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BGonline.org Forums
OLM Thurs. Jan 10th
Posted By: Matt Cohn-Geier In Response To: OLM Thurs. Jan 10th (myshlev)
Date: Friday, 11 January 2008, at 10:36 a.m.
Havard posted on this, but here goes for some practical OTB math.
4/1 4/o: Stick dances with 16 numbers, we leave a shot with 61, 51, 41, and 3's or higher (10 numbers). Alternatively, Stick comes in on the 4 point with 11 numbers, and we leave a shot with 61, 51, or 41 (6 numbers). He hits with 11 numbers in both cases.
16/36 is just under 1/2, 10/36 is just above 1/4, so let's say that together they're 1/8. 11/36 is just under 1/3, 6/36 is 1/6, so let's call it 1/18. Then we get (30%)(1/8 + 1/18) or about (1/3)(3/18) = 1/18. That's about 5.56% (2 numbers).
5/2 5/1: Stick dances (16 numbers), we roll 3's or higher (4 numbers), Stick hits with 11 numbers. That comes to just under 1/2 * 1/9 * 1/3, or 1/54. In other words, getting hit happens about 1/3 as often as the other variation. 5.56% divided by 3 is just over 1.5%.
Despite the fact that I used some pretty loose estimates, this is pretty close to what Havard got through direct calculation. 5.56% is off by only 0.2%, 1.5% is dead on.
There are other cases, like we clear the 4, Stick comes in on the 4, we roll two little numbers and end up leaving a shot the next time, but these variations are so negligible that they can be avoided in calculations.
On the other hand, not all of Stick's hits win, and gammon value isn't 0.5 at the score...
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