1 2 3
1 0.500 0.677 0.751
2 0.323 0.500 0.599
3 0.249 0.401 0.500Middle game cube benchmark
Why this?
At Backgammon Galaxy, I play mostly 3-point matches, because this is the match length where getting a game is easiest. But correct cube action at the beginning of 3-point matches is different than from money, so I’m a bit concerned that playing so many 3-pointers will bias my cube strategy in longer matches.
To get a better feel for the difference, this is a collection of backgammon positions that GNU Backgammon 4-ply considered solid double/takes at 3-away, 3-away, but not necessarily for money and longer matches. The positions are all from the early middle game (here defined as move number 12 at the most, counting both sides). By ‘solid double/take’ I mean, that both not doubling and passing would be at least a 0.07 error.
The positions are extracted semi-automatically from my database of games, analyzed by GNU Backgammon. For that reason sometimes they are shown as checker plays – this happens when one player failed to double. For the same reason, sometimes Black is on roll, sometimes White.
Finally, while GNU Backgammon at 4-ply thought all positions where clear double/take at 3-away, 3-away, the XG rollouts sometimes come to a different conclusion: One side has a pass, or a no-double.
A bit of theory
Let’s revisit how and why the cube actions are different at 3-away, 3-away than for money. The 3-point match equity table looks like this:
In the simple case, not considering gammons and recubes, when we pass an initial double we get to 0.401 match winning chances, losing about 10 percentage points compared to when the game began. If we take, a loss is expensive, we get to 0.249 match winning chances, an additional loss of about 15 percentage points.
So the risk from taking and winning is 0.151, and the potential gain from taking and winning is 0.35 for a take point of 0.302, based on the standard formula: \(TP= \frac{Risk}{Gain + Risk}\). So a pure 4-roll position, for example, would be a pass.
After taking, the gammon value with the cube at 2, is 0.497, not much different from the money gammon value of 0.5, so adding gammons into the mix has about the same effect as in money game.
After taking, the opponent’s take point for a future redouble, is just 0.249 which is higher than for money, since the cube would be dead. That means that the cube is a little more valuable to us than for money, because we don’t have to improve quite as much to use it efficiently.
For illustration purposes, let’s assume gammon- and backgammon probabilities that are similar to the opening position for money, like this:
| Regular | Gammon | Backgammon | Sum | |
|---|---|---|---|---|
| Player wins | 0.36 | 0.134 | 0.006 | 0.5 |
| Opponent wins | 0.36 | 0.134 | 0.006 | 0.5 |
| Sum | 0.72 | 0.268 | 0.012 | 1.0 |
Then, putting it all together, we can calculate take points under different assumptions, and compare to money in a nice table like this:
| Cube assumptions | Money game take point | 3-away, 3-away take point | Difference |
|---|---|---|---|
| Dead cube, no gammons | 0.250 | 0.302 | 0.052 |
| Dead cube, gammons | 0.307 | 0.345 | 0.038 |
| Both cube and gammons | 0.271 | 0.286 | 0.015 |
Sure enough, the table shows that the ‘simple’ take point (no gammons, no cube) that we just discussed, is significant higher at the score than for money. A little bit of the difference disappear when we introduce gammons; somewhat more when we introduce the cube.
The end result is that the take point at 3-away 3-away is about 1.5 percentage point higher than for money. It may not sound as much, but the difference is quite real, as the examples below will show.
Double/take positions
Below are 21 positions rolled out at 3-away, 3-away and for money. Although many of the examples are double/take both at the score and for money, the side on roll is always more inclined to double at the match score than for money. The side not on roll, is always closer to a pass at the score than for money.
Studying the positions can be useful to reinforce one’s impression of what it takes to have a sound double, and what a takeable position looks like – for money and at 3-away, 3-away.
