The Short Version
Casino games are games of chance with a built-in house edge. No strategy or system changes that in the player’s favor over time, and most players lose money over time. Only money that can be comfortably lost should ever be risked.
The edge itself comes from a simple gap. The probability of an event determines what a fair payout would be. The game then pays a little less than that. This article looks at that gap closely, because it is the same mechanism in nearly every game.
True Odds and Paid Odds
True odds describe the real chances. If an event has a probability of 1 in 6, then there are 5 ways for it not to happen for every 1 way it does, so the true odds are 5 to 1 against.
Paid odds are what the game actually pays on a winning bet. When the paid odds match the true odds, the bet is fair and has no edge. When the paid odds are lower, the difference is the edge.
A useful rule is that a fair payout equals the number of losing outcomes divided by the number of winning outcomes, paid per unit staked. Everything a casino charges on a bet can be found by comparing that fair figure with the posted one.
Example One: A Single Number on Roulette
On a single-zero wheel, one number wins and 36 do not. The true odds are 36 to 1 against, so a fair payout would be 36 units of profit per 1-unit bet. The table pays 35 to 1.
The expected result of a 1-unit bet is (35 − 36) / 37 = −1/37, or about 2.70% of the amount wagered. The missing unit of payout, spread across 37 equally likely outcomes, is what is kept on average.
Example Two: A Hypothetical Dice Bet
Two six-sided dice have 36 equally likely combinations, and 6 of them add up to seven. The probability of a seven is 6/36, or 1 in 6. The true odds are 5 to 1 against.
Suppose a hypothetical bet on “seven on the next roll” pays 4 to 1. A fair game would pay 5 to 1. Each 1-unit bet then has an expected result of:
- Win (probability 1/6): gain 4 units.
- Lose (probability 5/6): lose 1 unit.
That works out to (4 − 5) / 6 = −1/6, or about −16.7% of the amount wagered. A one-unit reduction in the payout, which sounds small, produces a large edge because the event is fairly rare and the bet resolves in a single roll. Single-roll wagers of this kind, known as proposition bets, tend to show the biggest gaps between true and paid odds for exactly this reason.
Why Payout Tables Matter More Than They Appear
A payout table is the game’s rule for converting probability into money. Small changes to the table can change the edge by a lot.
- Changing a payout by one unit changes the expected result by the probability of winning multiplied by that unit. For a rare event, that sounds small, but the edge is measured against a stake of just one unit, so the effect is meaningful.
- Adding a losing outcome without changing payouts raises the edge. The zero on a roulette wheel is the clearest case, and the extra pocket on a double-zero wheel makes it larger.
- Capping or reducing a top prize has an effect that is hard to feel because the top prize is rarely hit, but its effect on the average is still real. Reading a pay table on a machine game is largely a matter of checking such details.
None of these changes are visible in a single result. They show up only in the averages.
Odds Written Different Ways
The same payout can be written in several forms, which makes comparison harder than it needs to be. “5 to 1”, “6 for 1” and “6.00 in decimal terms” all describe a payout that returns 5 units of profit on a 1-unit stake, plus the stake itself. The “to” version excludes the returned stake and the “for” version includes it. Mixing them up can make a bet look better or worse than it is. Learning to convert odds between forms is a small skill that removes a lot of confusion.
Even Payouts That Are Not Even
Bets that pay 1 to 1 look fair, but only if the chance of winning is exactly 50%. On a single-zero wheel, a bet on red wins with probability 18/37, which is less than one half. The payout is 1 to 1, so the expected result is (18 − 19) / 37 = −1/37, about 2.70%.
The same figure as the single-number bet appears here, even though the two bets look very different. The even-money bets that are not even are a good reminder that payout size alone does not show whether a bet is good value; the probability has to be read with it.
Some Payouts Are Adjusted by Rules, Not Tables
Edges are not always written in a table. Rules about ties, such as push rules, can shift results without anything appearing in the payout line. A game might return the stake in one situation and take it in another, and the difference can be larger than a headline payout change.
What This Does Not Tell You
Knowing how the gap works gives you a way to describe a bet’s cost accurately. It does not give you a way to win. Comparing two bets lets you see which one has a lower expected cost per unit wagered, but a lower cost is still a cost. The average result is a loss, and individual outcomes will vary around it.
The reliable use of this knowledge is understanding. If a payout looks generous, the question to ask is how likely the event actually is, and whether the two numbers match. In a casino game, they never quite do.