Backgammon Chouettes

Chouettes

California rule

From:   Peter Anderson
Address:   pander612@hotmail.com
Date:   27 November 2001
Subject:   "California" rule for chouette
Forum:   rec.games.backgammon
Google:   IMSM7.460$Lk.138884@dfiatx1-snr1.gtei.net

In chouette play, sometimes we play what we call a "California" rule (don't know why it's called that) Goes like this: On the opening roll, the winner can either play the roll like normal, or has the option of rerolling (with both dice) if the cube is turned (and stays in the middle). Local strategy in this loose game is as follows: If you win the opener with a natural 3-1, 4-2, or 6-1, take the roll. Otherwise turn the cube and re-roll. Does anyone know if this is optimum?

Gary Wong writes:

GNU Backgammon thinks so. Assuming you're not allowed doubles on the reroll, its cubeless evaluation of the equity being on roll in the starting position with a centred 2-cube is +0.069, whereas the equities after each of the 15 legal opening rolls are: 31: 8/5 6/5 +0.108 61: 13/7 8/7 +0.078 42: 8/4 6/4 +0.077 65: 24/13 +0.065 53: 8/3 6/3 +0.037 54: 24/20 13/8 +0.031 62: 24/18 13/11 +0.024 63: 24/18 13/10 +0.023 64: 24/18 13/9 +0.021 32: 24/21 13/11 +0.017 43: 24/20 13/10 +0.016 52: 24/22 13/8 +0.013 51: 24/23 13/8 +0.008 21: 24/23 13/11 +0.002 41: 24/23 13/9 -0.001 So only 31, 61 and 42 are better than rerolling with a centred 2-cube. (65 is very close.)

Peter Anderson writes:

Thanks Gary. Exactly what I was wondering. However, the re-roll IS allowed doubles. How does that change the strategy?

Gary Wong writes:

If doubles are allowed, then gnubg thinks it is always better to turn the cube and re-roll than to play the first roll you get. The combination of the chance of the 6 possible doubles and the benefit of increasing the stakes in a position where you have an advantage without forsaking cube access is too valuable to keep even a initial 31. (To be precise, its evaluation of the cubeless equity for being on roll in the starting position when doubles are permitted is 0.061 on a 1-cube, and so 0.122 on a 2-cube. This is greater than the equity following any of the non-double opening rolls on a 1-cube, including 31 which is worth 0.108.) Cheers, Gary.

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