Well! Perhaps the New York backgammon geniuses might now reluctantly admit that the proposition they had just gotten crushed with (with 7 checkers off) was a close take; but there was no way that their inflated egos would allow them to back down from playing this one, where white has only 6 checkers off! Their opponent, they sneered, was due for a fall. He was trying to compensate for his low IQ and lack of talent by resorting to bean-counting. But even if he had rolled the position out, he had surely butchered the black side of the bear off. Somehow they rustled up a new bankroll. Once again it was the plodding experimental scientist alone against an army of the best and the brightest: but the result was the same this time as the last. The wise guys all got wiped out!
Muttering and snarling, they retreated; but our hero followed them again! “How about the 5 off position?” he proposed. Since by now you can surely anticipate the result, I will make the long story shorter. The boys lost a third and final time. On this go-round their decline was slower, for by now we have reached a position that is indeed a very close take. A fair result might even be that the take and pass break even; but by now the geniuses were stuck and steaming, and no doubt handled the redoubles (which our hero had also rolled out) sub-optimally. Here is the position as we would encounter it today, with a Snowie rollout result.
With no backgammon bots around, propositions became the preferred vehicle of competition for the backgammon elite and for those wishing to challenge them. There was a lot of randomness in money play if the opponents were closely matched; but once you had the right side of a juicy “prop,” it was hard to lose to the best player in the world. You might well start each prop game with a 10-15% advantage, and usually the games (which started in a mid game or endgame position) went fast. Best of all was to have the right side of a bear-off prop, as happened to me at the Cavendish Club in Los Angeles in 1980.
An Australian bookmaker had visited our club during one of his vacations in the U.S., and I had been playing him for the then astronomical sum of $50/pt: about equivalent to $200/pt. in today’s dollars. I was up a few points when he (White in the diagram below) redoubled me:
I was able to see that he only took off two checkers 1/6 of the time (with 65, 66, 55, 44 and 33), so that I would be on roll 5/6 of the time with 10 numbers (65, 64, 63, 66, 55, 44, and 33) to get off. I knew I needed to find 9 wins in 36 to be able to take, and on this basis alone I had 8 and a fraction. In addition, I saw that there was a real possibility of him not bearing off in two rolls. Guessing that this last factor was quite a bit greater than 1/36, I took. But as soon as I had done so, he challenged me. “You take this cube?” he said. “Would you like to play it now as a proposition? “I’ll give you 3 to 1 money odds, your $100 to my $300”!
Oh dear! My entire bankroll at the time was $10,000. I nonetheless agreed, and we began playing the bear off at lightning speed. But he won 11 of the first 13 games. Then, to my horror, he started yawning. “This is really a pretty boring little proposition,” he said, snuggling up to his female traveling companion. “Where do you want to eat?”
But the story has a happy ending. He agreed to play a few more backgammon games – and lost them. Now the position looked more interesting, and within an hour I had doubled my net worth. He quit down $10,000, paid me a bit in cash, and – miracle of miracles – sent me the rest a month later from Australia!