How La Partage and En Prison Rules Benefit Roulette Players

Roulette enjoys enduring popularity among casino players, largely thanks to its straightforward rules and rich assortment of betting options. Many unconventional variations of this casino staple have emerged over the years but traditional single-zero versions like French and European Roulette remain the ultimate player favorites.

This partiality comes as no surprise since players face better odds and lower house edges at single-zero tables compared to double-zero games where the casino holds twice as big advantage.

But it gets better as some single-zero variations offer two unique rules, La Partage and En Prison, that cut the house advantage in half, further improving players’ winning chances with specific bets. Continue reading to learn more about these favorable rules and find out how they benefit roulette players.

Bets Covered by La Partage and En Prison

Before we proceed any further, we would like to point out that the two rules in question apply to certain outside bets only. La Partage and En Prison cover even-money wagers that pay at odds of 1 to 1 and lose to the green zero, which gives the house its edge in roulette.

While dozens and columns also belong to the category of outside bets, they are beyond the scope of the two favorable rules. Players can take advantage of the latter when betting on:

How the La Partage Rule Works

When available, La Partage takes effect when you bet on even-money selections and the ball settles in the zero pocket. Rather than losing your entire wager as you normally would, the dealer will collect only half of the bet and give you back the other half.

The La Partage rule essentially cuts down your losses on even-money wagers to 50% when the zero lands. Here is an illustrative example to show you how this works.

How the En Prison Rule Works

Similarly to La Partage, En Prison is another player-friendly rule that applies to two-sided outside wagers like red/black, odd/even, and high/low. Under this rule, the player gets a second chance for a win instead of losing half of the bet when the zero is spun. The dealer places a marker on the unsuccessful wager to indicate it is ‘in prison’.

The bet remains on the layout for a second spin and gets released from the ‘imprisonment’ in the event of a win. The player practically breaks even as the dealer returns only the original wager without paying out any of the winnings. The rules regarding what happens when a second zero gets spun are largely casino-specific.

Impact on Players’ Expected Value

Roulette wheels contain green zero pockets for a reason and it is not to give you extra betting opportunities. The addition of the zero enables the house to retain a fixed percentage of players’ total wagers in the long term. Said percentage represents the house edge, i.e. the mathematical advantage the casino holds over its patrons.

The house edge is always grinding against roulette players regardless of what betting system they use. No strategy or betting pattern can possibly help them overcome the negative expectation inherent to this game of chance.

Expected Value in Single-Zero Roulette

Impact of La Partage on Expected Value

Impact of En Prison on Expected Value

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Expected Value in Single-Zero Roulette

Determining the expected value (EV) of roulette players is a fairly simple task. Under the European rules, roulette wheels contain a single zero, 18 black pockets, and 18 red pockets for a total of 37 numbers.

If you place a $1 wager on black, your probability of winning another dollar is 18/37 since there are 18 black pockets out of 37. The probability of losing your original dollar is slightly higher at 19/37. That being the case, the expected value of your bet on black can be calculated as follows:

• EV = ($1) x (18/37) + (-$1) x (19/37)
• EV = 18/37 + (-19/37)
• EV = – 1/37
• EV = -0.027027

It becomes clear the expected value of even-money wagers is -0.027027 for a house edge of 2.70%, which is to say you will lose approximately 0.027 cents out of every dollar you wager in the long term. In fact, the percentage coincides across all bet types in single-zero roulette, including inside wagers.

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Impact of La Partage on Expected Value

Both rules are advantageous to roulette players since they lead to a reduction of the house edge, causing them to lose less money in the long term. La Partage, in particular, cuts the casino’s advantage in half since the player loses only half their wager on even-money propositions when the zero shows up. The expected value calculations will be slightly different, however.

EV = (1) x (18/37) – (1) x (18/37) – 1/2 x (1/37)

EV = -0.013513

As you can see, your expected value is still negative but you will lose roughly 0.013 cents out of every dollar you bet on even-money propositions. It may not seem like much but as the saying goes, a penny saved is a penny earned.

Gambling losses can accumulate over time when you play consistently, so why not lose less if you have the chance? Respectively, the house edge drops from the standard 2.70% to 1.35% when this rule is in place.

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Impact of En Prison on Expected Value

En Prison has a similar impact on players’ negative expected value, reducing it to -0.013513 under the standard rules of French Roulette. There is a minuscule increase in negative expectation for single, double, and triple-imprisoned wagers as you can see in the table below.

It is fair to say the difference in the house edges is extremely negligible across variations of the rule. Depending on the circumstances, some variants of the imprisonment rule are slightly less advantageous to roulette players compared to La Partage.

The bottom line is you are better off playing games with either rule in place than variants where your even-money wagers lose outright when the dealer spins the zero.

En Prison Rule Variation	Expected Value of Even-Money Bets
Standard French Rules	-0.013513 (1.35% house edge)
Single En Prison	-0.013878 (1.38% house edge)
Double En Prison	-0.013703 (1.37% house edge)
Triple En Prison	-0.013701 (1.37% house edge)

En Prison and La Partage are two mutually exclusive rules, which is to say they cannot both be in place simultaneously. We recommend you check beforehand which one applies in your chosen roulette variation. Our observations are that La Partage is more common in online variants of the game.

Online Roulette Games with La Partage and En Prison

La Partage and En Prison are not restricted solely to landbased casinos. Players looking for thinner house edges can also find these advantageous rules in some online versions of the game. However, we should note the availability of La Partage and En Prison is not immediately obvious.

Our suggestion is to navigate to the game’s rules or the info section where this information is typically to be found. Or you can spare yourself the hassles and go for the roulette variants we have handpicked for you. Some of them rely on random number generation for the outcomes, while others are hosted by human dealers in real time for a more authentic gaming experience.