En prison is not la partage: the roulette number everyone copies wrong

The two rules, precisely

Both rules soften the zero on an even-money bet, and they do it differently.

• La partage: zero hits, you lose half the stake immediately. The bet is over.
• En prison: zero hits, the whole stake is locked for one more spin. If the bet wins that spin, the stake comes back — with no winnings. If it loses, the whole stake goes.

They feel like the same concession. They are not, because imprisonment gives you a second exposure to the zero.

The derivation, in full

Take red on a 37-pocket wheel. 18 pockets win, 18 lose, one is zero.

La partage

Expected value per unit staked:

EV = (18/37)(+1) + (18/37)(−1) + (1/37)(−½)
   = −1/74
   = −1.351351%

Exactly half the plain European edge of 1/37 = 2.7027%, which is the tidy result everyone remembers — and the reason the second rule gets assumed into the same box.

En prison

When zero hits, the stake is not reduced; it is put at risk again. On the imprisonment spin the bet wins with probability 18/37 (stake returned, nothing gained) and otherwise the stake is lost. So the imprisoned unit is worth 18/37 of itself, and the loss on that branch is (1 − 18/37) = 19/37.

EV = (18/37)(+1) + (18/37)(−1) + (1/37)(−19/37)
   = −19/1369
   = −1.387874%

19/1369 is not 1/74. The gap is 0.0365 percentage points, or 2.70% more cost for the same-looking rule.

Check it yourself in thirty seconds

1 ÷ 74 = 0.0135135… and 19 ÷ 1369 = 0.0138787… That is the entire claim. No model, no assumptions about play, no simulation: two fractions from the definition of the rules.

Why nearly everyone gets it wrong

Two reasons, and neither is carelessness exactly. First, double imprisonment — where a second zero re-imprisons rather than losing the stake — converges back towards the la partage figure, so a source describing that variant can honestly print 1.35%. Second, 1.35% is memorable and correct for the better-known rule, so it travels. Once a number is in enough places, it stops being checked.

Casinos apply these rules differently, and the house never announces which variant it deals. If you play even-money bets on a French wheel, the question worth asking at the table is not "do you have en prison?" but "what happens to an imprisoned bet if zero comes up again?"

What this is worth in money

At $50 a spin, 60 spins an hour, the difference between the two rules is about $1.10 an hour — small, which is exactly why nobody audits it, and exactly why it survives uncorrected. The point is not the dollar figure. The point is that a number published everywhere can be wrong, and that a reference which computes rather than copies will notice.

How this site produced these figures

Both values come from the roulette engine that builds our roulette pages, in exact rational arithmetic. The build refuses to publish if two invariants fail: every European bet must share one edge, and la partage must be exactly half the European baseline. A third check asserts that en prison costs strictly more than la partage — a structural fact that holds no matter what any reference says. The full chain is on the methodology page, and every computed figure on the site is published as open data at edges.json and edges.csv (CC-BY).

Cite this

If you use these figures, please link the page that derives them: https://www.allinblind.com/research/en-prison-house-edge/. If you think the derivation is wrong, we would genuinely like to know — tell us and, if you are right, the correction ships the same day with your name on it.

Both figures are computed in exact rational arithmetic by this site's roulette engine, which refuses to build unless la partage is exactly half the European baseline and en prison is strictly more expensive than la partage. Checked August 2026.