Backgammon for Winners by Robertie p. 178-180

[Beck]

It's concerning the sample game 3, move 85, the doubling of the cube involved.

I fully understand the fact, that if you're about to win 25% of the times the double is a take.
i do beleive that the example in this book is incorrect.

Robertie reasons, that since the doubler will make a winning throw 72% of the time, the taker have 28% of winning, hence it's a take. But he doesn't take into consideration the fact that the taker isn't guaranteed to win if the doublers doesn't win this roll.

Since the taker is also a 72% favorite to make his roll (should he survive long enough), isn't his real win% only 0,28*0,72=20%

[Robertie]

Your math is right for computing the taker's winning percentage -- it's only 72% times 28%, or about 20%. However, when he wins the cube is on 32, because he will redouble before rolling and the original doubler will be taking. So his wins (and a few of his losses) come at double the price of the games where he loses on the first shake. If you do all the math, you'll find he loses less by taking than by dropping.

Since this was a beginner's book, I didn't want to include all the math in the book -- hence the glib explanation for the correct play.