Roulette often looks like a game where every betting system eventually runs into the same mathematical problem: zero. On a single-zero wheel, red and black each cover 18 numbers, yet the green zero creates the casino’s advantage because even-money bets lose when it appears.
En Prison and La Partage Rules change what happens at that exact moment. Instead of losing the entire even-money stake when zero lands, the player either receives half the wager back or carries the original stake into another spin. The difference sounds small, but mathematically it cuts the standard single-zero roulette house edge on eligible bets from roughly 2.70% to about 1.35%.
PokerStars describes both rules as applying specifically to even-money bets and producing the same basic house-edge reduction.
Start With Standard Single-Zero Roulette
Before analysing the special rules, it helps to understand the baseline.
A European-style roulette wheel contains 37 pockets: numbers 1 through 36 plus a single zero. Eighteen numbered pockets are red and 18 are black. The same 18-versus-18 structure applies to odd/even and low/high bets.
Suppose you place $1 on red.
There are:
18 winning outcomes
18 losing black outcomes
1 losing zero
An even-money win produces $1 of net profit, while a loss costs $1.
Expected value becomes:
EV = (18/37 × $1) − (19/37 × $1)
EV = -$1/37
That equals approximately:
-2.7027%
The UK Gambling Commission describes house edge as the percentage the casino expects to retain on average from each hand or spin under normal patterns of play.
So the standard single-zero even-money bet carries roughly a 2.70% mathematical disadvantage.
How La Partage Changes the Zero Outcome
La Partage roughly means “the sharing.”
When zero appears on an eligible even-money wager, half of the original stake is returned rather than the entire amount being lost. PokerStars and Casino.org both describe the rule in this way.
Now reconsider the $1 red wager.
The possible results become:
18 red outcomes: +$1
18 black outcomes: -$1
1 zero outcome: -$0.50
Expected value is:
EV = (18/37 × $1) − (18/37 × $1) − (1/37 × $0.50)
The first two components cancel.
That leaves:
EV = -$0.50/37
or:
EV = -1/74 ≈ -1.35135%
The house edge has been cut almost exactly in half.
That is the central matematical advantage of La Partage.
How En Prison Reaches a Similar Result
En Prison handles zero differently.
Instead of immediately returning half the stake, the wager becomes “imprisoned.” It remains attached to the same even-money selection for another spin. If that selection wins on the next qualifying outcome, the original stake is generally released rather than producing a normal even-money profit. If it loses, the stake is lost.
Assume repeated zeros keep the wager in prison.
Let P represent the expected value of a $1 imprisoned bet.
On the next spin:
- 18 winning numbers return the original stake, creating $0 net result.
- 18 losing numbers cost $1.
- A zero keeps the situation unresolved.
The equation becomes:
P = (18/37 × $0) + (18/37 × -$1) + (1/37 × P)
Solving it gives:
P = -$0.50
So when the original spin lands zero, the imprisoned state has an expected cost of half the stake.
That creates the same overall house edge as La Partage:
approximately 1.35%
Why the Rule Only Helps Even-Money Bets
This benefit does not apply to every part of the roulette layout.
The eligible wagers are normally the three classic even-money categories:
Red / Black
Odd / Even
1–18 / 19–36
PokerStars specifically notes that En Prison and La Partage do not provide the same protection for inside bets, dozens, or columns.
A $1 straight-up wager on number 17 still loses its full stake if zero appears.
So a player cannot apply the 1.35% figure to roulette as a whole.
It is the house edge for eligible even-money wagers played under the applicable special rule.
That differance is important when comparing tables.
What the Reduction Means Over Turnover
A reduction from 2.70% to 1.35% can sound tiny until turnover becomes large.
Imagine $1,000 of total even-money wagering.
Under ordinary single-zero rules:
$1,000 × 2.7027% ≈ $27.03 expected loss
With La Partage or standard En Prison:
$1,000 × 1.35135% ≈ $13.51 expected loss
At $10,000 of turnover:
Standard rule ≈ $270.27 expected loss
Special rule ≈ $135.14 expected loss
These are long-run expectations, not predictions for one session. The Gambling Commission notes that actual return can differ from theoretical return over smaller samples because volatility and sample size matter.
Still, mathematically, cutting the edge in half remains significant.
En Prison and La Partage Feel Different in Practice
The two rules may have similar expected value, but the player experience is different.
La Partage resolves the zero immediately. Half the stake is returned and the round is finished.
En Prison delays resolution. The stake remains tied up while another spin determines whether it is recovered.
That creates a different cash-flow pattern even though the standard long-run expectation is similar.
There is also a practical complication: the treatment of a second consecutive zero can differ between casinos. Some rule sets leave the stake imprisoned again, while others may use another procedure.
That can slightly alter the exact calcuation, so checking the table rules matters.
A Lower Edge Does Not Create a Winning System
The special rules improve the maths, but they do not create positive expected value.
At 1.35%, the casino still retains a theoretical advantage over repeated eligible wagers.
Changing bet size does not alter that percentage.
Neither does doubling after losses, following colour streaks, or switching between red and black based on previous spins.
The useful strategic decision is simpler: when comparing otherwise similar single-zero tables, a table offering La Partage or favourable En Prison rules gives even-money wagers a lower mathematical cost.
That is a genuine rule-based improvement rather than a betting-system illusion.
En Prison and La Partage Rules reduce the house edge on eligible single-zero roulette bets from about 2.70% to roughly 1.35% by softening the financial impact of zero. The improvement is real, but the house still keeps a mathematical advantage. Before playing, check which rule applies, how repeated zeros are treated, and whether your chosen wager actually qualifies.