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 story—the 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!