Continues from Swiss Backgammon Championship I
By Robert Wachtel
Of one thing we can be sure: nothing resembling calculation will help us decide among these plays: the only tools upon which we can rely are some general concepts and a visual overview of the position. As the backgammon writer Danny Kleinman (a fine mathematician) said about situations like this one: “vision laughs at counting.”
On this basis we can tentatively reject the running play. Yes, we’d like to escape from our opponent’s home board and connect our checkers, as this play does. But unfortunately we are too far down in the race (16 pips after the roll). The principle: “down in the race; maintain contact” dictates.
The blocking play looks logical, then, for it is a contact maximizer. But it has a fatal flaw. Because it would leave me with so many awkwardly stacked checkers on the six and five points, I often wouldn’t be able to attack my opponent if he runs. And were I to roll a 6 in the next one or two shots, I’d have to break my outside blockade anyway.
The distribution play is correct. It maintains plenty of contact while taking advantage of the golden opportunity afforded by the double four of unstacking the six point. The equities: the running and blocking plays are almost exactly equivalent, with my side winning about 45.5% of the games/matches. The distribution play wins a little more than 47%.
Using this sort of rough-and-ready logic, I did find the right play. But my opponent rolled a timely double five (too bad I didn’t make the (wrong) blocking play!) And soon I was faced with an even more difficult decision.
What to do? There are three obvious choices:
(1) everybody out
This play has the obvious advantage of leaving no direct shots. However it leaves a total of ten indirect shots – and moreover, it relinquishes the last outpost in the opponent’s territory, the 21 point.
(2) run one
A nice play, with great coverage, but it exposes me to a lot of shots: all deuces and some pick-and-pass aces.
or (3) slot the four point
This is the pure, and seemingly most logical play: it holds fast to the anchor and starts a perfect board. But it leaves fifteen direct shots.
I looked at all of these plays and couldn’t decide among them. My time was running … then I saw a fourth way. It looked as ugly as (3) is beautiful, but there was some logic to it: maximum coverage with minimum exposure. So I finally chose it:
Montreux backgammon position 13
Unfortunately Mr. Didisheim produced a double ace. He switched me off the 21 point and by the time I was done dancing he had born off most of his checkers. I was very disappointed with myself and sure that I should have made play (3). Funny enough, all of the spectators – and there were at least ten, all of them with strong opinions – agreed that I had blundered. Each had his theory about what I should have done; but not a one thought my play might have been right.
But it was! At least according to this as this long Extremegammon rollout, that is:
So I left Switzerland as its vice-champion, and a new resolve to believe in my own problem-solving ability.