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Checker Problem |
A Controversial Move
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| From Backgammon Times, Volume 3, Number 2, Summer 1983. |
| Black to play 4-2. |
Not only that, but the cube position was critical. To be honest, I didn't record where the cube was (this was a while ago), but I believe it was with White. With the cube in the middle, we have no gammon because of the Jacoby rule, so hitting and making the 5 point with the idea of doubling on almost any comeback doesn't seem too bad. With the cube on the White side, things are a little different.
When all the howling had died down I continued to consider the two plays. Hitting sends a fourth man back and gives White excellent chances of making two of my inner points. However, with my three men back, White's chances of getting the timing for a back game were not good. Making the 5 point also gave White very few chances of going forward or attacking, and gave me a commanding lead in the race.
However, consider White's long and short term plans if I make the 4 point. What is his best roll? If he rolls double threes, making the 5 and 3 points, he is probably the favorite; but with him having three men back, a blot on the 2 point and my anchor on the 1 point—not to mention no builders for his two point—it is hardly a disaster. Moverover, if I hit and make the 5 point, then double threes make my 4 point, a point I feel may be the most important on the board. Of course, he will probably not roll anything but an average roll, and then let's look at his long term prospects.
By making the 4 point and leaving him with two blots in his lower inner board, it is hard to conceive of a good plan for him. Should he play loose for an all out back game? Seems like a poor choice; my gammon chances would be high. If he doesn't roll a six, I have excellent chances of making a 5-point prime next turn.
No matter how I look at it, it is hard to imagine that his long-term planning will be easier after I make the four point than if I send the fourth man back. Attack and back game seem like his most likely plans (if I don't hit). With four men back, however, and relieved of one of his two blots on the inner board, it seems that I have increased White's flexibility tremendously and made things easier, not harder on him, despite the extra lead in the race.
In fact, one could argue that my gammon chances are actually better after making the 4 point (not that I am thinking gammon yet). This is because I have a better board, and my opponent will have far more chances of running into serious timing problems and he may start to run out of moves soon.
I haven't played the position out enough times to say anything, but I have shown the problem to many players. After showing them the 4 point move, the better players never argue much.
In the actual game, I patiently explained some of my reasoning to the crew and when the best player consented, I made the 4 point. It worked like a charm. White was caught "Twixt and Tween" and soon his only hope was saving the gammon. This he was unable to do and for once the dice had justified my play. Things do not always work out so happily, as many a dissenting chouette captain knows.
As Barclay Cooke said about some positions in Paradoxes and Probabilities, this is one problem that the more I think about and the better I get, the more I think I was right. But the nice thing about backgammon is that perhaps a simulation would prove that I was wrong, and that's OK, too, because in that case I'll have learned something. And that's what it's all about.
| More articles by Dan Heisman |
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