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BGonline.org Forums
Yet Another EPC Question
Posted By: Joe Russell In Response To: Yet Another EPC Question (adambulldog)
Date: Tuesday, 25 January 2011, at 3:41 a.m.
You can analyze this position much more accurately if you realize that blue is much more than slightly better than a four roll position. To do so is not difficult. You need only count what doubles he needs in his next three shakes to be off in three the vast majority of the time. The answer is double 2's or better (2orB). Then simply determine the chances blue will not roll 2orB in three shakes. He will not roll 2orB on one shake 31/36. In three shakes his chances of not rolling 2orB = (31/36)^3.
Since most should know that 36^3 = 46656, all you need to do is cube 31. If you have trouble cubing 2 digit numbers in your head, you can use easier methods such as can be found in Art Benjamin's excellent book MATHEMAGICS. One such method is X*(X-1)*(X+1)+X = =x^3. 30*32=960*31=29760+31=29791. 29791/46656 = ~ 30/47= ~64%. ~64% of the time he will not roll 2orB in three shakes. ~36% of the time he will roll 2orB in his next three shakes.
In addition you have 14 shakes (6-2, 6-3, 6-4, 6-5, 5-4, 5-3, 5-2) on your first roll that give you very reasonable chances to get off in three without the help of 2orB. Also, 1-1 on your first roll gives you a chance to get off in three without 2orB.
All in all, blue's position is as likely to be a three-roll position as a four or more roll position. If it were a pure 4-roll position, white would have a healthy take, but based on him not getting three rolls half of the time he has a clear pass. D/P.
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