Payout Odds vs True Odds, One Example

Two different ratios get called odds, and they answer different questions. True odds describe how often the outcomes happen. Payout odds describe what the game pays when you win. The gap between them is the price. A single roulette number makes the gap visible without a speech about systems.

True odds on a single-zero wheel

A standard single-zero wheel has pockets 0 through 36. That is 37 pockets. A straight-up bet on one number wins on 1 pocket and loses on 36. The true odds against winning are 36 to 1. A fair game, the kind that would return your money over a huge number of spins, would pay 36 to 1: 36 units of profit for each 1 unit staked.

Against matters. Odds of 36 to 1 against mean 36 losses for every 1 win. The probability of a win is 1/37. The probability of a loss is 36/37. Both sentences match the same wheel.

The payout a standard table actually posts

A standard straight-up payoff is 35 to 1. You receive 35 units of profit, plus your stake back, when the number hits. Compare that with the fair 36 to 1. The table pays one unit of profit less than the true odds. That one unit, spread across all 37 pockets, is the house price on this bet.

You can see it as a full cycle. Stake 1 unit on every number, including 0. You have risked 37. Exactly one number wins and returns 35 profit plus the 1 unit stake, which is 36 back. The other 36 stakes are lost. Net result: minus 1 unit per cycle. The edge is 1/37 of the money staked, about 2.7 percent. What house edge means puts that idea in a wider frame. The cycle is the same idea with the arithmetic showing.

Where people swap the two ratios

Hearing 35 to 1 and repeating it as a 1 in 35 chance imports the payout into the probability. The chance on this wheel is 1 in 37. The 35 is a price. Using the price as the chance makes the bet look slightly less rare than it is, which flatters the game.

The same swap happens in reverse when someone calls a bet fair because the payout is large. Large compared with even money is not large compared with the true odds. 35 is large next to 1. It is still 1 short of 36. Inside and outside bets show the same pattern at different scales, which is why inside bets and outside bets belong next to this example.

A double-zero wheel widens the same gap

Add a 00 pocket and the wheel has 38 pockets. The true odds against a single number become 37 to 1. A table that still pays 35 to 1 is now two units of profit short of fair, not one. The edge on that bet is 2/38, which is 1/19, about 5.3 percent. The layout did not become more generous because the room looks livelier. The denominator grew and the posted 35 stayed.

Some bets on some wheels carry a different gap, and a printed variation beats a memory. The method does not change. Count the winning pockets, count the losing pockets, write the true odds, then read the posted payoff and subtract.

A two-line habit

Before you accept a stated price, write two lines. Line one: winning outcomes to losing outcomes. Line two: profit paid to stake required. If line two is shorter than line one, the game keeps the difference. If you cannot fill line one, you do not know the bet well enough to judge the price. That is a reason to wait, not a reason to guess a denominator.

Payout schedules are commercial choices sitting on top of physical chances. Knowing the gap is adult information. It is not a prompt to play, and the legal age where you are may be 21.

Frequently asked questions

What is the difference between true odds and payout odds?

True odds compare the number of losing outcomes with the number of winning ones. Payout odds are the profit the table posts when you win.

Why is a single-zero straight-up bet not 35 to 1 against?

Because 36 pockets lose and 1 wins. The chance is 36 to 1 against. The usual payment is 35 to 1.

Does a bigger payout mean a better bet?

Only if you compare it with the true odds of that specific event. A large payout can still be short of a fair price.