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BGonline.org Forums
Simple Wisecarver positions
Posted By: AP In Response To: Simple Wisecarver positions (Ray Kershaw)
Date: Tuesday, 20 June 2017, at 3:49 p.m.
Explaining these types of positions essentially comes down to understanding how to quantify cube value after each play. There does seem to be a gap in current bg theory in this space, but I will lay out a few thoughts and hopefully others can help push it forward.
Let’s start with the diagram you posted.
•If White holds the cube now, what value can he hope to get from the cube later?
o After the correct checker play, this value is very small; he can only use the cube later in the game for gain if he rolls 2/1 followed by a Blue miss. With such small potential future value of the cube for White, he has more incentive to turn now.
o After the incorrect checker play, White has a higher upside if he holds on the cube now because Blue now misses with any 1 as opposed to only missing with 2/1.
• If White cubes now, what is the value that Blue can get from the cube?
o After the correct checker play, Blue can cash the game after any Red miss.
o After the incorrect checker play, Blue gets less value from holding the cube because Red can take some cubes.
One tool to help visualize these numbers is the Rollout statistics in GNU where you can see some numbers behind the qualitative explanations above. For example, you can see that if White holds the cube now, then after the correct checker play he will be able to use the cube 34 times out of 1296, and after the incorrect checker play it will be 187/1296. One clear way to help push the theory further in this space would be if there was a way to drill into the equity gain from each of these 34 times. If you could do this, you would see that in 30 of these times White can use the cube, it wouldn’t be for any value (i.e. cubing a gin position). White can only gain value after 2/1, 2/1 sequence (4/1296).
I think a similar framework can be used to analyze the second position. For example, if White doubles to 2:
• After the correct checker play, Black will get the opportunity to recube to 4 about 31.5% of the time, and 56% of these will be passes.
• After the incorrect checker paly, Black will get the opportunity to recube to 4 slightly less at 29.5%, but now 82% will be passes.
These numbers at least give some clue for why White is more reluctant to double after the correct checker play. In order to more fully explain it, I would want to be able to drill into the rollout statistics to see the roll sequences and equities behind the numbers. To my knowledge, the current generation of bots does not provide these numbers.
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