| |
BGonline.org Forums
match equity window and win chance for this position
Posted By: Daniel Murphy In Response To: match equity window and win chance for this position (Bob Koca)
Date: Wednesday, 7 September 2011, at 6:28 p.m.
The more common use of match equities for doubling decisions is for finding your doubling window, doubling point or cash point, and then to double or not, depending on where you are in the market window, whether the cube is live or not, whether you have significant market losers and so forth. Trailing 6-away 2-away, Blue could recall that when Leader is 2-away the bottom of Trailer's last roll doubling window is quite high. If Blue were to calculate the bottom of his last roll doubling window, he would find that his double risks 11% to gain 7% so his doubling window opens at 11/18 = 22/36 = 61%.
1-away 2-away 2-away 50% 4-away 33% 5-away 26% 6-away 11% But this is not a last roll position. If Blue does not double, White might. And there is another method of calculation which is usually quite a bit more tedious but is appropriate for some positions. Like this one. Recalling that cube action can affect game winning chances, Blue can estimate GWC and compare his average match equity after winning or losing with the cube doubled or not.
If Blue does NOT double now, clearly he wins 17/36 times by hitting. Another 2 rolls (4-4 and 5-5), are probably about 50/50, so let's give him one of those, too. In the other 17/36 times Blue has rolled at best 5-4, and White is on roll. Cube action? Since Blue's redouble is automatic, Blue's take now risks 11% to gain 39%, so his takepoint is 22%. Can he win that often? I doubt it. White has a very good bearoff board despite the gaps. Most doubles work. 3's fill a gap. Only 5's are completely wasteful. 6-1, 3-1 and 1-1, average or poor race numbers, are great game winning numbers since they hit and point on the 5 or 3 point. Some other numbers pick and pass. Recall that an 8-roll vs. 8-roll position wins 67%. Perhaps recall that 7-roll vs. 8-roll positions and 8-roll vs. 9-roll positions win in the high 80%'s. Here, after a nonhitting roll, White appears to be about more than a full rolls ahead. Plus he has his hitting/pointing number vig. If Blue took, I believe he would hit an immediate direct or indirect shot about 5% of the time, but I'm going to put Blue's GWC at 20% at best.
Which means Blue should pass White's double. Which means that after No Double, Blue wins 18/36 games.
And if Blue doubles? Give White one of the 17 games in which Blue has hit. Since 20% of 17 is 3.4, give Blue his 3.4 games. Net result: after Double/Take Blue wins 20.4 games in 36. That's about 56%.
Now for the match equities:
No double -> half the time Blue has 26%, half the time he has 11%. I'm fudging the 4-4 and 5-5 outcomes. Blue's average match equity is 18.5%. Double/Take -> Blue attains 33% match equity 56% of the time, for an average equity of 18.66% match equity.
Conclusion: Blue has a close decision but he should double now even though, as we have seen, Blue's GWC is below the bottom of his last-roll doubling window.
Like Casper said, you hate to be doubled (and have to pass) after a miss.
| |
BGonline.org Forums is maintained by Stick with WebBBS 5.12.