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BGonline.org Forums
Vegas blotting 61 play
Posted By: John O'Hagan In Response To: Vegas blotting 61 play (poseidon)
Date: Sunday, 18 November 2012, at 11:01 p.m.
Interesting problem. One of those where you lose a lot on 2 numbers while gaining a little on the remaining 34. Which is greater? Plus we need to consider the trailer's 4-cube takepoint ATS.
What is the trailer's 4-cube takepoint ATS? Neil's numbers are not designed to work when the leader is 2a so you need to either memorize the MWC's for all 2a scores or use some other method. OTB, I think 2a-8a gives the leader about 87% so the trailer's takepoint is 13%.
Will the trailer have a take after either play if hit? If Blue plays 6/off 6/5, he will have 4 men off vs. 5 after 6/off 1/off. That translates to about 16%/23% IF white's spares are perfectly distributed on his 6-5-4 points AND Blue is flush down to the ace point. White figures to come pretty close to perfect distribution but Blue's gap on the 2-point hurts a lot. I would guess this defect reduces Blue's winning chances by about 6% making them 10%/17% after the two plays. Therefore Blue should pass if hit after the safer play and would have a take after the bolder play.
So, ignoring gammons and losing if not hit right away, 6/off 6/5 wins 25/36 and loses 11/36. Blue's MWC are then 25/36 x his MWC at 6a-4a (about 36% accd to Neil's numbers). That comes to 9 wins in 36 matches or 25% MWC.
6/off 1/off wins 23/36 + some of the 13/36 Blue gets hit. If Blue's CUBELESS chances after being hit are 17%, we know his CUBEFUL chances are less than that. How much less? Lamford's rule that cube ownership increases the cube owner's winning chances by 1/6 is usually pretty close. Here that would suggest that 83% cubeless translates into 97% cubeful. All of these games are assumed to end at the 2 level so 97% of the time it will be 2a-8a and 4a-6a the other 3%. This averages out to about 13.7% MWC for Blue. I'll raise that to 14% since the leader's redoubling window is pretty small ATS. 14% of 13 is 1.82 so Blue's MWC are only about 24.82/36 x 36% which totals a little less than the 25% MWC Blue gets after 6/off 6/5.
If Blue takes two men off and White hits, should White redouble right away? That would be premature. The leader's redoubling window is pretty small ATS - I think it opens around 83% and closes at 87%. So redoubling right away is wrong since White will be just barely into the doubling window. Better to wait and gradually improve until White is real close to the upper end of the doubling window.
So taking the extra checker off is the wrong play even though it will allow you to take a redouble if hit vs. being forced to pass if hit after making the correct play!
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