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BGonline.org Forums
Basic racing concept!
Posted By: Joe Russell In Response To: Clear from the rear? (Max Levenstein)
Date: Friday, 17 June 2011, at 7:50 a.m.
You are 9 pips behind and your opponent owns the cube. After the play you will be down 5 pips, if you do not hit. Your opponent will become a strong favorite if he rolls 5 or a 6, 20 numbers.
With 5-5 and 6-6, you will lose the game unless you respond likewise, and even then you still be a significant underdog. The other 18 rolls that contain a 5 or a 6 average 9.5 pips, so with one of these you will be down an average of 14.5 pips, on shake with your opponent owning the cube.
In a race of this length, with this lead, and owning the cube, your opponent will win over 70% of the time, say 72%. Summarizing, when he rolls a 5 or a 6, he wins 5% with 5-5 or 6-6 + 18/36(non-doubles containing a 5 or a 6) *.72 = .41%.
He gets more wins when he does not roll a 5 or a 6. His average roll then will be 6.25 pips. He will have a lead of about 10.5 pips, since double 3's and double 4's account for much of his average roll. You will be on shake with 16 numbers to point on him. Those 16 numbers should win 85% of the time.
When you can't point on him, it means you rolled a 5 or a 6. You should be a small underdog in these positions, as you will not even be able to hit loose with a 6. You might win 47% of these.
Summarizing again, your opponent wins 41% of the time by escaping on his first roll and when he does not he wins 16/36 * (16/36* .15 + 20/36*.53)=.16 for a total of 57%. Your negative equity, without considering gammons, is .57-.43*2 + -.28 points.
Can you do better than -.28 points equity by hitting him? Obviously you can. If you hit, he has 14 numbers that hit back. He will win about 13.5 of these and gammon you between 20 and 25% of the time. On the other 22 numbers you should win around 80%, that gives you 17.6 wins on the misses, and you may win a gammon 2 or 3% of those. Summarizing the hit, you win .5/36 (after being hit) + 17.6(after being missed) =18.1/36, about 50%.
Even though you win half the games with a hit, you will still have negative equity as you will be gammoned more often. He should get about 9% gammons (.225*14/36 =.087) You will get about 2% gammons. Your negative equity is 2*(.09 -.02) = .-14, better than the -.28 by not hitting.
The important thing to learn from this position is that is is very dangerous to let a game develop into a race when your opponent has the lead in the race and owns the cube.
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