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Backgammon Boot Camp #41 (EndContact Positions)
Posted By: Taper_Mike
Date: Monday, 2 March 2015, at 7:00 a.m.
In Response To: Backgammon Boot Camp #41 (EndContact Positions) (Igor)
When you consider the onroll advantage is 4 pips, the race is tied. If Blue rolls an average roll of 8, but misses the shot, the race will still be tied.
Blue has 14 numbers that hit, including some of his poorest racing numbers. After a hit, if Blue owns the cube, he can play on cautiously to see whether he can win a rare gammon. At the first sign of risk, he can cash. If he has already doubled then he must play to the end. In that case his winning chances after a hit are still very high. I’ll ignore gammons, and estimate an effective win rate at 95%.
If Blue misses the shot, then the position converts to a noncontact race that is tied. At DMP, Blue’s GWC would be 50%. With the cube in play, the cube owner probably has GWC around 53.5%. When Blue does not double, he should win 53.5% of the 22 games where he misses the shot.
With these assumptions in place, let’s see if we can put some numbers on this. First, the nodouble scenaro. When he hits, Blue should win 35 or 36 times in 36. Throw in a gammon in 1.5 or 2 games, and the effective win rate comes out at about 100%, or a little more. Let’s ignore gammons, and call this 37 wins in 36 tries (times 14/36).
No Double
P( Hit and Win ) = 14/36 * 37/36 = 40.0%
P( Miss and Win ) = 22/36 * 0.53.5% = 32.7%
P( Win ) = 72.7%
P( Lose ) = 100%  72.7% = 27.3%
Net Points Won( cube on 2 ) = 2 * (72.7%  27.3%) = 0.90
Double/Take
P( Hit and Win ) = 14/36 * 95% = 36.9%
P( Miss and Win ) = 22/36 * 0.47.5% = 29.0%
P( Win ) = 66.0%
P( Lose ) = 100%  66.0% = 34.0%
Net Points Won( cube on 4 ) = 4 * (66.0%  34.0%) = 1.28
The result shows there is some leeway. Even if the numbers are off a little bit, Double/Take should still be correct.
Mike

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