acepoint’s home

 

2 vs 2 checkers (Chuck Bower)

• If your opponent is off in 75% or more rolls it’s a redouble/pass.
• If your opponent has more winning rolls (better distribution), it’s a redouble/pass
• If you have more wining rolls, it’s always a take
• If there is an identical distribution it’s only a take when you have proper redoubles after surviving opponents roll (not true for 43!)

3 vs 3 checkers (Achim Mueller)

(will follow)

 

General checker play (Kit Woolsey)

• Taking one checker off with one die is almost always right
• Taking one checker off with a combination of the dice is mostly right
• Fill gaps (with an ace aim for the 4- or 1-point)
• Play from the highest to the lowest stack

Wards adjusted pipcount (Jeff Ward, Walter Trice)

• Start with both pipcounts
• Add two pips for each extra checker
• If there are more than two checkers at the acepoint. add two pips for each additional checker
• If there are more than two checkers on the deucepoint add one pip for each additional checker
• Substract one pip for each extra occupied homeboard point
• Add half a pip for each checker in the outfield

Point of last take in low-wastage positions (Walter Trice)

• -5, /7, down
• /10, +1, up
• switch at 62 

Checker distribution

We start with an easy example and compare a few positions with an equal pipcount of the player but with different checker distribution on one side:

Pip counts: gnubg 11, ace 13

Position ID: UgAAEAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.119
	0.559 0.000 0.000 – 0.441 0.000 0.000
Cubeful equities:
1.	No double	+0.188
2.	Double, pass	+1.000	+0.812
3.	Double, take	-0.097	-0.285
Proper cube action:		No redouble, beaver (25.9%)

We now change the distribution of the green checkers:

	CL	ND	NR	D/RD
661	0.119	0.016	0.188	-0.097
553	0.265	0.266	0.359	0.325
544	0.299	0.346	0.413	0.445
643	0.351	0.402	0.456	0.580

We can see, that between the worst distribution 661 (no double/beaver) and the best 643 (redouble/take) is a cubless equity difference of 0.232 (0.351-0.119).

Pip counts: gnubg 12, ace 14

Position ID: jAAAIAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.145
	0.572 0.000 0.000 – 0.428 0.000 0.000
Cubeful equities:
1.	No double	+0.277
2.	Double, pass	+1.000	+0.723
3.	Double, take	+0.191	-0.087
Proper cube action:		No redouble, take (10.7%)

Again we change the distribution of the green checkers:

	CL	ND	NR	D/RD
662	0.145	0.208	0.277	0.191
644	0.242	0.323	0.372	0.394
554	0.248	0.337	0.381	0.408
653	0.294	0.401	0.431	0.525

Between the worst distribution (662) and the best (653) is a cubeless equity difference of 0.149.

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%)

And again we’ll change the distribution of the green checkers:

	CL	ND	NR	D/RD
444	0.117	0.128	0.228	0.035
552	0.163	0.207	0.276	0.197
633	0.202	0.141	0.256	0.174
651	0.256	0.249	0.338	0.338
642	0.291	0.335	0.409	0.439
543	0.293	0.335	0.399	0.470
443	0.354	0.429	0.475	0.617

The cubeless equity difference between the worst (444) and the best distributions (443) is now 0.237.

Some conclusions:

• It looks like the best distribution on three different points is “2-away” + “1-away”.On future pages I’ll call this “gd” (good distribution).
• Next best seems to be 2 checkers on one point and the remaining checker “1-away” or three checkers in a row. This is also a gd.
• The further away two checkers are, the worse a position is.
• Two checkers on the same point with a distance of at least 3 to the third checker is just bad. I’ll call it “bd” (bad distribution).
• Three checkers on the 4-, 5- or 6-points (no distribution) on greens side of the board is also a bd.
• All checker distributions which don’t fall into category gd or bd are “ad” (average distribution).
• The opponent usually needs doubles, so three checkers on one point doesn’t hurt him so much.
• The cube position (centered or owned by the roller) usually doesn’t make a difference. There are only few “no redouble but initial double” positions.

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

Player on roll is 3 pips behind

In this section we take a look at positions where the player on roll is behind 3 pips. This is probably the most difficult chapter. I took two positions for a rollers pipcount of 10, 11, 12, 13, 14 and 15 each. 

