What this comparison can and cannot show
Roulette is a game of chance with a built-in house edge. No strategy, system, pattern or timing changes the odds in the player’s favor over time, and most players lose money over time. Nobody should gamble money they cannot afford to lose. Comparing payouts with true odds explains why the game costs money on average; it does not identify a bet that avoids the cost.
Two ways of describing the same bet
The true odds of a bet describe how the chances actually fall. On a single-zero wheel with 37 pockets, a bet that covers n pockets wins in n of 37 outcomes and loses in the other 37 − n. The true odds against it are written as (37 − n) to n.
The paid odds, or payout ratio, are what the table actually pays on a win, such as 35 to 1. If paid odds equaled the true odds, the game would be fair, and on average neither side would gain. Casino roulette pays less, by design.
Odds conversion between ratios, fractions and percentages is routine arithmetic, so only the direct comparison matters here.
Pocket by pocket, single-zero wheel
| Bet | Winning pockets | Chance | True odds against | Paid |
|---|---|---|---|---|
| Straight up | 1 | 1/37, about 2.70% | 36 to 1 | 35 to 1 |
| Split | 2 | 2/37, about 5.41% | 35 to 2, about 17.5 to 1 | 17 to 1 |
| Street | 3 | 3/37, about 8.11% | 34 to 3, about 11.3 to 1 | 11 to 1 |
| Corner | 4 | 4/37, about 10.81% | 33 to 4, about 8.25 to 1 | 8 to 1 |
| Six line | 6 | 6/37, about 16.22% | 31 to 6, about 5.2 to 1 | 5 to 1 |
| Dozen or column | 12 | 12/37, about 32.43% | 25 to 12, about 2.08 to 1 | 2 to 1 |
| Red/black, odd/even, low/high | 18 | 18/37, about 48.65% | 19 to 18, about 1.06 to 1 | 1 to 1 |
In every row the paid odds sit slightly below the true odds. The shortfall looks tiny when written as a ratio, which is part of why it is easy to overlook.
Where the gap comes from
The payouts are set as though the wheel had 36 pockets. For a bet covering n of the numbers, a fair 36-pocket wheel would pay (36 − n) to n. For the straight bet that is 35 to 1, for the corner (36 − 4) to 4, or 8 to 1, and for red or black 18 to 18, or 1 to 1. In each case the posted payout is exactly the 36-pocket fair payout.
The real wheel has an extra pocket, the zero. It is not covered by the number bets, and it is not red, black, odd, even, low or high. It adds one more losing outcome to every standard bet, without adding any payout. So each bet wins as often as a 37-pocket wheel allows but pays as if there were 36 pockets.
A hypothetical check. Suppose a straight bet of 1 unit were placed on all 37 pockets in turn, one spin each, in an idealized sequence in which each pocket comes up exactly once. The 36 losing bets cost 36 units. The single winner returns 35 units of profit, so the net result is 35 − 36 = −1 unit over 37 units staked, or −1/37 per unit. A fair payout would need 36 to 1 for that to be zero. A real session will not be this tidy; the example just shows what the averages work out to.
The same calculation for a corner bet of 1 unit: it wins 8 on 4 pockets and loses 1 on 33, so 32 − 33 = −1 over 37, again −1/37. The “missing” amount is the same for every row of the table, which is why the edge is the same across standard bets.
Why the gap is hard to see at the table
Several features make the shortfall easy to miss.
- The ratio looks fair. A payout of 35 to 1 sounds close to the 36 to 1 true odds. The 1 unit difference seems small next to a payout of 35 units.
- Wins are vivid. A large payout is memorable, while the 36 smaller losses that precede it fade, a form of selective memory.
- Framing effects. Quoting a payout as “35 to 1” emphasizes the prize and says nothing about the 36 to 1 chance against it. The way odds are presented affects how attractive a bet seems, and framing effects of this kind are well known.
- Short sessions hide it. The house edge is a long-run average. Over a few dozen spins, a player can be well ahead or well behind; the law of large numbers only makes the average dependable over very many spins.
What a payout ratio tells you and does not
A payout ratio tells you how much a win returns. Combined with the number of winning pockets, it gives the chance and the average result per unit staked. It does not tell you what will happen next. A bet that pays more is not a better bet; it is a rarer win, and its average cost per unit is the same as the rest.
The same logic applies to wheels with two zeros. A double-zero wheel has 38 pockets but typically uses the same payouts, so the gap between paid and true odds is double: a straight bet at 35 to 1 against true odds of 37 to 1 loses 2 units over 38 pockets, or 2/38 per unit, about 5.26 percent. The effect on expected value is direct: the extra pocket doubles the cost per unit staked.
Using this sensibly
Knowing the gap does not change the game, but it helps keep expectations realistic. Playing roulette costs money on average, and the cost scales with the amount staked. If you choose to play, decide the amount beforehand as an entertainment cost, and stop when it is spent. If gambling is causing you concern, a local support service can help.