The Jacoby Rule

The Jacoby Rule is the money-play counterpart to the Crawford Rule. Where Crawford regulates the cube in late-match scenarios, Jacoby regulates the value of gammons and backgammons in money play: under the rule, a gammon counts as a gammon — that is, doubles the cube value — only if the doubling cube has been turned at least once during the game. If the cube has not been turned, a gammon counts as a single game; a backgammon also counts as a single game.

The rule is named after Oswald Jacoby, the bridge and backgammon champion who, together with John R. Crawford, codified the modern doubling-cube ruleset in The Backgammon Book (1970). It is standard in nearly all money-game contexts. It is not used in match play.

1. The Formal Definition

In a money game played under the Jacoby Rule:

A gammon (the loser has not borne off any checkers) is worth 2× the cube value if and only if the cube has been turned at least once during the game.
A backgammon (the loser has not borne off and has at least one checker on the bar or in the winner's home board) is worth 3× the cube value under the same condition.
If the cube has not been turned during the game (i.e., the cube remains at its starting value of 1, in the middle of the board), the game counts as a single regardless of position — even an obvious gammon position pays out 1 point at end.

Note the consequence: the cube value at the end of the game is multiplied by the gammon multiplier, but the gammon multiplier only applies once the cube has been touched at all.

2. Why the Rule Exists

The rule was introduced to repair a specific game-theoretic incentive that distorts money play in the absence of the rule.

Without the Jacoby Rule, a player with a strong gammon position has incentive to delay doubling. Consider the following sequence:

Player A reaches a position with, say, a 50% chance of winning a gammon and a 30% chance of winning a single. (Total winning probability: 80%; loss probability: 20%.)
If Player A doubles, the cube goes to 2. The expected payoff is $0.50 \times 2 \times 2 + 0.30 \times 1 \times 2 - 0.20 \times 1 \times 2 = 2.0 + 0.6 - 0.4 = 2.2$ points.
If Player A does not double, the expected payoff is $0.50 \times 2 + 0.30 \times 1 - 0.20 \times 1 = 1.0 + 0.3 - 0.2 = 1.1$ points.
The double doubles the expected payoff, as expected — but only because gammons still count.

Now suppose Player A is, before doubling, fully confident the gammon will materialise (say a 90% gammon probability). The double is "wasted" — it doubles a gammon that would have happened anyway. Worse, in some positions doubling could lose: the opponent's correct response is often to drop the cube, conceding 2 points at value 1, when in fact left undoubled the game would have played out as a gammon worth 2 points at value 1. The opponent's drop costs Player A the gammon win.

The Jacoby Rule eliminates this distortion. Under Jacoby, the gammon counts only if the cube is turned. So the player with the strong gammon must double to capture the gammon multiplier at all. This forces efficient cube action at exactly the moment the player has a clear positional advantage.

In the example above, under Jacoby:

If Player A does not double and wins the gammon, the gammon does not count. Payoff: $0.50 \times 1 + 0.30 \times 1 - 0.20 \times 1 = 0.6$ points.
If Player A doubles and the opponent takes, the gammon does count. Payoff: $2.2$ points as computed above (assuming a take).
If Player A doubles and the opponent drops, payoff is exactly 2 points (the drop).

The double is now clearly correct, and Player A is no longer incentivised to slow-play the gammon position.

3. The Cube Owner and the Jacoby Rule

A subtlety: once the cube has been turned, the gammon multiplier applies for the entire remainder of the game, regardless of subsequent cube action. So the rule's "switch" is one-directional. Once flipped on, it stays on.

This has an important corollary in cube ownership scenarios. If Player A doubles and Player B takes, the cube is now owned by Player B at value 2. The Jacoby switch is on. If Player B subsequently wins a gammon, it counts at $2 \times 2 = 4$ points. The Jacoby Rule does not exempt later-game gammons; it only exempts the very specific case where the cube never gets turned.

4. Beaver, Raccoon, and the Jacoby Combination

Money play traditionally permits cube escalations beyond the standard double:

Beaver — When Player A doubles to 2, Player B may, instead of accepting at 2, beaver to 4 — immediately re-doubling without taking. Player A then has a fresh take/drop decision at the new value.
Raccoon — Player A may, if beavered, raccoon to 8 by the same mechanism.

These escalations are conventional in money play but are not part of tournament match play. Combined with the Jacoby Rule, beavers and raccoons make money play a strikingly volatile format: a confident initial double can be aggressively re-escalated by an opponent who believes the double was incorrect.

The Jacoby Rule applies regardless of beaver / raccoon — the rule simply requires that the cube has been turned at all. A beaver counts as a cube turn for Jacoby purposes.

5. Automatic Doubles

Some money-game customs also include automatic doubles on the opening roll: if both players roll the same number on the opening die-each-to-determine-who-goes-first, the cube is automatically advanced one level. This can occur multiple times in succession (e.g., two doubles in a row produces an opening cube at 4) and is usually capped at a pre-agreed limit (often 4 or 8).

Under Jacoby + automatic doubles, the cube is already turned at the start of the game in many sessions, which effectively neutralises the Jacoby Rule for that game. Players in serious money sessions often opt out of automatic doubles for this reason: the Jacoby Rule provides better long-run game balance when the cube starts at 1.

6. Why Jacoby Is Not Used in Match Play

In match play, gammons always count. There is no Jacoby Rule in tournament backgammon. The reason is structural: match play already has a different equity surface (the Match Equity Table) that determines the value of cube turns, and the Match Equity Table inherently accounts for gammon prices at each score. The Jacoby distortion that exists in money play does not appear in match play because the score-dependent gammon price already creates the right cube incentives.

The clearest example: at certain match scores the gammon price is so high that the trailing player should delay the cube until they have maximised gammon probability — but the MET-derived gammon value, combined with the Crawford Rule, produces a different equity calculation than money play. The two formats are governed by two different rule sets for two different equity geometries.

7. Practical Summary

Context	Gammons / backgammons count?	Beavers / raccoons allowed?	Automatic doubles allowed?
Money play, Jacoby Rule on	Only if cube has been turned	Yes (by convention)	Optional, often capped
Money play, Jacoby Rule off	Always count	Yes (by convention)	Optional
Match play (any score, including post-Crawford)	Always count	No	No
Crawford game itself	Always count; cube is removed	No	No

The combination of Jacoby and Crawford produces a clean rule structure: in money play, the cube turn gates gammon value; in match play, the cube is suspended for one critical game. Together they make competitive backgammon — both money and match — playable as a formal game of decision theory, free of the worst incentive distortions that the unmodified cube would otherwise produce.