Pip counts: gnubg 7, ace 10
Position ID: JQAAwAIAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.529
	0.765 0.000 0.000 – 0.235 0.000 0.000
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.037	+0.037
3.	No double	+0.639	-0.361
Proper cube action:		Redouble, pass

 

Pip counts: gnubg 7, ace 10
Position ID: JQAAYAgAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.423
	0.712 0.000 0.000 – 0.288 0.000 0.000
Cubeful equities:
1.	Double, take	+0.791
2.	Double, pass	+1.000	+0.209
3.	No double	+0.520	-0.271
Proper cube action:		Redouble, take

 

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Pip counts: gnubg 8, ace 11
Position ID: KQAAEAYAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.349
	0.675 0.000 0.000 – 0.325 0.000 0.000
Cubeful equities:
1.	Double, take	+0.576
2.	Double, pass	+1.000	+0.424
3.	No double	+0.417	-0.159
Proper cube action:		Redouble, take

 

Pip counts: gnubg 8, ace 11
Position ID: GgAAIAUAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.514
	0.757 0.000 0.000 – 0.243 0.000 0.000
Cubeful equities:
1.	Double, take	+0.986
2.	Double, pass	+1.000	+0.014
3.	No double	+0.625	-0.360
Proper cube action:		Redouble, take

 

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Pip counts: gnubg 9, ace 12
Position ID: HAAAQAUAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.424
	0.712 0.000 0.000 – 0.288 0.000 0.000
Cubeful equities:
1.	Double, take	+0.759
2.	Double, pass	+1.000	+0.241
3.	No double	+0.527	-0.231
Proper cube action:		Redouble, take

 

Pip counts: gnubg 9, ace 12
Position ID: KgAAgAMAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.214
	0.607 0.000 0.000 – 0.393 0.000 0.000
Cubeful equities:
1.	No double	+0.325
2.	Double, pass	+1.000	+0.675
3.	Double, take	+0.245	-0.080
Proper cube action:		No redouble, take (10.6%)

 

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Pip counts: gnubg 10, ace 13
Position ID: MgAAQAkAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.317
	0.659 0.000 0.000 – 0.341 0.000 0.000
Cubeful equities:
1.	Double, take	+0.473
2.	Double, pass	+1.000	+0.527
3.	No double	+0.416	-0.057
Proper cube action:		Redouble, take

 

Pip counts: gnubg 10, ace 13
Position ID: SgAAEAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.022
	0.511 0.000 0.000 – 0.489 0.000 0.000
Cubeful equities:
1.	No double	+0.080
2.	Double, pass	+1.000	+0.920
3.	Double, take	-0.345	-0.425
Proper cube action:		No redouble, beaver (31.6%)

 

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Pip counts: gnubg 11, ace 14
Position ID: YQAAQAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.314
	0.657 0.000 0.000 – 0.343 0.000 0.000
Cubeful equities:
1.	Double, take	+0.552
2.	Double, pass	+1.000	+0.448
3.	No double	+0.431	-0.121
Proper cube action:		Redouble, take

 

Pip counts: gnubg 11, ace 14
Position ID: igAAIAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.032
	0.516 0.000 0.000 – 0.484 0.000 0.000
Cubeful equities:
1.	No double	+0.127
2.	Double, pass	+1.000	+0.873
3.	Double, take	-0.256	-0.382
Proper cube action:		No redouble, beaver (30.5%)

 

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Pip counts: gnubg 12, ace 15
Position ID: YgAAgAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.236
	0.618 0.000 0.000 – 0.382 0.000 0.000
Cubeful equities:
1.	No double	+0.340
2.	Double, pass	+1.000	+0.660
3.	Double, take	+0.320	-0.020
Proper cube action:		No redouble, take (2.9%)

The position above is nonetheless an initial double. 

 

Pip counts: gnubg 12, ace 15
Position ID: VAAAQAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity		+0.051
	0.526 0.000 0.000 – 0.474 0.000 0.000
Cubeful equities:
1.	No double	+0.141
2.	Double, pass	+1.000	+0.859
3.	Double, take	-0.154	-0.296
Proper cube action:		No redouble, beaver (25.6%)

 

Some conclusions:

• 9 vs 6 pips is always a redouble/pass.
• 10 vs 7 is usually a redouble/pass. Only if roller has a bd and his opponent has at least ad then it turns to a redouble/take.
• 11 vs 8 is always a redouble/take.
• 12 vs 9 is usually a redouble/take. Only if the roller has a bd and his opponent has at least a ad then it turns to a nodouble/take.
• 13-10 covers everything in the range of redouble/take (gd vs ad) to no double/beaver (bd vs gd).
• 14-11 covers everything in the range of redouble/take (gd vs ad) to no double/beaver (bd vs gd).
• 15-12 covers everything in the range of initial double/take (gd vs. bd) to no double/beaver (bd vs gd).
• 16-13 is always a no double.