Roulette odds: what each bet pays and why the zero decides it

Roulette odds: what each bet pays and why the zero decides it

Roulette is one of the few casino games whose entire mathematics fits on a napkin. One wheel, a fixed payout table and a single extra pocket explain why every bet on the layout costs the same in the long run.

The wheel and the extra pocket

A European wheel has 37 pockets: the numbers 1 to 36 plus a single zero. Eighteen numbers are red, eighteen are black, and the zero is green and belongs to neither. Roulette in Tonza Originals runs on the European layout with one zero rather than the American double-zero wheel.

Payouts are built as if the zero were not there. A single number pays 35 to 1, which would be an exactly fair price across 36 equally likely outcomes. There are 37 of them, and the gap between 36 and 37 is the entire business model.

What every bet pays

Bets divide into inside bets, placed on numbers, and outside bets, covering large groups. The table lists the standard set in full.

BetNumbersPayoutWin chanceHouse edge
Straight up135:12.70%2.70%
Split217:15.41%2.70%
Street311:18.11%2.70%
Corner48:110.81%2.70%
Six line65:116.22%2.70%
Dozen or column122:132.43%2.70%
Red, even, 1-18181:148.65%2.70%

The last column never moves. A straight-up number and a bet on red are the same product at the same price; they differ only in how the result is spread over time.

Why the zero decides everything

The straight-up bet is the clearest case. You win once in 37 spins and collect 36 units, 35 in winnings plus your own stake, and lose one unit on the other 36 spins. Across 37 spins you risk 37 units and get 36 back. The shortfall is 1/37, or 2.70%.

Even-money bets arrive at the same number by another route. Eighteen winning pockets out of 37 is 48.65%, not 50%. The missing percentage points on each side of the bet are the green pocket, split between red and black.

That is where the stated 97.3% RTP comes from: 97.3 units returned per 100 wagered, averaged over an unbounded number of spins. Across a single session variance dwarfs that edge, so a short run tells you nothing about it.

One edge, very different rides

Equal mathematics does not mean an equal experience. A dozen bet lands roughly every third spin and moves the balance in small steps. A straight-up number produces long dry stretches broken by a return of 36 stakes.

For a given bankroll those are two different games. On a straight-up number, a run of 50 consecutive losing spins turns up in roughly a quarter of attempts, which is ordinary rather than unlucky. Stakes in Originals run from 0.1 to 10,000 in your account currency, so the unit size is worth choosing against the swing you are willing to sit through.

Combined bets, and what is actually verifiable

A common move is to blanket the layout with several bets and win on almost every spin. Two dozens at one unit each cover 24 numbers out of 37: a win arrives on 64.9% of spins and returns one unit, while the other 35.1% take both. Over 37 spins that pushes 74 units across the table for an average result of minus two. The same 2.7%.

Progressions such as the Martingale behave identically: they change the shape of the outcome, many small gains against a rare heavy loss, and leave the average alone. Negative-expectation bets do not add up to a positive one in any order or any combination.

What can be checked is the spin itself. The result is built from a server seed whose hash is published before the round, your own client seed and a nonce. Afterwards the seed is revealed and the number can be recomputed by hand. The step-by-step method is on the provably fair page.

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