• More on Broken Primes

    This position occurred this week when I was running a training session for relative beginners. All of the class gave virtually no thought to doubling this position as Black, but I stopped them rolling so we could do some analysis. Long experience of broken primes over the last few years has taught me just how powerful they can be.

    My students did not have the benefit of having a huge number of similar reference positions to call upon, but I did. Remember that most doubling decisions are made by reference to one’s store of backgammon knowledge. Of course, we add calculation on top of the initial subjective analysis to arrive at a decision, but you cannot play top-class backgammon without having a personal library of thousands of reference positions.

    A beginner looking at this position sees only White’s five-and-a-half-point home board and does no further analysis.

    An expert sees more. Firstly, any 2 by Black is nearly always a winning roll. However, if Black fans, White needs to a number of things to win the game. He needs to cover the blot on his 2-pt, he then needs to escape two checkers from behind a broken prime. To do that he will need to roll two 2’s and then two 5’s or 6’s.

    That is a lot to ask while all the time Black is threatening to roll a two and probably win the game. When you need to do a number of things to win a game the percentage chance of doing so is the product of the chances of the individual events occurring.

    If things do go well for White, he will win some gammons and that must be taken into consideration as well. The position is highly volatile so if it is a double Black should be doubling now and not after he rolls the winning 2.

    My opinion was that this was indeed a correct double for Black. My students were somewhat surprised by this but agreed to double. Black went on to win a gammon. In fact, Black wins this position two-thirds of the time and about a quarter of those wins are gammons. White wins the rest of the games and a third of his wins are also gammons.

    A long rollout shows that the double is correct, and it is an error not to double now. The take is, of course, very easy. I would not expect many players to drop as White, but you never know in backgammon. The key point is to be able to recognise that Black has a double in the initial position and to be able to do that you need a reasonable amount of experience. That is why both playing experience and hours of study are necessary to become an expert at the game.


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