Position 1
3-away, 3-away
Analyzed in Rollout
No double
Player: 73,84% (G:3,02% B:0,10%)
Opponent: 26,16% (G:2,68% B:0,08%)
Double/Take
Player: 74,11% (G:3,04% B:0,07%)
Opponent: 25,89% (G:2,71% B:0,08%)
Cubeful Equities:
No double: +0,871 (-0,129)
Double/Take: +1,053 (+0,053)
Double/Pass: +1,000
Best Cube action: Double / Pass
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 73,86% (G:3,02% B:0,04%)
Opponent: 26,14% (G:2,52% B:0,08%)
Double/Take
Player: 74,13% (G:2,95% B:0,04%)
Opponent: 25,87% (G:2,52% B:0,09%)
Cubeful Equities:
No double: +0,754 (-0,095)
Double/Take: +0,849
Double/Pass: +1,000 (+0,151)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 2
3-away, 3-away
Analyzed in Rollout
No double
Player: 68,34% (G:20,05% B:2,05%)
Opponent: 31,66% (G:8,13% B:0,65%)
Double/Take
Player: 68,54% (G:20,65% B:2,80%)
Opponent: 31,46% (G:8,91% B:1,01%)
Cubeful Equities:
No double: +0,834 (-0,152)
Double/Take: +0,986
Double/Pass: +1,000 (+0,014)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 68,30% (G:19,79% B:1,12%)
Opponent: 31,70% (G:7,60% B:0,27%)
Double/Take
Player: 68,56% (G:20,02% B:1,12%)
Opponent: 31,44% (G:7,67% B:0,28%)
Cubeful Equities:
No double: +0,740 (-0,042)
Double/Take: +0,782
Double/Pass: +1,000 (+0,218)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 3
3-away, 3-away
Analyzed in Rollout
No double
Player: 65,91% (G:24,59% B:2,02%)
Opponent: 34,09% (G:7,59% B:0,48%)
Double/Take
Player: 65,57% (G:25,68% B:4,39%)
Opponent: 34,43% (G:8,14% B:0,72%)
Cubeful Equities:
No double: +0,799 (-0,097)
Double/Take: +0,896
Double/Pass: +1,000 (+0,104)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 65,97% (G:24,76% B:1,34%)
Opponent: 34,03% (G:7,63% B:0,27%)
Double/Take
Player: 66,16% (G:24,55% B:1,29%)
Opponent: 33,84% (G:7,49% B:0,27%)
Cubeful Equities:
No double: +0,718 (-0,027)
Double/Take: +0,746
Double/Pass: +1,000 (+0,254)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 4
3-away, 3-away
Analyzed in Rollout
No double
Player: 69,13% (G:13,40% B:0,47%)
Opponent: 30,87% (G:6,28% B:0,25%)
Double/Take
Player: 69,29% (G:13,98% B:0,63%)
Opponent: 30,71% (G:6,63% B:0,40%)
Cubeful Equities:
No double: +0,793 (-0,113)
Double/Take: +0,906
Double/Pass: +1,000 (+0,094)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 69,19% (G:12,98% B:0,36%)
Opponent: 30,81% (G:6,15% B:0,15%)
Double/Take
Player: 69,37% (G:13,52% B:0,33%)
Opponent: 30,63% (G:6,22% B:0,16%)
Cubeful Equities:
No double: +0,730
Double/Take: +0,721 (-0,010)
Double/Pass: +1,000 (+0,270)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 3,4%
Rollout:
1296 Games rolled with Variance Reduction.Position 5
3-away, 3-away
Analyzed in Rollout
No double
Player: 64,86% (G:25,92% B:1,39%)
Opponent: 35,14% (G:8,94% B:0,78%)
Double/Take
Player: 64,47% (G:27,45% B:2,06%)
Opponent: 35,53% (G:9,55% B:1,00%)
Cubeful Equities:
No double: +0,762 (-0,095)
Double/Take: +0,857
Double/Pass: +1,000 (+0,143)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 64,69% (G:26,19% B:0,95%)
Opponent: 35,31% (G:8,21% B:0,39%)
Double/Take
Player: 64,76% (G:26,94% B:0,92%)
Opponent: 35,24% (G:8,47% B:0,42%)
Cubeful Equities:
No double: +0,671 (-0,040)
Double/Take: +0,711
Double/Pass: +1,000 (+0,289)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 6
3-away, 3-away
Analyzed in Rollout
No double
Player: 62,31% (G:33,81% B:1,43%)
Opponent: 37,69% (G:12,75% B:1,34%)
Double/Take
Player: 62,46% (G:34,40% B:2,25%)
