Question for Robertie or anyone else who cares to chime in.

Chapter 27, problem 430

Why take any risk? why not play 10/3 and avoid any hit? No return shot at all and you're not vunerable to a bad double next roll.

Am I missing something? please advise...


PS- Great book BTW, really improved my game :-)

Good catch. 10/3 is indeed better than 13/6, both because it leaves fewer shots (0 instead of 1) and because it creates more rolls to immediately make the 1-point (5 -- 66, 44, 22, and 42 -- instead of 3 -- 54 and 44).

Nonetheless, current Snowie rollouts make 13/9 13/10 (!?) the best play, creating slightly more gammons than 10/3 at the expense of a tiny number of extra losses. However, I can't articulate any good reason why this should be true. Clearing the midpoint obviously avoids problems if Black throws a sequence of ones, and it's possible that all the plays are so close together that this becomes a decisive idea. But that just means it's a poor problem and shouldn't have been included in the book.

The best play is 10/7 10/6. Follow the link below:

http://www-math.mit.edu/~tchow/rober...bertie430.html

Due to Snowie: 10/3 is the best, almost as good as 13/9-13/10

Sounds like this is turning into a battle of the bots! It seems to me, given the various rollout results, that any statement about what is "best" in this position should be qualified with the conditions of the rollout.

An XG 3ply, 2592 game rollout favors 10/7 10/6 (agreeing with the GNUBG
rollout that was previously linked) over 10/3, but the equity difference of -0.011 is pretty slim. Using the same rollout data 13/10 13/9 wins the most games, followed by 10/3. However 10/7 10/6 wins 10% more gammons than 13/10 13/9 which is why it comes out on top of the equity heap.

If this were a match play situation (e.g. DMP) where gammons did not matter than 13/10 13/9 would be the choice due to winning the most games.


XG rollout details:

1. Rollout¹ 10/7 10/6 eq:+1.183
Player : 90.37% (G:41.83% B:0.32%)
Opponent: 9.63% (G:1.33% B:0.08%)
Confidence: ± 0.005 (+1.178<E<+1.188)
Duration: 11 minutes 19 seconds

2. Rollout¹ 10/3 eq:+1.172 (-0.011)
Player : 91.02% (G:39.40% B:0.33%)
Opponent: 8.98% (G:1.48% B:0.08%)
Confidence: ± 0.005 (+1.167<E<+1.177)
Duration: 9 minutes 56 seconds

3. Rollout¹ 10/6 5/2 eq:+1.147 (-0.036)
Player : 90.40% (G:38.79% B:0.33%)
Opponent: 9.60% (G:1.59% B:0.08%)
Confidence: ± 0.005 (+1.142<E<+1.152)
Duration: 9 minutes 42 seconds

4. Rollout¹ 13/6 eq:+1.142 (-0.041)
Player : 90.48% (G:37.62% B:0.35%)
Opponent: 9.52% (G:1.44% B:0.07%)
Confidence: ± 0.005 (+1.137<E<+1.147)
Duration: 8 minutes 02 seconds

5. Rollout¹ 13/10 13/9 eq:+1.126 (-0.057)
Player : 92.46% (G:29.60% B:0.24%)
Opponent: 7.54% (G:0.70% B:0.03%)
Confidence: ± 0.005 (+1.121<E<+1.131)
Duration: 11 minutes 11 seconds


¹ 2592 Games rolled with Variance Reduction.
Dice Seed: Random
Moves and cube decisions: 3 ply


eXtreme Gammon Version: 1.13

13/9 13/10 isn't just better for sequences of 1's, it's also better for not leaving indirects or directs when opp rolls an ace. But it doesn't go for the closeout & gammon as aggressively as 10/7 10/6 does.