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That annoying 43

Posted By: Stick
Date: Friday, 7 January 2011, at 9:31 a.m.

Taken from the recent OLM I thought two down from the midpoint, 13/10 13/9, was clear. When the rollout tells me I'm wrong and others such as Neil and Rich agreed with me, I start to question things. (the only downside is MCG & Chuck also made this play which has me questioning why I even considered it to begin with) My first step is to look at how the bot plays all the immediate rolls (assuming no cube decisions) for both plays. Here the bot plays, in my opinion and XGR+'s opinion, everything correctly. It may make one small error but that's all it's likely to be, a small error, and won't have any major effect on the results.

Now that that's out of the way I have to question whether one play will lead to a certain type of game the bot isn't likely to understand as well as the other play. Here I don't think that applies. Both resulting positions aren't only normal, but pretty much the same. What's even worse for trying to figure out what's going on is that neither play is likely to result in different types of positions. The bot will have similar decisions down the road for both plays.

That all checks out, so now I toss on a stronger rollout just to see what happens. My rollout 4 ply/4 ply huge rollout is posted below. Also underneath it are the original 3 ply results. While my rollout is shorter and still has more variance left in it, it has reached the 99.8% confidence level and as you can see, the numbers are more or less in agreement with the 3 ply rollout. I will extend my rollout eventually but doubt much will change. If it does, I'll be sure to report back.

Now it seems like maybe we're wrong, that playing two off the midpoint is not the right path. What aren't we understanding? Well, according to the bot two down off the mid loses more gammons than the other play. This makes sense, more blots and more shots for our opponent to shoot out. What confuses me a bit is that two off the mid wins less gammons than the semi front loading play of 9, 5. 9, 5 puts 11 men in the zone and is not that well distributed whereas 10, 9 puts 12 men in the zone and has a much better distribution. As to which play would have won more games had you asked me beforehand I honestly wasn't sure. According to XG 9, 5 apparently wins at least half a percent more games.

On to the next step, playing the position out until my carpel tunnel tells me to quit. I wanted to play 10, 9 out more than anything to understand how it was unfolding. What I noticed is that on the next roll after most sequences there are some awkward numbers, namely [41 51 61] or some other numbers that left the blots in even more danger next turn [53 65 or any running the back checker number] After the other play, 13/9 8/5, do we have the same issues? No, only [61] is a little awkward still and [53 65 +] only leave the single blot target in the outfield.

I still really haven't convinced myself that 13/9 8/5 is better here than 13/10 13/9. I did consider other things like how the race affected the position or the stripping the midpoint theory, but I still came up with nothing concrete I can take away from it. If a similar position were to come up tomorrow I'd probably play 13/10 13/9.

FWIW, there are some bot errors I ran across in playing out the position pasted after the rollouts. I included the bot's 3 ply analysis followed by the rollout. These results don't affect the overall value of the rollouts imo because as stated earlier, these positions can arise after either play. Just a point of interest for those who like to see when the bot is also a donkey.

is Player 2

score: 0
pip: 153
15 point match
pip: 140
score: 0

is Player 1
XGID=-b---BE-C---bDa-bc-c-b--A-:0:0:1:43:0:0:0:15:10
to play 43

1.Rollout113/9 8/5eq: +0.056
Player:
Opponent:		 50.54% (G:17.04% B:1.14%)
49.46% (G:13.15% B:0.64%)		Conf: ± 0.012 (+0.044...+0.068)
Duration: 7 hours 59 minutes
2.Rollout113/10 13/9eq: +0.031 (-0.025)
Player:
Opponent:		 50.07% (G:16.19% B:1.18%)
49.93% (G:14.07% B:0.74%)		Conf: ± 0.012 (+0.019...+0.043)
Duration: 8 hours 06 minutes
1 2592 Games rolled with Variance Reduction.
Dice Seed: 21140344
Moves and cube decisions: 4 ply
Search interval: Huge

1.Rollout113/9 8/5eq: +0.065
Player:
Opponent:		 50.65% (G:16.86% B:1.17%)
49.35% (G:13.14% B:0.64%)		Conf: ± 0.009 (+0.056...+0.074)
Duration: 3 hours 06 minutes
2.Rollout113/10 13/9eq: +0.021 (-0.043)
Player:
Opponent:		 49.97% (G:16.13% B:1.13%)
50.03% (G:13.95% B:0.70%)		Conf: ± 0.009 (+0.012...+0.030)
Duration: 3 hours 08 minutes
1 7776 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply

#1 - The bot thought this to be a huge ND on 3 ply. Rollout confirms my action.
is Player 2

score: 0
pip: 130
15 point match
pip: 92
score: 0

is Player 1
XGID=bABB-BD-C-------abbccb-A--:0:0:1:00:0:0:0:15:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 53.43% (G: 35.26% B: 1.26%)
Opponent Winning Chances: 46.57% (G: 8.60% B: 0.40%)
Double/Take
Player Winning Chances: 53.48% (G: 35.95% B: 1.19%)
Opponent Winning Chances: 46.52% (G: 8.52% B: 0.36%)
Cubeless Equities
No Double:+0.351
Double:+0.733
Cubeful Equities
No Double:+0.279 (-0.030)
Double/Take:+0.309
Double/Drop:+1.000 (+0.691)
Best Cube action: Double / Take
Rollout details
1296 Games rolled with Variance Reduction.
Dice Seed: 21140344
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.018 (+0.261...+0.297)
Confidence Double: ± 0.029 (+0.280...+0.337)
Double Decision confidence: 95.8%
Take Decision confidence: 100.0%
Duration: 5 minutes 21 seconds

