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leading 3a6a, cube action ?

Posted By: smcrtorchs
Date: Thursday, 9 May 2013, at 7:05 p.m.

In Response To: leading 3a6a, cube action ? (Klaus Evers)

Well 3a 6a is a peculiar score. Below is how I understand it.

Leaders GP with cube at 2 = 11/32 = roughly 1/3, with cube at 4 =0

trailers GP with cube at 2 = never mind. Trailer will double with first opportunity so winning an unredoubled gammon will be very rare, with cube at 4 trailer's GP = 40/60 or 0.66

Now the more gammon based a double is at 3a6a, the less it is a double. This is especially true if opponent has a high winning gammon percentage as well. I will assume wins and gammons for both positions and I believe I might be quite wrong, but it does not really matter. So let's say 66 win percentage at the first pos with 25% of gammons for blue and 8% gammons for white. As the trailer wins 34% he should redouble at least lets say 45% of the time. This means that leader's average gammon price is 1/3*55% = roughly 0.18 let's say 0.2 to make it easy. 25% * 0.2= 5%. Trailer's gammons are worth 8%*0.66 = 5.3% so gammons for both players have almost the same value. So basically in the first position blue is doubling with less than 66% of winning chances and his opponent has very good recube vig. I would say it is a ND

For the second position, I will estimate the win percentage for blue at 70%, with 35% gammons and again 8% gammon percentage for white. Average GP for leader should be a bit higher since trailer will redouble less often, but I will use 0.2 again as it is a bit higher than 0.18. So... 35% * 0.2 = 7% and white's gammons are worth 8% * 0.66 = 5.3%, so blue can add 1.7% to his win percentage. I will make the total 72% for easiness. I calculated trailer's dead take point around 28%. If we put white's recube big in the equation, this looks like a double take to me. If blue is at 72% already then he should have considerable market losers.

As I understand it, the bottom line is that at no gammonish positions with low - medium volatility like a 5 point holding game you can double almost as if it was a normal match score. This is because in such types of positions the double comes not from the gammons but from the wins. Other aspects such as the different take point and the early late ratio, could be taken into account as well, but I would not recommend memorising another table.

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