True Odds vs Payout Odds: Where the House Edge Lives
The house edge lives in a single number: the difference between true odds and payout odds. True odds are the honest mathematics of a bet, the actual chance an outcome occurs, expressed as a ratio.
The house edge lives in a single number: the difference between true odds and payout odds. True odds are the honest mathematics of a bet, the actual chance an outcome occurs, expressed as a ratio. Payout odds are what the casino agrees to pay when that outcome lands. Every casino game is built so payout odds fall short of true odds, and that shortfall, compounded over thousands of spins, rolls, and hands, is the house edge. Consider a single number on a European roulette wheel. It has 37 pockets, so the true odds against hitting one chosen number are 36 to 1. Yet the house pays only 35 to 1. That missing unit, spread across all possible bets, produces a 2.70% edge, or roughly 2.7 ENT lost per 100 staked over time. The same gap appears everywhere, though its size varies enormously: about 0.5 ENT per 100 in blackjack played with correct strategy, several ENT per 100 in most roulette and craps bets, and far more in certain proposition and lottery-style wagers. Understanding this gap turns confusing marketing (biggest jackpot, best odds) into a simple comparison: look at the house edge, not the prize.
What is the difference between true odds and payout odds?
True odds are the exact mathematical probability of an outcome, expressed as a ratio against winning. Payout odds are what a casino actually pays a winning bet. The house edge is the gap between the two, quietly collected on every wager.
Every wager carries two numbers: the true odds, a neutral statement of probability with no commercial interest attached, and the payout odds, the rate the house has chosen to pay a winner. If the two matched, the game would be mathematically fair, breaking even over time. No casino runs its core games this way; payout odds are always shaded shorter than true odds, and that shading is the house edge.
How does the house edge appear on a single number in roulette?
A European wheel carries 37 pockets, so the true odds against any single chosen number are 36 to 1. The casino, however, pays only 35 to 1 on a winning straight bet. That missing unit, spread evenly across every number on the layout, produces the wheel's 2.70% house edge.
On a European roulette wheel, 37 pockets mean the true odds against any single chosen number are 36 to 1: 36 losing pockets for every winning one. A fair casino would pay 36 units of profit per unit staked. Instead, a winning straight-up bet pays 35 to 1. That missing unit, averaged across the layout, is the wheel's 2.70% edge, about 2.7 ENT lost per 100 staked. American wheels add a second zero, stretching the true odds further without raising the payout, pushing some bets toward a 5.26% edge.
One missing unit, spread across a wheel, becomes a 2.70% edge.
Why does a craps place bet pay less than its true odds?
A place bet on the 4 wins with true odds of 2 to 1, since three ways make a 4 against six ways make a 7. The house instead pays 9 to 5, a shorter payout that manufactures its edge on that wager.
In craps, a place bet on the 4 wins whenever a 4 lands before a 7. Three combinations make 4 and six make 7, so the true odds against the bet are 2 to 1; a fair payout would return two units of profit per unit staked. The house instead pays 9 to 5, and that shortfall is where its edge lives. Tucked beside it sits a rare exception: the free odds bet, made behind an existing line wager, paid at the true odds with no additional edge on that portion of the stake.
Is a bigger jackpot or higher payout proof of a better bet?
No. A large advertised payout only reflects how rare the winning outcome is, not how fair the bet is. The number worth comparing is the house edge, the gap between true odds and payout odds; a bet with a huge headline prize can still carry a punishing edge underneath.
Marketing emphasizes the size of a jackpot: the bigger the number, the more exciting the bet looks. But a giant top prize is simply the flip side of a rare outcome, and rarity alone says nothing about value. The only number that measures value is the house edge. A game can advertise an enormous payout while carrying a brutal edge, because the true odds against that rare outcome are stretched even further than the payout suggests. The wager that quietly pays close to true odds, even with a modest prize, is mathematically the better bet.
How do house edges compare across popular casino games?
Edges range from razor-thin to enormous depending on the bet. Blackjack played with correct basic strategy sits near a 0.5% edge, most roulette wagers run between 2.70% and 5.26%, craps varies bet by bet, and certain proposition and lottery-style wagers carry edges far beyond any of these.
Comparing the gap between true odds and payout odds across games shows how dramatically the house edge can shift depending on the wager chosen, even within the same casino floor.
- Blackjack, played with correct basic strategy: about 0.5% edge, roughly 0.5 ENT per 100 staked.
- European roulette (single zero): 2.70% edge, about 2.7 ENT per 100 staked.
