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BootCamp problem
Posted By: Daniel Murphy In Response To: BootCamp problem (pontiac)
Date: Friday, 17 February 2012, at 9:04 p.m.
This is an interesting problem with fascinating details that I have wasted much time over.
(1) as Blue I'd expect a cube from White after my play because (a) he hits 21/36 or 24/36 times and his excellent prime makes most of his hits huge market losers, and (b) looking at White's missing numbers, which include some large ones (most of his worst racing numbers hit), as White I'd take any redouble.
(2) 18/15 18/14 obviously leaves 8.33% fewer hits but generates fewer than 8.33% additional wins, mainly because of the very good chance that White will hit two checkers immediately (5/36) or later (maybe 40% of the time after the 16/36 rolls that hit one checker). There are very interesting differences in how White will play his next move (for example, almost always slotting the bar after 18/11, almost never after 18/15 18/14) and how that affects Blue's immediate response and White's chance of closing the deal, but the main feature is, as I mentioned, White's excellent chances of hitting two checkers after 18/15 18/14, which all but eliminates Blue's winning chances.
(3) I'd guess that after a hit Blue might retain GWC of about 2% for being closed out plus 2% for a quick 1-6 from the bar plus 2% for a 1 followed by a 6 out or a later 1-6 from the bar plus 2% for accidents = 8% winning chances if only 1 checker is hit.
(4) All in all, looking at GWC after immediate hits, racing GWC after immediate nonhits, and secondary chances of being hit, I have 18/15 18/14 winning .336 + .030 = 36.6% and 18/11 winning 0.264 + .055 = 31.9%, the exact figures mattering not much at all except the 4.7% more wins 18/15 18/14, because I have to compare that to the extra gammon risk. Call it 5%.
Which is lot less than 8.33%. Why? Basically, above I gave Blue an 80% chance of winning after being missed, gave Blue his 8% chance of winning after being hit on the 18 point (so 8% of 24/36 games became 5.5% of all games), and reduced that 8% a lot after 18/15 18/14 because of all the times a two checkers are hit (so 8% of 21/36 games became 3% of all games).
(5) Recalling that I expect the cube to be turned,
At 4a7a, 2a7a = 84%, 4a5a = 58%, 4a3a = 43%, so changing a loss to a win gains 26% MWC, changing a loss to a gammon loss loses 15% MWC. So about 3/5 of an additional win balances 1 additional gammon loss.
At 7a6a, 5a7a = 57%, 7a4a = 30%, 7a2a = 16%, so changing a loss to a win gains 27% MWC, changing a loss to a gammon loss loses 14% MWC. So about 1/2 of an additional win balances 1 additional gammon loss.
In other words, to play 18/15 18/14 with its 5% extra wins, I can allow no more than about 8% additional gammon losses leading 4a7a, and about 10% additional gammon losses trailing 7a6a. Figuring White's main gammon chances as being from either hitting two checkers immediately (5/36) or hitting one followed by a fan followed by hitting a second checker (which I guess to happend about 35% of the time he hits one checker immediately) I unfortunately get about 9% more gammon losses for 18/15 18/14. Give or take 3% :)
So.
I'd play 18/11 leading 4a7a, and 18/15 18/14 trailing 7a6a. Pretty sure 18/11 is right at 4a7a, and 18/15 18/14 is not a big error at 7a6a.
Oh -- also, trailing 7a6a I'd want to redouble to 4 after a miss unless White has rolled a big doublet. But not leading 4a7a because White's take point would be a low low 16%. All the more reason to play 18/15 18/14 trailing 7a6a so I can redouble 15/36 of the time instead of 12/36 of the time.
I don't have Bootcamp but for money, then, 18/15 18/14 should be marginally right or wrong. If right, I think it's an odd and interesting exception; more often, I think, you'd rather expose one blot to a double hit than expose two blots to one direct shot. You could probably easily construct a position where leaving two blots instead of one on the bar point is a huge blunder. But these choices don't seems to come up very often. Perhaps the reason for is that you're more likely to be waiting to clear the bar point with a doublet, and only running when that's forced with a 6-X or other number you can't play in your board.
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