52,2	56,4	60,6	62,7	64,8	69,0	71,3	75,8	80,0	85,3
66	11,1	14,8	24,2	29,8	31,6	35,4	42,9	46,5	50,3	52,4	54,3	58,1	60,4	64,9	69,7	75,4

Explanation
Red:	No Double/Beaver
Green:	Double/Take
Orange:	Double/Take (though less than25% cubeless)
White:	Double/Pass

* 43 vs 33/43 is a small take, because of the possibility of rolling 21 twice in a row.