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My thoughts over the board

Posted By: Daniel Murphy
Date: Wednesday, 7 October 2009, at 10:45 p.m.

In Response To: My thoughts over the board (Frank_N_Stein)

I looked at this and discovered it was not just a blunder. It is the blunder of all blunders to pass this.

Ah well, Gnubg 2- 3- and 4-ply are all way off here, too.

I have stated many times I am clueless with match equities and I quess at it. ... If I take and lose I am 9-10 crawford and unless I win gammon next game I have to play two games to win. If I drop the cube its 9-9 and most likely the next game will be the last game.

Let's be a bit more rigorous. So you were leading 9-8/11. Which is 2-away 3-away.

Memorizing all three point match equities is easy. There are nine scores in the 3-point match table but only four that must be memorized.

(1) 1-away 1-away, 2-away 2-away and 3-away 3-away are 50%.

(2) 2-away 1-away is about 32%, so 1-away 2-away is 68%.

(3) 3-away 1-away is about 25%, so 1-away 3-away is 75%.

(4) 3-away 2-away is about 40%, so 2-away 3-away is 60%.

The take/drop arithmetic is also not hard.

Take and win -> 100% match equity.

Take and lose -> 32% match equity.

Drop -> 50% match equity.

So, leading 2-away 3-away, taking a 2-cube risks 50-32 = 18% to gain 100-50 = 50%. The equation is Risk divided by (Risk plus gain) = Take point.

R/(R+G) =

18/(18+50) =

18/68 = must be a little more than 25%, since 18/72 would be 25%. 26.5%.

Having done that exercise (or having memorized that take point), if you then estimated that you would not win anywhere close to 26.5%, then you would have made a bad drop. But at least you'd have gone about it the right way ;-

To decide whether to take, you don't have to figure out how often you win. You only have to figure out if you win often enough to take. The magic number here is about 9.5 wins in 36 games.

I'd see that 20 numbers hit a second checker but you may anchor and win perhaps 2 of those games; 4 numbers hit nothing and you should win at least 3 of them. That's 5 wins in 24 rolls so far. Can you win 4.5 games of the remaining 12 numbers that hit only your blot in White's homeboard? I would think so. First, you can still escape after being hit. Second, for White to close out two checkers, you need to cooperate and hit him first. Sometimes you come in on the ace, or come in on the deuce but White fails to hit another checker, and sometimes you don't come in at all. If White closes out two checkers, you still win about 15%. If White closes out only one checker you win about 60%. You might take the average and give yourself about 5 more wins from those 12 games (which is pessimistic, since it ignores the times you don't get closed out), and you have 10 wins in 36, enough to take.

I believe a long rollout would show that Blue actually wins about 12 games in 36.

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