Opponent: 37,54% (G:13,77% B:1,78%)
Cubeful Equities:
No double: +0,615 (-0,248)
Double/Take: +0,864
Double/Pass: +1,000 (+0,136)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 62,26% (G:33,32% B:0,93%)
Opponent: 37,74% (G:12,35% B:0,95%)
Double/Take
Player: 62,46% (G:34,17% B:0,99%)
Opponent: 37,54% (G:12,63% B:1,02%)
Cubeful Equities:
No double: +0,542 (-0,091)
Double/Take: +0,634
Double/Pass: +1,000 (+0,366)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 7
3-away, 3-away
Analyzed in Rollout
No double
Player: 67,45% (G:21,24% B:2,26%)
Opponent: 32,55% (G:8,05% B:0,75%)
Double/Take
Player: 66,74% (G:22,62% B:5,39%)
Opponent: 33,26% (G:8,67% B:0,89%)
Cubeful Equities:
No double: +0,784 (-0,094)
Double/Take: +0,879
Double/Pass: +1,000 (+0,121)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 67,20% (G:21,36% B:1,24%)
Opponent: 32,80% (G:7,89% B:0,39%)
Double/Take
Player: 67,05% (G:21,78% B:1,40%)
Opponent: 32,95% (G:7,85% B:0,36%)
Cubeful Equities:
No double: +0,703 (-0,026)
Double/Take: +0,729
Double/Pass: +1,000 (+0,271)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 8
3-away, 3-away
Analyzed in Rollout
No double
Player: 63,32% (G:28,35% B:0,77%)
Opponent: 36,68% (G:7,68% B:0,49%)
Double/Take
Player: 63,76% (G:29,33% B:1,20%)
Opponent: 36,24% (G:8,17% B:0,79%)
Cubeful Equities:
No double: +0,704 (-0,154)
Double/Take: +0,858
Double/Pass: +1,000 (+0,142)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 63,34% (G:28,13% B:0,58%)
Opponent: 36,66% (G:6,89% B:0,35%)
Double/Take
Player: 63,68% (G:28,77% B:0,67%)
Opponent: 36,32% (G:7,35% B:0,37%)
Cubeful Equities:
No double: +0,632 (-0,053)
Double/Take: +0,686
Double/Pass: +1,000 (+0,314)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 9
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,26% (G:28,97% B:2,59%)
Opponent: 33,74% (G:8,04% B:0,66%)
Double/Take
Player: 66,09% (G:30,01% B:4,18%)
Opponent: 33,91% (G:8,92% B:1,15%)
Cubeful Equities:
No double: +0,831 (-0,169)
Double/Take: +1,031 (+0,031)
Double/Pass: +1,000
Best Cube action: Double / Pass
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,56% (G:27,73% B:1,42%)
Opponent: 33,44% (G:7,32% B:0,36%)
Double/Take
Player: 66,55% (G:28,81% B:1,45%)
Opponent: 33,45% (G:7,60% B:0,39%)
Cubeful Equities:
No double: +0,740 (-0,104)
Double/Take: +0,844
Double/Pass: +1,000 (+0,156)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 10
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,26% (G:28,97% B:2,59%)
Opponent: 33,74% (G:8,04% B:0,66%)
Double/Take
Player: 66,09% (G:30,01% B:4,18%)
Opponent: 33,91% (G:8,92% B:1,15%)
Cubeful Equities:
No double: +0,831 (-0,169)
Double/Take: +1,031 (+0,031)
Double/Pass: +1,000
Best Cube action: Double / Pass
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,20% (G:23,68% B:0,31%)
Opponent: 33,80% (G:4,38% B:0,18%)
Double/Take
Player: 66,51% (G:23,88% B:0,35%)
Opponent: 33,49% (G:4,56% B:0,18%)
Cubeful Equities:
No double: +0,750 (-0,034)
Double/Take: +0,784
Double/Pass: +1,000 (+0,216)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 11
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,56% (G:22,17% B:1,86%)
Opponent: 33,44% (G:8,37% B:0,63%)
Double/Take
Player: 66,63% (G:22,94% B:3,48%)
Opponent: 33,37% (G:9,39% B:0,89%)
Cubeful Equities:
No double: +0,778 (-0,117)
Double/Take: +0,896
Double/Pass: +1,000 (+0,104)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,75% (G:22,02% B:0,99%)
