Propositions
Danny Kleinman, 1980
Vision Laughs at Counting, Vol 2, © 1980 Danny Kleinman

Backgammon lends itself to propositions. A proposition differs from an ordinary backgammon game in that it starts from a different position or a different set of rules.

Usually the proposition is intended to establish empirically some judgment about that particular game. But sometimes the person offer to play the proposition may already know, either from analysis or from prior experience. This in itself is a reason to be cautious in accepting a challenge to wager on a proposition.

Some classic propositions involve:

1. 15 men against 13, with one side having removed the two back men.

Black has only 13 checkers

2. The “perfectly timed” back game, with one side having 5 men each on the other’s one, two, and three point while the other side is ready to bear off with 5 each on the four, five, and six point.

Black is playing a back game; white is trying to bear off

3. Different rules for each side, with one side taking two rolls at a turn and the other side calling any shake but doublets instead of rolling the dice.

In any such porposition, the player with the greater experience at playing it is apt to have a significant advantage.

Sometimes a proposition is a truly close bet, even a totally fair bet. But the skills of the two opponents may differ. If you wouldn’t want to play Alan Martin heads up for money, for example, you shouldn’t accept his offer to play a fair proposition. For you wouldn’t prove which side was right, only that Alan Martin could beat you at backgammon.

In fact, there are lots of other things you could “prove” by playing a proposition besides what you purport to establish:

• That one side rolled especially well or poorly;
• That your sample consisted of too few games; or
• That both sides did not understand the proper stategy for this proposition.

One kind of simple proposition pits move against move. To settle which move is better the two players alternate sides of the position in which they advocate different moves. Each finishes the game taking his own move.

A more frequent kind of proposition involves a dispute over whether a given position constitutes a pass or a take. In this case there is no need to alternate sides, for the passer doesn’t advocate finishing the game at all: He simply pays the taker the one unit he is willing to concede by passing. The taker, on the other hand, receives the cube at 2 and lets the passer roll the dice and finish out the game.

A related proposition is designed to estaglish a fair settlement value for a position. One player may contend a game is worth 12 point, while the other claims it’s worth more. In such a case, the player who says it’s worth more pays the player who denies this 12 point to finish out the game, with the cube remaining wherever it was when the difference of opinion arose.

If you want to settle whether a particular position constitutes a double, you must revert to the procedure of alternating sides. The nondoubler plays the position without turning the cube, but the doubler plays the position with his opponent owning the cube at twice its value before the double.

An improvement, from the standpoint of eliminating some of the unfairness of the dice, is to contract for a series of 36 (or some multiple of 36) games, starting each game in the series with a different shake for the side on roll, but using each nondoublet twice. This is especially advisable in positions where a hit or a miss on the very next shake figures to be decisive.