Tuesday, 2 November 2010
You Tell Me!
Some positions defy analysis. When this roll occurred in game Three of Mochy v. Birkhahn, Birkhahn (White) played 13/10, 13/12, much to the surprise of this observer and indeed the rest of the gallery. I can't say that I would even have had this in my list of candidates!
White trails 1-4 to 11.
A major problem for players and bots alike is that there are thousands of ways to play this, so we need to do some pretty severe sorting before we get to a list of viable plays. I think that here we can discount plays that break White's prime, his major asset. I also can't bring myself to include any plays that split the anchor. There are three usual reasons for splitting an anchor: to facilitate escape, to try for a higher anchor and to improve coverage of the outfield. White isn't trying to escape as he trails in the race. He can get a higher anchor with this roll in safety. Red has no checkers in the outfield. Not only is there no reason to split the anchor, but Red will welcome it as a chance to develop his terrible stacks by hitting.
After this, we can divide our candidates into three sections; plays that leave the anchor where it is, plays that move to the 21pt and plays that move to the 20pt. The third section of course contains only one play, 22/20(2), while the first and second include various plays from the midpoint.
Over the board, I would have not seen much further than 22/20(2). It has some things going for it, notably the end of Red's small threat to prime those checkers and the opening up of 5-5 and 4-4 to jump out and get back into the race. The drawback is that it eases Red's problems for the moment, allowing him to dump checkers behind the anchor and wait for a fly shot to run out with a tempo or a 6-6.
Plays that go with 22/21(2) are these: (a)13/11; (b)13/12, 6/5; (c)13/12(2).
I like these plays in that order. (a) offers three rolls to make the six prime next and with some degree of safety. Red won't hit with a 6-1 and will only hit with a 6-3 because he has to blot with that number anyway. (b) appears to be slightly inferior as it only gives two rolls to make the six prime and Red should probably hit with 6-2 as well as 6-3. In addition, having a spare on the 6pt is better than one on the 5pt. The spare on the 5pt can't play fives or ones and if Red does hit in the outfield, then ones will be duplicated as a hitting number. (c) is completely safe, but only leaves one number to make the six prime.
The group where White stays on the 22pt is of course the largest of all. Two of these we can eliminate straight away. 13/11(2) has the same drawbacks as 13/12(2) above and 13/9 leaves no numbers at all to make the six prime. This leaves us with (a) 13/10, 13/12, (b) 13/10, 6/5 and (c) 13/12, 13/11, 6/5. These are very hard to order. (a) has 12 numbers to make the six prime but offers Red the chance to hit his way out with all sixes except 6-4, where he will prefer to make his 2pt. (b) has 14 numbers to make the six prime, with the same drawbacks as (a) and the additional weakening of the spare on the 6pt. I make those two about equal. Play (c) only leaves three numbers to make the six prime and again weakens the spare on the 6pt, but it's pretty safe. Red won't want to hit with 6-1 and might choose not to with 6-2.
I think that leaves us with a list of five candidates. (a) 22/20(2). (b)22/21(2), 13/11. (c)13/10, 13/12. (d) 13/10, 6/5. (e) 13/12, 13/11, 6/5.
Now all that we need to do is feed these into the bot and see what comes out the other end. I have tried truncated rollouts on lower settings on both Gnu and Snowie, with inconclusive results, so I am now waiting for a longer one to finish in Gnu. One thing that I can say is that all these plays are fairly close and that one or two others are probably almost as good! Kudos to Martin though, for finding an imaginative and distinctly more gammonish alternative to the more stolid, 22/20(2). A very long and time-consuming rollout on Gnu 2-ply indicates that all these five plays are within 0.02 of each other, really too close to call. 24/20(2) was best, but not by any convincing margin. Basically, the position is so static that nothing much is going to change in the next roll or two!