Opponent: 33,25% (G:7,98% B:0,40%)
Double/Take
Player: 66,87% (G:22,39% B:1,02%)
Opponent: 33,13% (G:8,18% B:0,40%)
Cubeful Equities:
No double: +0,721
Double/Take: +0,712 (-0,008)
Double/Pass: +1,000 (+0,279)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 2,8%
Rollout:
1296 Games rolled with Variance Reduction.Position 12
3-away, 3-away
Analyzed in Rollout
No double
Player: 65,19% (G:27,99% B:5,46%)
Opponent: 34,81% (G:6,60% B:0,33%)
Double/Take
Player: 64,35% (G:28,90% B:10,63%)
Opponent: 35,65% (G:7,02% B:0,51%)
Cubeful Equities:
No double: +0,792 (-0,075)
Double/Take: +0,868
Double/Pass: +1,000 (+0,132)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 65,39% (G:27,20% B:2,73%)
Opponent: 34,61% (G:6,62% B:0,25%)
Double/Take
Player: 65,26% (G:27,59% B:2,93%)
Opponent: 34,74% (G:6,89% B:0,32%)
Cubeful Equities:
No double: +0,743 (-0,041)
Double/Take: +0,784
Double/Pass: +1,000 (+0,216)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 13
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,66% (G:21,87% B:1,78%)
Opponent: 33,34% (G:6,59% B:0,27%)
Double/Take
Player: 66,45% (G:22,98% B:3,21%)
Opponent: 33,55% (G:7,23% B:0,60%)
Cubeful Equities:
No double: +0,797 (-0,107)
Double/Take: +0,904
Double/Pass: +1,000 (+0,096)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,58% (G:21,88% B:1,17%)
Opponent: 33,42% (G:6,14% B:0,22%)
Double/Take
Player: 66,89% (G:21,88% B:1,19%)
Opponent: 33,11% (G:6,25% B:0,22%)
Cubeful Equities:
No double: +0,734 (-0,034)
Double/Take: +0,769
Double/Pass: +1,000 (+0,231)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 14
3-away, 3-away
Analyzed in Rollout
No double
Player: 67,40% (G:19,51% B:1,69%)
Opponent: 32,60% (G:7,86% B:0,76%)
Double/Take
Player: 67,48% (G:20,06% B:3,62%)
Opponent: 32,52% (G:9,25% B:0,94%)
Cubeful Equities:
No double: +0,752 (-0,141)
Double/Take: +0,894
Double/Pass: +1,000 (+0,106)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 67,56% (G:19,29% B:1,00%)
Opponent: 32,44% (G:7,87% B:0,35%)
Double/Take
Player: 67,55% (G:19,48% B:1,05%)
Opponent: 32,45% (G:7,89% B:0,35%)
Cubeful Equities:
No double: +0,671 (-0,034)
Double/Take: +0,705
Double/Pass: +1,000 (+0,295)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 15
3-away, 3-away
Analyzed in Rollout
No double
Player: 64,07% (G:35,22% B:2,06%)
Opponent: 35,93% (G:11,02% B:1,72%)
Double/Take
Player: 64,39% (G:35,84% B:3,37%)
Opponent: 35,61% (G:12,54% B:2,23%)
Cubeful Equities:
No double: +0,732 (-0,268)
Double/Take: +1,035 (+0,035)
Double/Pass: +1,000
Best Cube action: Double / Pass
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 64,28% (G:34,84% B:1,18%)
Opponent: 35,72% (G:10,98% B:0,81%)
Double/Take
Player: 64,54% (G:35,15% B:1,12%)
Opponent: 35,46% (G:10,94% B:0,80%)
Cubeful Equities:
No double: +0,655 (-0,146)
Double/Take: +0,802
Double/Pass: +1,000 (+0,198)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 16
3-away, 3-away
Analyzed in Rollout
No double
Player: 63,42% (G:30,48% B:4,32%)
Opponent: 36,58% (G:10,19% B:1,62%)
Double/Take
Player: 63,19% (G:30,89% B:7,60%)
Opponent: 36,81% (G:11,54% B:1,57%)
Cubeful Equities:
No double: +0,750 (-0,094)
Double/Take: +0,844
Double/Pass: +1,000 (+0,156)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 63,29% (G:29,95% B:2,95%)
Opponent: 36,71% (G:9,95% B:0,59%)
Double/Take
Player: 63,34% (G:30,18% B:3,12%)
Opponent: 36,66% (G:10,11% B:0,64%)
Cubeful Equities:
No double: +0,642 (-0,054)
