Casino Odds and Bonus Maths: What the Numbers Actually Are
This page contains no strategies for beating a casino, because none exist. What it contains is arithmetic: the published edge of common games, what each rule change costs, and which decisions actually belong to the player.
The house edge, by game
These figures come from the rules of the games themselves and can be derived with a calculator. They describe the long-run share of each stake retained by the operator:
| Game | House edge | Where the number comes from |
|---|---|---|
| European roulette, any bet | 2.70% | 37 pockets, straight-up paid at 35 to 1 |
| American roulette, most bets | 5.26% | The added double zero, same payouts |
| Blackjack, basic strategy | ≈0.5% | Depends strongly on the specific table rules |
| Blackjack, casual play | 2–3% | The difference is decision errors, not luck |
| Baccarat, banker bet | 1.06% | Includes the standard 5% commission on wins |
| Baccarat, tie bet | 14.4% | The single worst common bet on a casino floor |
| Online slots | typically 3–8% | Varies by title and by the configuration deployed |
Two practical conclusions follow immediately. Choosing a single-zero roulette table over a double-zero one halves the cost of playing. Avoiding the baccarat tie bet removes a wager that costs roughly fourteen times more than the banker bet at the same table.
Rule changes worth checking at a blackjack table
Blackjack is the one common game where the posted rules materially change the maths. These are the differences to look for before sitting down:
- Blackjack paying 6 to 5 instead of 3 to 2 — this single change adds roughly 1.4% to the house edge and outweighs every other rule at the table.
- Dealer hitting soft 17 rather than standing — worth about 0.2% against the player.
- Doubling allowed after splitting — worth about 0.14% in the player's favour.
- Number of decks: fewer decks favour the player slightly, all else equal.
If a table pays 6 to 5 on blackjack, no amount of correct play compensates for it. Walking to a different table is a larger improvement than any strategy adjustment available at the first one.
What betting systems actually do
Martingale doubles the stake after each loss, producing many small wins and one loss that erases them. Fibonacci and d'Alembert are gentler versions of the same idea. Every progression reshapes the distribution of results; none changes the expected value, because the expected value is fixed by the paytable.
There is also a hard stop built into the table: the maximum bet. A doubling sequence reaches it after a modest number of losses, which is precisely when it needs the largest wager to recover.
Bonus terms: where the value actually is
A bonus is defined by its wagering requirement, not its headline. Compare two offers on a 100 deposit:
| Offer | Bonus | Wagering | Turnover required |
|---|---|---|---|
| A | 100% up to 100 | 40× bonus | 4,000 |
| B | 50% up to 50 | 10× bonus | 500 |
Offer A looks twice as generous and requires eight times the turnover. At a 4% average house edge, generating 4,000 of turnover costs about 160 in expectation — more than the bonus is worth. Also check which games contribute, at what percentage, the maximum bet allowed while a bonus is active, and the expiry window.
The decisions that are genuinely yours
- Which game to play — the difference between 0.5% and 14.4% is entirely a choice.
- Which table variant — 6 to 5 versus 3 to 2, single zero versus double zero.
- How much to stake, and whether that amount moves with results. It should not.
- How long to play. Total turnover is what the edge applies to, so session length is the main driver of expected loss.
- Whether deposit limits are set in the account before the session rather than intended during it.
What no tip can do
No sequence of bets, no timing, no pattern-reading and no software changes the edge of a game. A page promising otherwise is selling something. Gambling can become a problem behaviour; GamCare and Gamblers Anonymous operate independently of any operator, and licensed operators are required to offer self-exclusion.
Quick answers
Which common bet is worst?
The baccarat tie at about 14.4%, followed by most side bets.
Does a system reduce the edge?
No. It changes the shape of results, not their average.
Is blackjack really 0.5%?
With basic strategy and favourable rules. At 6 to 5 payouts it is closer to 2%.
How do I compare two bonuses?
Calculate the turnover each requires, then multiply by the average house edge of the games that contribute.