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Rollout and Comments
Posted By: eXtreme Gammon
Date: Tuesday, 1 December 2009, at 12:09 a.m.
In Response To: Hit or not (eXtreme Gammon)
Here is the rollout
is Player 2
score: 2
pip: 685 point match pip: 53
score: 2
is Player 1XGID=DBCBaBBbbcbcb:1:1:1:21:2:2:0:5:10 to play 21
1. Rollout^{1} 8/5* eq: +0.263
Player:
Opponent:66.40% (G:0.66% B:0.01%)
33.60% (G:4.56% B:0.15%)Conf: ± 0.001 (+0.262...+0.264)
Duration: 4 minutes 14 seconds2. Rollout^{1} 4/2 3/2 eq: +0.246 (0.017)
Player:
Opponent:68.25% (G:0.07% B:0.00%)
31.75% (G:0.10% B:0.00%)Conf: ± 0.001 (+0.245...+0.247)
Duration: 1 minute 54 seconds3. XG Roller+ 4/1 eq: +0.215 (0.048)
Player:
Opponent:67.55% (G:0.09% B:0.00%)
32.45% (G:0.12% B:0.00%)4. XG Roller+ 3/2 3/1 eq: +0.206 (0.057)
Player:
Opponent:67.11% (G:0.07% B:0.00%)
32.89% (G:0.18% B:0.00%)5. 3 ply 4/3 4/2 eq: +0.203 (0.060)
Player:
Opponent:67.18% (G:0.07% B:0.00%)
32.82% (G:0.15% B:0.00%)^{1} 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 4 plyeXtreme Gammon Version: 1.10, MET: eXtremeGammon
Phil's question was : "You win fewer games, you lose a lot more gammons, and you only win a tiny bit more gammons. How can the hit be correct?????
My answer: "By hitting you basically void any redouble ability of the opponent. 8/5* which is 0.290 cubeless become only 0.267 cubeful. So holding the cube is worth only 0.023. For 4/2 3/2 cubeless=0.359 cubeful=0.246 so the cube worth 0.113, almost 5 times more.
The idea is that when you hit your opponent will almost never redouble (if he hits he’ll play for the gammon, and if he misses you’ll clear the blot and have a huge race advance (you're about 95% favorite) ).
If you don’t hit you are basically in a race. The opponent will have the ability to redouble very often. The cubeful equity of 0.246 is equivalent to 37.7% wins as there are no gammons (0.246+1)/2=0.377. The cubeless Winning percentage shows 31.7% chances to win. So in that position holding the cube give the opponent 6.0% more chance to win the game.
Compare that to the your opponent 33.6% winning chances (and 4.6% gammon) if you hit: You actually lose 4.1% more game by not hitting. With a gammon price of 0.502 (XG MET) it is worth to take the risk.
Note that it’s a posteriori analyze. There is no way I would have made that analyze over the board."
Like Daniel Murphy pointed the source of the problem is comparing Cubeless winning chances to Cubeful equities. Just a quick note: You can see the cubeless equity by moving the mouse over the move.

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