Double/Take: +0,697
Double/Pass: +1,000 (+0,303)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 17
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,15% (G:24,46% B:2,49%)
Opponent: 33,85% (G:7,38% B:0,49%)
Double/Take
Player: 66,17% (G:25,61% B:5,05%)
Opponent: 33,83% (G:8,13% B:0,86%)
Cubeful Equities:
No double: +0,820 (-0,110)
Double/Take: +0,930
Double/Pass: +1,000 (+0,070)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,33% (G:23,87% B:1,69%)
Opponent: 33,67% (G:7,25% B:0,23%)
Double/Take
Player: 66,56% (G:24,47% B:1,81%)
Opponent: 33,44% (G:7,38% B:0,24%)
Cubeful Equities:
No double: +0,753 (-0,031)
Double/Take: +0,784
Double/Pass: +1,000 (+0,216)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 18
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,97% (G:24,43% B:2,58%)
Opponent: 33,03% (G:10,30% B:0,56%)
Double/Take
Player: 67,02% (G:24,87% B:4,92%)
Opponent: 32,98% (G:11,48% B:0,61%)
Cubeful Equities:
No double: +0,810 (-0,153)
Double/Take: +0,963
Double/Pass: +1,000 (+0,037)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,87% (G:24,43% B:1,77%)
Opponent: 33,13% (G:9,69% B:0,23%)
Double/Take
Player: 66,90% (G:25,01% B:1,87%)
Opponent: 33,10% (G:9,86% B:0,24%)
Cubeful Equities:
No double: +0,728 (-0,042)
Double/Take: +0,770
Double/Pass: +1,000 (+0,230)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 19
3-away, 3-away
Analyzed in Rollout
No double
Player: 73,91% (G:5,95% B:0,08%)
Opponent: 26,09% (G:1,39% B:0,06%)
Double/Take
Player: 74,50% (G:6,10% B:0,12%)
Opponent: 25,50% (G:1,28% B:0,07%)
Cubeful Equities:
No double: +0,873 (-0,127)
Double/Take: +1,073 (+0,073)
Double/Pass: +1,000
Best Cube action: Double / Pass
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 74,32% (G:5,85% B:0,08%)
Opponent: 25,68% (G:1,38% B:0,04%)
Double/Take
Player: 74,68% (G:5,67% B:0,08%)
Opponent: 25,32% (G:1,36% B:0,04%)
Cubeful Equities:
No double: +0,820 (-0,075)
Double/Take: +0,894
Double/Pass: +1,000 (+0,106)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 20
3-away, 3-away
Analyzed in Rollout
No double
Player: 66,52% (G:29,61% B:1,02%)
Opponent: 33,48% (G:7,47% B:0,42%)
Double/Take
Player: 66,45% (G:30,52% B:1,42%)
Opponent: 33,55% (G:7,93% B:0,52%)
Cubeful Equities:
No double: +0,849 (-0,151)
Double/Take: +1,085 (+0,085)
Double/Pass: +1,000
Best Cube action: Double / Pass
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 66,50% (G:28,75% B:0,63%)
Opponent: 33,50% (G:7,23% B:0,29%)
Double/Take
Player: 66,58% (G:30,08% B:0,64%)
Opponent: 33,42% (G:7,36% B:0,30%)
Cubeful Equities:
No double: +0,729 (-0,151)
Double/Take: +0,879
Double/Pass: +1,000 (+0,121)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Position 21
3-away, 3-away
Analyzed in Rollout
No double
Player: 61,69% (G:28,96% B:0,79%)
Opponent: 38,31% (G:9,37% B:0,49%)
Double/Take
Player: 61,99% (G:29,19% B:1,65%)
Opponent: 38,01% (G:11,08% B:0,61%)
Cubeful Equities:
No double: +0,588 (-0,152)
Double/Take: +0,741
Double/Pass: +1,000 (+0,259)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.Moneygame
Analyzed in Rollout
No double
Player: 61,56% (G:28,46% B:0,72%)
Opponent: 38,44% (G:8,96% B:0,30%)
Double/Take
Player: 61,93% (G:28,83% B:0,67%)
Opponent: 38,07% (G:8,85% B:0,32%)
Cubeful Equities:
No double: +0,517 (-0,085)
Double/Take: +0,602
Double/Pass: +1,000 (+0,398)
Best Cube action: Double / Take
Rollout:
1296 Games rolled with Variance Reduction.