Casino games are games of chance with a built-in house edge. No strategy, system or timing changes the odds in the player’s favor over time, and most players lose money over the long run. Nobody should gamble money they cannot afford to lose. Reading payout notation correctly helps you see what a bet costs; it does not make any bet profitable.
What “X to Y” means
A payout written “X to Y” means that for every Y units you wager, a win pays X units of profit, in addition to the return of your stake. The first number is the profit, and the second is the amount wagered.
- 1 to 1 (even money): bet 10, win 10 profit, receive 20 in total.
- 3 to 2: bet 10, profit 15, receive 25 in total. This is the common blackjack natural payout.
- 6 to 5: bet 10, profit 12, receive 22 in total.
- 35 to 1: bet 1, profit 35, receive 36 in total. This is the single-number payout in roulette.
You can also reduce the ratio to a profit per unit: 3 to 2 is 1.5 per unit, 6 to 5 is 1.2 per unit, 35 to 1 is 35 per unit.
“To” versus “for”
Some layouts and displays write “for” instead of “to”. “35 for 1” means that for 1 unit wagered you receive 35 units back in total, which includes your stake. Your profit is therefore 34, which is the same as 34 to 1. The “for” form always looks larger by one. Slot pay tables and some side bets are written this way, so it is worth checking which word is used before comparing two payouts. Mixing them up can make a worse payout look better than it is.
From a ratio to a break-even probability
For a payout of X to Y, the bet breaks even when the win probability equals Y / (X + Y). If the real chance of winning is below that figure, the bet has a negative expected value and a house edge; if it is equal, the bet is fair; if above, it would favor the player. Real casino bets do not sit above it.
Some examples:
- 1 to 1: break-even is 1/2, or 50 percent. A single-zero roulette even-money bet wins 18/37, about 48.65 percent, which is below it.
- 3 to 2: break-even is 2/5, or 40 percent.
- 35 to 1: break-even is 1/36, about 2.78 percent. A single number on a single-zero wheel wins 1/37, about 2.70 percent. The gap is small and is the whole edge: about 2.70 percent of the stake, on average.
- 4 to 1: break-even is 1/5, or 20 percent. The craps wager on a total of seven wins 6 times in 36, about 16.7 percent, so it falls short by a wide margin. That wager belongs to the family of proposition bets.
This is the same logic used when a payout is compared with the true odds, and the conversion steps are covered further in the articles on odds conversion and break-even probability.
Converting to decimal form
Many displays use decimal notation. To convert, add 1 to the profit per unit. A 3 to 2 payout becomes 1 + 1.5 = 2.5; 6 to 5 becomes 2.2; 35 to 1 becomes 36. The decimal figure is the total returned per unit staked, including the stake. This is the same as the “for” form: 36 for 1 equals 35 to 1.
Comparing two payouts
When the same event is offered at two different payouts, the one with the larger profit-per-unit is better for the player, other things equal. The comparison is simple for blackjack naturals: 1.5 versus 1.2 per unit, a difference of 0.3 units per unit staked every time a natural occurs. A rule variation like this one can move the house edge noticeably, which is why number of decks and other rules deserve a look on the same visit.
For bets with different probabilities, compare expected value instead. Multiply each payout by its win probability, subtract the loss probability times the stake, and compare per unit wagered. The payout alone says little: a large ratio on an unlikely event can be a worse price than a modest ratio on a likely one, which is why long-shot side bets tend to be expensive.
Other ways payouts are described
- Odds against: “5 to 1 against” means 5 chances of not happening for every 1 of happening, so the probability is 1/6. This is the language of true odds. A payout of 4 to 1 on something that is 5 to 1 against is below fair.
- Commission-style payouts: some bets pay 1 to 1 minus a percentage of winnings, which has the same effect as a lower ratio.
- Pay tables: slot machines and video poker list several payouts at once. A pay table is read the same way, but each line has its own probability, and the overall return is the sum. Details are in the video poker pay table article.
A note on short-term results
A good-looking ratio does not guarantee a good outcome. Short runs of wins and losses are dominated by chance, and small samples can make any bet look generous or stingy. The true cost shows only over many bets. If gambling is causing you worry or harm, a local support service can offer confidential help.