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, what a second zero does is a house rule, and some houses run a different rule from the one priced above. Where an imprisoned stake stays in prison through any number of zeros and is freed by its first win, or where half of it is returned on a second zero, the cost is exactly la partage's 1/74, so a source describing one of those is right to say 1.35%. Where a second zero imprisons the stake again and each win only lifts it one level, it comes to about 1.37% (1.3701% with no limit on the levels, 1.3704% when a third zero loses it), about halfway between the two. Under single imprisonment, where a second zero loses the stake, it is 19/1369. 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.
Frequently Asked Questions
- What is the exact house edge of la partage?
- Exactly 1/74, or 1.3514% - precisely half the plain European edge of 1/37.
- What is the exact house edge of en prison?
- Exactly 19/1369, or 1.3879%, for single imprisonment: when zero hits, the stake is locked for one spin and wins it back with probability 18/37.
- Why do most sources say both are 1.35%?
- Because 1.35% is right for la partage, and for the house rules that free an imprisoned stake on its first win however many zeros come first, or return half of it on a second zero. Double imprisonment, where each win only lifts the stake one level, costs about 1.37%. None of this justifies quoting the single-imprisonment figure as 1.35%.
- Does this change how I should play?
- Marginally: prefer la partage over en prison when a casino offers both, and ask what happens to an imprisoned bet on a second zero. The larger lesson is about sources, not strategy.
Corrected on 18 October 2026: this page said double imprisonment converges to la partage's 1.35%. Solved exactly, re-imprisoning on every zero costs 1.3701%, about halfway between en prison's 1.3879% and la partage's 1.3514%.
Corrected on 19 October 2026: the note above gave 1.3701% for re-imprisoning on every zero without saying what a win does to a stake imprisoned twice. 1.3701% holds when each win lifts it one level, with no limit (1.3704% when a third zero loses it); when a win frees it outright, or half is returned on a second zero, the cost is exactly 1/74, as for la partage.
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.