![]() Though black’s decision to redouble or keep the cube precedes white’s decision to pass or take, the logical order for evaluating cube decision is pass-or-take first, turn-or-keep the cube second. Should black double to 4? Should White take? Perhaps black’s 85% wins break down into 79% plain games and 6% gammons. Furthermore, white’s three outfield checkers, plus his open one and two points, put him in some gammon danger. I’d say black wins about 85% of the time. White may continue dancing on black’s five-point board until (finally!) black escapes with a 6. Because his 5’s have been killed, the crashing of his board decelerates. Black still gets a chance to escape with a 6.įailing this, black won’t necessarily lose. ![]() ![]() But white is a 25-to-11 underdog to roll an immediate 6. He’ll break his six point before any other, of course. Suppose, for example, black cracks on the fourth shake. But black has good winning chances even if he doesn’t escape before cracking. In 5 rolls: 1 − 25 × 25 × 25 × 25 × 25 36 × 36 × 36 × 36 × 36 = 84 %ĭoes 77% therefore represent black’s winning probability in Example 1? If so, that would mean white had a bare take.We may calculate the chances of rolling a particular number (in this case, a 6) in n shakes by subtracting the nth power of 25/36 from 1. (Though the average roll is 8.17 pips, the average roll not containing a 6 is only 7.20 pips.) On the average, he will have four rolls in which to roll a 6 before he must break an inside point. How much time does black have? He can play 23 pips with the checkers on the 8 and 17 points. Then white may enter and attack black’s back man to win quickly with a powerful redouble. Unless he does so in time, his board will crack. To bring the win home, black must roll a 6 to escape his back man.
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