The two roulette rules that halve the edge on even-money bets

An even-money bet on a European wheel gives the house 2.70 per cent. Two old French rules cut that figure to about half, they apply only to even-money bets, and they are not interchangeable. We work both of them out from the pockets, because the difference between them is small, real and never printed anywhere near the table.

What the bet starts with

Thirty-seven pockets, eighteen of them red, eighteen black, one green zero. Back red for one unit and you win one unit 18 times in 37 and lose one unit 19 times in 37. Expectation is 18/37 minus 19/37, which is minus 1/37, or 2.70 per cent of everything staked. The zero is the entire edge: it is the pocket that makes the bet lose nineteen times while paying as though it lost eighteen, and it is the pocket both rules are about. The same conversion from edge to return, for this bet and seven others, is in house edge and return as one figure written twice.

La partage: half the stake comes back

Under la partage — “the division” — zero does not take the whole even-money bet. Half the stake is returned and half is lost, and the hand is over. The eighteen wins and eighteen losses are unchanged; the thirty-seventh outcome now costs half a unit instead of one. Expectation becomes 18/37 minus 18/37 minus half of 1/37, which is minus 0.5/37, or 1.35 per cent. Exactly half the original edge, because exactly half of the only losing pocket was handed back.

En prison: the bet gets one more spin

Under en prison the stake is not returned. It is locked on the layout for one more spin, and what happens next depends on that spin: if the bet wins, the stake comes back with no winnings; if it loses, it is gone. Zero again on the second spin is a house matter and varies by table — the usual treatment keeps the bet imprisoned, which makes almost no difference to the figure.

Run it through. Eighteen times in 37 the first spin wins and pays. Eighteen times in 37 it loses. Once in 37 the bet is imprisoned, and from there it returns the stake 18 times in 37 and loses it 19 times in 37. The expected cost of imprisonment is 19/37 of a unit, and it occurs 1/37 of the time: 19 divided by 1,369, which is 1.39 per cent.

So the two rules are not the same rule

1.35 against 1.39. The gap is four hundredths of a percentage point — four pence per £100 staked — and it exists because la partage settles immediately at half the loss while en prison sends half a stake back through a wheel that still has a zero on it. A table offering the choice is rare; a table offering one or the other is common enough in French-rules rooms, and the one to prefer, marginally, is the one that pays you out on the spot.

Wheel and rule	Even-money house edge	Expected loss per £100 staked
European, no partage or prison	2.70%	£2.70
European, la partage	1.35%	£1.35
European, en prison for one spin	1.39%	£1.39
American (double zero), la partage	2.63%	£2.63
Any inside bet, either rule	unchanged	unchanged

What the rules do not touch

Only even-money bets. Red and black, odd and even, high and low — those are the three pairs, and nothing else qualifies. A straight-up number, a split, a street, a dozen and a column are all settled normally when zero lands, which means the 2.70 per cent on those bets stays exactly where it was. A player covering a dozen and a colour is running half the stake at 1.35 per cent and half at 2.70, and the blended figure is nearer the worse one than the table layout suggests.

The rules also do not fix a double-zero wheel. Applied to American roulette, la partage halves the loss on two pockets out of 38, which takes the even-money edge from 5.26 per cent to 1/38, or 2.63 per cent. Better than it was, and still worse than a plain European table with no French rules at all. For scale: 1.35 per cent on a French table is good by the standards of the floor and still not the cheapest thing in the building, since the odds bet behind a craps point pays true odds and carries no edge at all. That ordering is the one thing to carry away: wheel first, rule second. The number of pockets is worth more than any courtesy applied to the zero. Our page on playing roulette online safely covers how to tell which wheel a lobby has actually loaded, which is the question that decides everything above.