Analyzed in 3 ply
Player Winning Chances: 49.69% (G: 28.83% B: 0.77%)
Opponent Winning Chances: 50.31% (G: 8.48% B: 0.44%)
Cubeless Equities
No Double:+0.206
Double:+0.421
Cubeful Equities
No Double:+0.198
Double/Take:+0.027 (-0.171)
Double/Drop:+1.000 (+0.802)
Best Cube action: No Double / Take

#2 - XG 3 ply wanted me to take this. Rollout again confirms.
is Player 2

score: 0
pip: 116
15 point match
pip: 84
score: 0

is Player 1
XGID=-CBBbBB-Caa--------bbbcb-A:2:-1:-1:00:0:0:0:15:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 76.15% (G: 7.31% B: 0.17%)
Opponent Winning Chances: 23.85% (G: 4.96% B: 0.23%)
Double/Take
Player Winning Chances: 79.93% (G: 7.91% B: 0.36%)
Opponent Winning Chances: 20.07% (G: 5.69% B: 0.45%)
Cubeless Equities
No Redouble:+0.546
Redouble:+1.207
Cubeful Equities
No Redouble:+0.913 (-0.087)
Redouble/Take:+1.135 (+0.135)
Redouble/Drop:+1.000
Best Cube action: Redouble / Drop
Rollout details
1296 Games rolled with Variance Reduction.
Dice Seed: 21140344
Moves and cube decisions: 3 ply
Confidence No Redouble: ± 0.005 (+0.908...+0.918)
Confidence Redouble: ± 0.012 (+1.124...+1.147)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 10 minutes 04 seconds

Analyzed in 3 ply
Player Winning Chances: 76.20% (G: 7.57% B: 0.14%)
Opponent Winning Chances: 23.80% (G: 4.01% B: 0.16%)
Cubeless Equities
No Redouble:+0.559
Redouble:+1.057
Cubeful Equities
No Redouble:+0.902 (-0.054)
Redouble/Take:+0.955
Redouble/Drop:+1.000 (+0.045)
Best Cube action: Redouble / Take

#3 - XG wanted me to cash, me and the rollout said no!
is eXtremeGammon

score: 0
pip: 173
15 point match
pip: 127
score: 0

is Player 1
XGID=baA--BE-BAA-bBa-bc-b-b--A-:0:0:1:00:0:0:0:15:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 69.79% (G: 48.48% B: 6.05%)
Opponent Winning Chances: 30.21% (G: 5.60% B: 0.37%)
Double/Take
Player Winning Chances: 70.31% (G: 48.91% B: 6.01%)
Opponent Winning Chances: 29.69% (G: 5.38% B: 0.32%)
Cubeless Equities
No Double:+0.895
Double:+1.853
Cubeful Equities
No Double:+1.050
Double/Take:+1.578 (+0.529)
Double/Drop:+1.000 (-0.050)
Best Cube action: Too Good to Double / Drop
Rollout details
1296 Games rolled with Variance Reduction.
Dice Seed: 21140344
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.025 (+1.025...+1.074)
Confidence Double: ± 0.033 (+1.545...+1.611)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 28 minutes 16 seconds

Analyzed in 3 ply
Player Winning Chances: 68.72% (G: 46.68% B: 4.57%)
Opponent Winning Chances: 31.28% (G: 6.02% B: 0.40%)
Cubeless Equities
No Double:+0.835
Double:+1.697
Cubeful Equities
No Double:+0.990 (-0.010)
Double/Take:+1.445 (+0.445)
Double/Drop:+1.000
Best Cube action: Double / Drop

#4 - Wanted me to take, such a fish.
is eXtremeGammon

score: 0
pip: 139
15 point match
pip: 118
score: 0

is Player 1
XGID=-b--BBE-BAAAa---bbbbbb--A-:0:0:-1:00:0:0:0:15:10
on roll, cube action?


Analyzed in Rollout
No Double
Player Winning Chances: 72.70% (G: 17.78% B: 1.08%)
Opponent Winning Chances: 27.30% (G: 7.76% B: 0.50%)
Double/Take
Player Winning Chances: 73.83% (G: 18.85% B: 1.13%)
Opponent Winning Chances: 26.17% (G: 6.90% B: 0.45%)
Cubeless Equities
No Double:+0.563
Double:+1.230
Cubeful Equities
No Double:+0.816 (-0.184)
Double/Take:+1.049 (+0.049)
Double/Drop:+1.000
Best Cube action: Double / Drop
Rollout details
2592 Games rolled with Variance Reduction.
Dice Seed: 21140344
Moves and cube decisions: 3 ply
Confidence No Double: ± 0.013 (+0.803...+0.829)
Confidence Double: ± 0.020 (+1.029...+1.069)
Double Decision confidence: 100.0%
Take Decision confidence: 100.0%
Duration: 39 minutes 41 seconds

Analyzed in 3 ply
Player Winning Chances: 71.69% (G: 14.22% B: 0.76%)
Opponent Winning Chances: 28.31% (G: 8.38% B: 0.48%)
Cubeless Equities
No Double:+0.497
Double:+1.007
Cubeful Equities
No Double:+0.709 (-0.105)
Double/Take:+0.815
Double/Drop:+1.000 (+0.185)
Best Cube action: Double / Take

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