This article originally appeared in the August 2000 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
Can Blue take when playing like outlined in the story?
Apart from this not being my first 64-cube, but my second (the first one was a sad story, the less being said about it, the better), this was a true storythe game happened exactly that way. And if you have done the math, or read Robertie's Advanced Backgammon, or both, you will know that this position is a slim, slim take, so I was confident the take had been correct.
Yet, a few rolls down the road I had offered to settle, and in doing so I would probably have to give up a little, being the one offering as well as the favourite. So the question is, could I afford to do so and still take the double in the first place?
At the given cube level, the game is worth −15.84 if I take versus −16 if I drop. This means I cannot give up more than .16 overall in settling. The probability of reaching the position that prompted the settlement offer is 2/36 * 5/6 = .046. This mean that if I give up more than .16 / .046 = 3.48 points by settling, I should not have taken in the first place.
Now 3.48 is quite a lot, in the settling position on the 64-cube the game is worth 3.56 points, so unless I am kind enough to settle for nothing (and I'm not), the take is still correct with the settlement offer. But, I hadn't considered this over the table, and had no business being so sure about it!