Calculate a simple take point
Equity in an unlimited money game means the expected net points won per game. Imagine a centred cube at 1 with no gammons and no further doubles. Passing loses one point. Taking gives +2 on a win and −2 on a loss. At a win chance of 25%, a take is worth (0.25 × 2) − (0.75 × 2) = −1, exactly equal to passing. More than 25% favours taking under these assumptions.
The example is intentionally short enough to count. Ivory can finish on 34 rolls. If Ivory rolls 1–2, Umber has a chance to finish before Ivory’s next turn. Count that narrow route to victory before deciding whether to accept Ivory’s double.
Ivory has one checker on 4. Umber’s chances begin with Ivory rolling 1–2 in either order, at most 2 out of 36. Even if Umber always finished after that, they would fall well below a 25% take point.
Borne off · Ivory 14/15 · Umber 13/15
Double before the market disappears
A market loser is a sequence after which an opponent who could take now would correctly pass. If many likely exchanges swing you from double/take to double/pass, waiting can cost a point on your best paths. Count the paths where your position improves enough, and also those where you lose the advantage or the chance to offer again.
Volatile contact positions can change much faster than ordinary races. When your opponent is on the bar against a strong board and you have another direct hit available, a good roll plus a dance can transform the game. Weigh that improvement against the rolls that leave a return shot or let the opponent escape. A racing lead or a hit threat on its own does not establish the right cube decision.
Umber has a checker on the bar and a blot on 1. Ivory’s 2 can hit from 3, and a 5 could also reach 1 from 6. If Ivory hits and Umber stays out, the chance of a gammon rises.
Price gammons, recubes and playing on
The 25% calculation assumes that every win and loss is a single and there is no recube. Gammon losses raise the cost of taking. Gammon wins improve the value of taking. The right to redouble can increase a taker’s equity, especially when a few strong rolls would reverse the position. A dead cube cannot add that recube value.
Sometimes the opponent should already pass, yet continuing at the present stake has higher equity thanks to gammon or backgammon potential. This is called being too good to double. Compare the guaranteed points from a pass with the distribution of outcomes if you play on, including the chance of losing or later having to offer the cube anyway. Match scores can change the value of each outcome.
Practice question
In the no-gammon, no-recube example, what is a take worth at a 30% chance of winning?
Show answer
−0.8 points, because 0.30 × 2 − 0.70 × 2 = −0.8. Passing loses 1, so taking has the higher equity.