Doubling cube theory

The 25% take point

Without gammons and with a dead cube, the money-playtake point is 25%. The arithmetic:

Take EV = 2 × p − 2 × (1 − p) = 4p − 2
Pass EV = −1
Take EV = Pass EV  →  4p − 2 = −1  →  p = 0.25

Picture the position four times. Pass all four and you lose 4 points. Take all four and win one, and you lose 3 × 2 and win 2 — again −4. So: take whenever you can win more than 25% of the time, then adjust. Owning the cube lowers the line: in pure races the practical take point is about 21–22% (GNU Backgammon rollouts say take with 22.0% at 100 vs 112 pips, pass with 18.2% at 100 vs 115). It goes up when the opponent threatens gammons (their wins cost you 4, not 2) — a blitz where you win 29.8% but lose a gammon 38.1% of the time is a clear pass — and down when you have gammon chances of your own.

Cube actions by winning chances (money play)

In contact positions no percentage table is reliable: gammons move every line. What holds everywhere: double inside the doubling window (below), which closes at the opponent's take point — about 25%, about 22% in a race, more when they can lose a gammon. Pure races have almost no gammons, so there the lines are sharp: the doubler's pass line sits around 78–79% winning chances, the mirror of the taker's 21–22%. GNU Backgammon rollouts at about 100 pips, you on roll:

The doubling window

The window is the equity range where doubling is correct and the opponent should take. Double too early and you hand over a cube they'll happily use against you; double too late and they simply pass, capping a big win at 1 point.Volatility is the trigger: the swingier the next exchange of rolls, the earlier you should turn the cube — “double when this roll might make them pass next turn.”

Too good to double

When your position is so strong that a double forces an instant pass, doubling can be a mistake: you bank 1 point while the position was on its way to a gammon worth 2.Playing on is correct when your gammon chances outweigh the risk of the game turning around — and holding the cube means the opponent can never re-enter the auction.

Cube ownership is an asset

A double-and-take hands the cube to the taker — only they may redouble(rules of ownership). That option has real value:live-cube equity, blended from the cubeless and dead-cube extremes by Janowski-style formulas. Practical upshot: the taker can play slightly worse positions than raw percentages suggest, because the recube threat is working for them.

Match play: everything bends to the score

In matches, points are not equal — going from 6 to 7 in a 7-point match is worth far more than going from 0 to 1. Match equity tables (MET) convert scores into match-winning chances; Kazaross-XG2 is the modern standard and GNU Backgammon's default. Sample values from it:

Take points now come from the MET rather than the flat 25%: a trailer facing a cube that puts the match on the line needs far more than 25%, while a comfortable leader should take conservative cubes and avoid gammonish ones. TheCrawford rule and post-Crawford free drops are the score-based extremes of the same logic.

Race cubes in one line

Pure races have formula answers — a lead of about 8% of your count to double, 9% to redouble, and more than 12% means the opponent should pass. That is the 8-9-12 rule, for money play and races of about 100 pips; the match score moves the lines (at 0-0 in a 3-point match, a 12% lead is already a pass). The counting methods and the rule live inpip counting.

The vocabulary — beaver,cube life, EMG — is in the glossary. For where cube rules differ by format, seematch vs money play.