Roulette in Depth

The French Rules La Partage and En Prison

How the la partage and en prison rules return part of an even-money stake when zero lands, and how that lowers the roulette house edge to about 1.35%.

On this page
  1. Context and caution
  2. The problem the rules address
  3. La partage
  4. Working out the edge
  5. En prison
  6. The edge under en prison
  7. What the rules do not cover
  8. A practical summary

Context and caution

Roulette is a game of chance with a built-in house edge. The rules below reduce that edge on certain bets, but they do not remove it. No rule, system or timing makes roulette profitable for the player over time, most players lose money in the long run, and nobody should gamble money they cannot afford to lose.

The problem the rules address

On a single-zero wheel, even-money bets such as red or black cover 18 of 37 pockets. When the ball lands in the zero, every even-money bet loses. That single pocket is the whole source of the house edge on those bets: 1/37, about 2.70%.

Some tables, historically associated with French-style roulette, change what happens on that one outcome. Whether a venue offers these rules, and how exactly it words them, is a local choice, so the details below describe the general idea rather than a universal standard.

La partage

In French, partage means “sharing” or “splitting.” When the ball lands on zero, an even-money bet is not lost entirely. Half the stake is returned to the player and the casino keeps the other half. Winning and losing on the other 36 numbers works as normal.

With a hypothetical $10 bet on red:

  • Red wins: the player gains $10.
  • Black wins: the player loses $10.
  • Zero: the player gets $5 back and loses $5.

Working out the edge

Per $1 staked, on a single-zero wheel:

  • Win: probability 18/37, gain $1.
  • Lose on a black outcome: probability 18/37, lose $1.
  • Zero: probability 1/37, lose $0.50.

The expected result is 18/37 − 18/37 − 0.5/37 = −0.5/37, which is about −$0.0135. That is a house edge of roughly 1.35%, half of the 2.70% on a standard bet. The rule halves the cost because it halves the one losing outcome that favors the house.

En prison

En prison means “in prison.” The stake is not paid or taken when zero lands. It is held, or “imprisoned,” for the next spin.

  • If the next spin wins for that bet (for example, red comes up for a bet on red), the stake is released to the player. There is no profit on it: the player simply gets the original stake back.
  • If the next spin loses, the stake is lost.
  • If zero lands again, the rule depends on the venue. In some versions the stake stays imprisoned for another spin, and in others it is lost.

Using a hypothetical $10 stake: zero lands, the $10 is held; the next spin is red, so the player gets $10 back. If it is black, the $10 is lost.

The edge under en prison

Suppose, as a simplification, that a second zero simply loses. Then a zero on the first spin leads to a 18/37 chance of getting the stake back (net 0) and a 19/37 chance of losing it (net −1). The expected loss from zero is 19/37 per $1, and the overall expected result per $1 staked is (1/37) × (−19/37) = −19/1369, about −1.39%.

If the stake instead remains imprisoned on repeated zeros, the value of an imprisoned $1 can be worked out directly. Call it v. On the next spin it returns $1 (net 0) with probability 18/37, loses $1 with probability 18/37, and stays imprisoned with probability 1/37. So v = −18/37 + v/37, which gives v × 36/37 = −18/37, and v = −0.5. An imprisoned stake is worth, on average, minus half a dollar, exactly like la partage. The edge in that version is therefore about 1.35%.

So the two rules give very similar results: about 1.35% to 1.39%, depending on the wording. En prison has a noticeable feel difference. Under la partage, the outcome is settled at once. Under en prison, the player waits one more spin, which means the stake is still at risk and the final result can look better or worse than it would have been.

What the rules do not cover

The rules apply only to even-money bets: red, black, odd, even, low and high. Straight bets, splits, dozens and other bets lose entirely on zero as usual, so their edge stays at 2.70% on a single-zero wheel. The rules also do nothing on double-zero wheels unless a venue specifically adopts a similar rule, and the extra zero there is a separate matter.

The rules reduce the percentage cost per dollar staked. They do not guarantee anything about a given session. If a player wagers more because the rate seems lower, the expected total loss can go up, not down. A lower house edge is still a house edge, and the long-run result is still a loss on average. This echoes a general point about how games are compared: what matters is the edge together with how much and how fast money is wagered, which is why cost per hour and speed of play matter as much as the percentage.

A practical summary

  • Without a French rule, an even-money bet has a 2.70% edge on a single-zero wheel.
  • With la partage, the edge is about 1.35%.
  • With en prison, the edge is about 1.35% to 1.39%, depending on whether repeat zeros release or keep the stake.
  • Straight and other non-even-money bets are unaffected.
  • A lower figure makes roulette cheaper to play, not safe. Anyone who finds it hard to stop gambling can contact a local support service.

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