Backgammon Problems from 2009 Paris Open

By Robert Wachtel

Here are a few more problems this year’s French Backgammon Open. While previously, everyone in the group of strong players – except for Falafel – got it wrong, these positions have received the unanimous – and mistaken – consent of this seminar of experts, with most of us meekly following the leader when we sensed that a consensus was forming.

A trivial-looking little problem, which occurred early on in one of my matches. I was about to routinely make the 8 point with the 4-1, as almost anyone would, when I stopped to look around for something better. The race is close, and White has some attacking chances. Why not squelch them by buttoning up with 23/22 and then hit with 8/4 (which duplicates fours as well)? If you are missed, you will have a big advantage. If you are hit, you have an anchor and there is always White’s blot on the ace point to shoot at. Over the board I persuaded myself to make this non-routine play. Later, when I presented it to the group, every one of them (to my delight) agreed that 23/22, 8/4* was obvious. Here is how the two plays look:

Play # 1, 13/8

Play #2, 23/22, 8/4*

And then there was this puzzling one. It came up early in a 15-point match against the studious young Japanese player, Noriyuki Hosaka.

I hit and covered, the natural play, but I had some doubts. Afterwards I wondered what I had been thinking. Black is way ahead in the race with only one man back and White has a good board, so why take this risk? What is wrong with the simple 13/8, 7/3?

Indeed, when I showed this one to the group, my fears were confirmed. Immediately one of the world’s best backgammon players said: “Well, there’s one thing I’m sure of: I’m not hitting.” Within a few minutes, everyone else was in lockstep. Nobody thought hitting was right, and in fact there was some general jeering and sneering at the play I had made. Here’s how the two options look:

The hit play

The non-hit play

Backgammon Problems' Solutions

As you know, the crowd was wrong in both cases.

In the first position, 13/8 is right by a big margin: in fact 22/23, 8/4 is a “whopper-size” (greater than .1 equity difference) blunder.

In the second position, rollouts say that hitting is clearly right, though I must admit I don’t quite know why.

Aside from the major theme of this article -- that it is very difficult not to succumb to the herd mentality when people you respect all agree on something – I am afraid that these two cases tend to undermine one of the most fundamental assumptions we all make about the game: that we can solve backgammon problems by “logical analysis.”

In each case, the natural, instinctive move was the right one. Unfortunately a second look revealed a compelling – but mistaken -- logical argument for an alternative play. Apparently what we are encountering here is “vision laughs at logic,” a variation of the phenomenon that mathematician Danny Kleinman drew attention to by calling one of his books Vision Laughs at Counting.

Paris Backgammon Open Winners

The “European doubles” event, with 28 teams and 4 rebuys, was won by the American team of Ray Fogerlund and Sasan Taherzadeh, with yours truly and partner Alan Grunwald finishing just out of the money.
The Open (78 entrants) was won by Giorgio Castellano of Italy, with the ever-popular Michihito Kageyama (aka Michi) of Japan coming in a close second.
The advanced division, with 24 entries, was won by Thomas Löw of Germany.
The “pro/am doubles” (16 teams) was won by Artur Muradian of Armenia, using himself as partner.
The 8-player super jackpot (which some of us could not enter for scheduling reasons) was won by Thierry Manouck (France), with Steen Grønbech of Denmark finishing second.
The DMP knockout, (64 players) was captured by Piergiorgio D'Ancona of Italy
The Cyrus qualifier was won by Mads Peter Andersen of Denmark.
And this year Lynn Ehrlich somehow wrested the “elegance trophy,” a special prize, away from the former title holder, Falafel!