Backgammon

A SECOND position from the Ace Point Club in New York. My opponent had trapped two of my men behind his 4-point prime but had played weakly to allow one of them to reach my 1-point. I then escaped the other man to reach this position.

I thought for a few moments, did some calculations and then redoubled him to 8. He snatched the cube with nothing more than a a moment's thought, simultaneously castigating me for offering such a weak double. I rolled 32 and played 11/6. He pondered for a moment or two but decided not to redouble to 16 (which would have been a bad mistake) and rolled. The dice gods were watching over me as he rolled 51! I easily won a gammon and 16 points whilst my opponent ranted and raved over my appalling double. But was he right?

Let's do all the sums. On 8 rolls (33, 44, 55, 66, 64, 46, 65, 56), I win immediately. On 4 rolls (45, 54, 63, 36), I will leave a single shot. On 5 rolls (53, 35, 26, 62, 22), I will leave a double shot. On the remaining 19 numbers, I will leave a triple shot. A single shot gets hit one third of the time, a double shot half the time and a triple shot three-quarters of the time. Doing the arithmetic on this clearly shows that my opponent will hit me in 18 games out of every 36, or half of the time. When he doesn't hit me, I am therefore an extremely heavy favourite to win a gammon.

If he passes my redouble in 36 games, he will lose 144 points. If he takes, he will lose 18 gammons, costing him 288 points, but win 18 single games (144 points), giving him a net loss of 144 points. Thus, at best, this is a very borderline take.

But wait: will he always win when he hits on an occasion like this? Definitely not. He has a blot on his 2-point and he still has to contain black's blot after he has hit it. Black also already has four men off. All of this means that black will win quite a few games, even after he has been hit. This turns a borderline take into a clear pass. My opponent's rantings should have been directed at his own analytical capabilities.