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Odds, House Edge and Strategy Math: The Numbers Behind Every Casino Game
Every casino game comes down to two numbers: how likely you are to win, and what you're paid when you do. The gap between them is the house edge. This section shows how to work it out, game by game.
| Probability | Favourable outcomes ÷ all outcomes |
|---|---|
| Odds (against) | Unfavourable outcomes to favourable outcomes |
| House edge | Expected loss as a share of each bet |
| Lowest edges in our data | Blackjack with basic strategy, dice and crash, baccarat banker |
| Highest edges in our data | Baccarat tie at 8 to 1, triple-zero roulette |
All guides in this section
This section is about odds, house edge and the math behind casino strategy. If you understand three ideas, you can size up any game in a few minutes: probability (how likely a result is), odds (the same information written as a ratio), and the house edge (how much the payout falls short of what the true odds would justify).
Everything here is built on numbers we calculated or simulated ourselves, checked against published sources.
The three numbers that decide every bet
Britannica's entry on gambling defines probability as the number of favourable outcomes divided by the total number of outcomes, and odds as the ratio of unfavourable to favourable outcomes. A casino then sets a payout. When the payout is lower than the true odds, the difference is the house edge:
house edge = 1 − (probability of winning × total return per unit bet)European roulette single number: 1 − (1/37 × 36) = 1/37 = 2.70%. The bet pays 35 to 1, so a win returns 36 units including your stake.
That one formula works for roulette, dice, crash and anything else with fixed odds. Games with more complex outcomes, like blackjack and baccarat, need a full enumeration or simulation, which is what we did.
House edge comparison across games
The table below brings together the house edge from each of our datasets. Lower is better for you. "Expected loss per 100 USDT" is the house edge applied to 100 USDT of total bets.
| Bet | House edge | Expected loss per 100 USDT | Source of the number |
|---|---|---|---|
| Blackjack, basic strategy (6 decks, S17, DAS, 3:2) | 0.47% ± 0.036 | 0.47 USDT | Our 10M-hand simulation |
| Crypto dice (any target) | 1.00% | 1.00 USDT | Our dice data |
| Crash / limbo (any cash-out) | 1.00% | 1.00 USDT | Our crash simulation |
| Baccarat banker (5% commission) | 1.06% | 1.06 USDT | Our exact calculation, 8 decks |
| Baccarat player | 1.24% | 1.24 USDT | Our exact calculation, 8 decks |
| Craps don't pass | 1.36% | 1.36 USDT | Our exact calculation |
| Craps pass line | 1.41% | 1.41 USDT | Our exact calculation |
| Blackjack, basic strategy, 6:5 payout | 1.83% ± 0.036 | 1.83 USDT | Our 10M-hand simulation |
| European roulette (single zero) | 2.70% | 2.70 USDT | Our roulette data |
| American roulette (double zero) | 5.26% | 5.26 USDT | Our roulette data |
| Triple-zero roulette | 7.69% | 7.69 USDT | Our roulette data |
| Baccarat tie (pays 8 to 1) | 14.36% | 14.36 USDT | Our exact calculation, 8 decks |
A few notes on how to read it:
- Blackjack figures are Monte Carlo estimates with a standard error of about 0.036 percentage points, and assume perfect basic strategy. In our simulation, switching the blackjack payout from 3:2 to 6:5 added 1.36 points, close to the 1.39 points the Wizard of Odds lists for the same rule change (the small gap comes from different baseline rules, not sampling error, because both payouts were scored on the same hands).
- Baccarat figures are exact, from enumerating every possible deal with 8 decks. They match the Wizard of Odds figures of 1.06%, 1.24% and 14.36%.
- Roulette and craps figures are exact and match the Wizard of Odds roulette and craps pages (2.70%, 5.26%, 7.69%; pass 1.41%, don't pass 1.36%).
- Dice and crash use a published 1% edge; the limbo code on Stake's provably fair page uses a house edge factor of 0.99.
How to use our odds and strategy guides
- Odds vs probability, explained with roulette and dice examples. How to convert between the two, and how comparing payout odds with true odds reveals the house edge.
The math in this section powers the strategy pages elsewhere on the site:
- Roulette betting systems tested: Martingale, D'Alembert and Fibonacci against a 100 USDT bankroll.
- Baccarat strategy by the numbers: why the banker bet is the lowest-edge choice and the tie is the worst.
- Crash auto-cashout targets compared: why every target has the same 1% edge.
- Slot RTP, explained: the same house edge idea, written as return to player.
Why betting systems don't change the edge
A betting system changes your stake sizes, not the odds of each bet. We tested this with 50,000 simulated sessions per system on a European wheel, betting red from a 100 USDT bankroll:
| System | Reached 150 USDT goal | Average total wagered | Loss per 100 USDT wagered |
|---|---|---|---|
| Flat 1 USDT | 2.43% | 989.4 USDT | 2.71 USDT |
| Martingale | 48.67% | 233.3 USDT | 2.77 USDT |
| D'Alembert | 52.30% | 597.3 USDT | 2.84 USDT |
| Fibonacci | 48.50% | 475.1 USDT | 2.62 USDT |
Every system lost between 2.62 and 2.84 USDT per 100 USDT wagered, clustered around the wheel's 2.70% house edge. Systems that "won" more often did so by risking a larger loss in the sessions that went wrong.
Try the numbers yourself
For blackjack, the blackjack strategy calculator shows the best play for any hand, which is what the 0.47% figure above assumes.
The crypto angle
Crypto-native games like dice and crash often publish their house edge in the game's own code, which makes the math easy to check. It doesn't make it more favourable: a 1% edge still means an expected loss of 1 USDT per 100 USDT wagered. If you hold your bankroll in USDT, the house edge is the main force moving your balance over time; in a volatile coin, price swings are added on top.
Frequently asked questions
What is the house edge?
The house edge is the casino's average profit on a bet, expressed as a percentage of the amount wagered. A 2.70% edge means you lose 2.70 USDT per 100 USDT wagered on average over the long run. It comes from paying winners slightly less than the true odds would justify. It is the same thing as 100% minus the RTP.
Which casino game has the lowest house edge?
Among the games we have calculated, blackjack played with perfect basic strategy under good rules came lowest, at about 0.47% in our 6-deck simulation. Crypto dice and crash with a published 1% edge, and the baccarat banker bet at about 1.06%, are next. Side bets like the baccarat tie are far worse.
Can a betting system lower the house edge?
No. Systems like Martingale change how big your bets are and when you make them, but every individual bet still carries the same edge. Our roulette simulation of Martingale, D'Alembert and Fibonacci found each lost about the same share of the money wagered as flat betting.
Is odds the same as probability?
No. Probability compares favourable outcomes to all outcomes; odds compare unfavourable outcomes to favourable ones. A single roulette number on a European wheel has a probability of 1 in 37 (2.70%) but odds of 36 to 1 against. Our odds vs probability guide shows how to convert between them.
Sources
- Gambling: Chances, probabilities and odds — Encyclopaedia Britannica
- Roulette Basics — Wizard of Odds
- Baccarat Basics — Wizard of Odds
- Craps Basics — Wizard of Odds
- Blackjack Rule Variations — Wizard of Odds
- Provably Fair: Game Events — Stake.com