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BGonline.org Forums
Cube when you'll probably leave a blot
Posted By: Daniel Murphy In Response To: Cube when you'll probably leave a blot (Snua)
Date: Thursday, 17 November 2011, at 12:14 a.m.
By your calculations, you estimated that the opponent only wins 25%. So why would you be afraid to double? Your estimate is close enough for both the take decision and the doubling decision. White has a close but clear take. Blue has a great double because he's close to White's take point and has plenty of market losing sequences.
Over the board, I'd certainly start by estimating White's cubeless noncontact game winning chances. I get about 20% (here's how1).
Looking at the position, that's enough information to know I should double -- immediate and future shots aren't going to turn this into a "no double." For the take, though, I'd make sure that White also wins a few times by hitting a shot.
White hits about 9% of the time on his next roll (here's why2).
If White wins 9% of the time by hitting an immediate shot plus 20% of the time when he misses or has no shot, his cubeless GWC is about 27%3.
I'd stop here because, again, my estimate seems close enough to decide that White should take. I don't want to look further and calculate future shots, because (1) I don't need to (2) future shots will be increasingly unimportant, and (3) every simplification or error I may have made will throw off my answer. For example, 20% surely overestimates White's race wins when Blue rolls a 6 and White misses, and also when Blue rolls 3-3 5-4 5-5 4-4 2-2 1-1 or 3-2. On the other hand when Blue rolls 5-3 5-2 5-1 4-3 4-2 4-1 3-1 or 2-1, White's racing chances should go up quite a bit. On the other other hand, If Blue delays long enough, White may not still be around waiting for a shot.
If I wanted to account for non-immediate hits, then I might say this:
About half the time, the game is more or less resolved on the next sequence with White hitting (9% wins) or with White not hitting and retaining perhaps 10% racing chances on average. So that's 9% plus 10% of 41% = 13.1%. The other half of the time, the position repeats, and so on, so White's winning chances are about 13% + 6.5% + 3.25% + 1.6% + 0.8 ... What did I get? About 26%. I'd guess that's a little too low, mainly because whenever Blue rolls a number that doesn't hit or clear the 10 point, White's racing chances go up.
Sometimes future-future shots are very important, but I think generally you can get close enough for the decision you need to make by looking no further than the immediate shots. Fudge a little for future sequences if it looks like you should, but there are a lot of ways to make mistakes trying to be exact.
1Pipcount is 73 to 84. 73 + (10% of 73) + 2 = 82.3 = point of last take = 78% GWC for Blue. White's 1.7 pips worse than that, so I raise Blue's GWC by 3.4% to get 81.4%, and round down to 80% because of a rough guess at the effect of features like the gap on the 4 point, and actually down to 80% because it makes the arithmetic easier. So White's cubeless noncontact GWC is about 20%.
212/36 numbers leave a shot, all the sixes plus 3-3. Note that 5-2 does not leave a shot. White's return hits after the sixes average 11/36, because the 6-4 disaster is balanced by 6-3 which hits and covers. So we have 11/36 * 11/36 = 121/1296 = 9.3%, plus 2/1296 for the 3-3.
3That's just 9% plus 20% of 91% = 27.2%.
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