- American roulette (double zero) and some roulette side bets: up to 5.26% edge.
- Craps place bet on the 4: true odds of 2 to 1, paid at 9 to 5, a clear house-favoring gap.
- Craps free odds bet (behind a line bet): paid at true odds, a 0% edge on that portion of the stake.
- Proposition and lottery-style bets: true odds stretched so far beyond the payout that edges can run into the double digits.
Compare the edge, not the jackpot; a big prize just means a bigger gap.
What is the difference between odds quoted 'to 1' and 'for 1'?
Odds quoted as 'to 1' describe pure profit on a winning bet, on top of the returned stake. Odds quoted as 'for 1' describe the total return, stake included, which works out to exactly one unit less profit than the same number quoted the first way.
Reading a payout board carefully matters as much as knowing the underlying true odds. When a payout reads '35 to 1', the player keeps the stake and receives 35 units of profit, a total return of 36 units. Some tables instead quote '36 for 1'. That phrasing sounds identical to the true odds above, but it is not: 'for 1' folds the stake back into the number shown, so '36 for 1' actually pays only 35 units of profit, the same as '35 to 1'. Confusing the two can make a bet look far more generous, or stingier, than its true odds justify.
'For 1' quietly folds your own stake back into the number on the sign.
Why would a casino ever pay a bet at true odds?
The free odds bet in craps is the rare exception, paid at exact true odds with no edge of its own. It exists only as an add-on behind another wager that already carries the house's edge, so it does not change overall profitability.
It seems strange that a casino would pay a wager at true odds with zero edge attached, yet craps does exactly this with its free odds bet. A player first makes a line bet, such as the pass line, carrying its own small edge. Only after that bet is established can free odds be added behind it, and that portion is paid at the honest, unshaded true odds. The concession costs the house nothing overall, because the free odds bet cannot stand alone; it is always attached to a wager that already guarantees the casino a profit.
What does a mathematically fair bet actually look like?
A fair bet pays exactly the true odds, giving it a zero house edge; players and the house would break even over a large enough sample. No standard casino game offers this on its core wagers, which is precisely how casinos remain profitable.
A truly fair bet is easy to define: the payout odds equal the true odds, exactly, with nothing shaded off. Flip a coin for even stakes and call heads or tails, and you have found one of the few genuinely fair bets anywhere, a zero edge proposition where neither side holds an advantage. No commercial casino floor offers this on its central games. Every table game, every slot machine, and every side bet is engineered so payout odds fall short of true odds by some margin, however small. That margin is the entire commercial purpose of the game, the quiet toll that makes a casino a business rather than a charity.
A coin flip for even money is one of the few truly fair bets in existence.
The house always knows this
The house edge is just the gap between true odds and payout odds; compare that gap, not the jackpot, before you place a bet.
Frequently asked
What does a 2.70% house edge actually mean in real terms?
It means that, averaged over a very large number of bets, the casino keeps about 2.70 ENT out of every 100 ENT staked on that wager. Any single spin can go either way; the edge only describes the long-run average, not a single outcome.
Is European roulette really better for players than American roulette?
Mathematically, yes. European roulette has a single zero pocket and a 2.70% edge, while American roulette adds a second zero, stretching the true odds without raising the payout, which pushes many of its bets toward a 5.26% edge, close to double the cost to the player over time.
Does playing perfect basic strategy remove the blackjack house edge?
No. Correct basic strategy shrinks the edge dramatically, down to roughly 0.5% on most rule sets, but it does not erase it. The house still pays slightly less than true odds on the underlying hands, so a small structural edge always remains.
Is any casino bet ever truly free of a house edge?
Craps offers one genuine exception: the free odds bet placed behind a pass or come bet, which pays at exact true odds. It carries a 0% edge on its own, though it can only exist attached to a wager that already favors the house.
Why do proposition and lottery-style bets carry such large edges?
Their winning outcomes are extremely rare, so the true odds against them are enormous, often thousands to one. Casinos pay a headline number that sounds generous but still falls far short of those true odds, producing edges much larger than table games.
What's the simplest way to compare two different casino bets?
Ignore the size of the top prize and compare the house edge directly: the percentage gap between true odds and payout odds. The wager with the smaller gap costs less per 100 staked over time, regardless of how large its jackpot looks.
Sources & further reading
ENTBlog is educational. Every casino game carries a house edge, so the mathematically expected result of play is a net loss over time. Play for entertainment, within limits you set in advance. Nothing here is financial advice or a promise of winnings.