Why does a roulette number pay 35:1 while a baccarat Banker bet pays less than even money after commission? Why can a slot advertise 96% RTP while a craps wager has its own house-edge percentage?

The answer is mathematics, but each game reaches those numbers differently. This guide explains How Casino Odds Are Calculated across several familiar games.

Instead of treating odds as one universal formula, we will look at how wheels, cards, dice, paytables, and software create different probability models – and why apparently similar wagers can have very different long-term costs.

Roulette Starts With the Number of Pockets

Roulette offers one of the clearest examples of casino probability.

A double-zero American wheel contains 38 possible pockets: 1 through 36, 0, and 00.

Suppose you wager on red. There are 18 red numbers, so the probability of winning is:

18 ÷ 38 = 47.37%

The bet pays 1:1.

If the game contained only 36 red and black numbers, an even-money payout would be mathematically balanced. The two green zero pockets change that equation.

When either 0 or 00 appears, the normal red and black bets lose. That creates the standard 5.26% house edge on double-zero roulette.

Single-zero roulette has only 37 pockets. With one green zero instead of two, the standard house edge falls to about 2.70%.

The lesson is simple: adding or removing one pocket changes the odds even though the table looks almost identical.

Blackjack Odds Depend on Rules and Decisions

Blackjack cannot be calculated with one simple fraction because the probability changes as cards are removed from the deck.

Player decisions matter as well.

Consider a hand of 11 against a dealer’s 6. The expected value of hitting, doubling, or taking another action is determined by the composition of remaining cards, dealer rules, and payout structure.

Rule variations also affect the overall house advantage.

Wizard of Odds’ blackjack calculator includes variables such as number of decks, whether the dealer hits or stands on soft 17, doubling after splits, surrender, resplitting, and whether blackjack pays 3:2 or 6:5.

This is why a statement such as “blackjack has a 0.5% house edge” is incomplete without mentioning rules and strategy.

Under one rule set, optimal basic strategy may produce an edge near that range. Change the blackjack payout or several table rules and the calculation changes.

The mathematics is therefore conditional rather than fixed.

Craps Begins With 36 Dice Combinations

Two six-sided dice produce 36 ordered outcomes.

Some totals appear much more often than others.

A 2 can only happen as 1+1, so it has one combination. A total of 6 has five combinations. A 7 has six and is therefore the most common total.

From there, each craps wager can be analyzed according to its win conditions and payout.

Consider an Any Craps wager covering totals 2, 3, or 12. There are four winning combinations out of 36, creating an 11.11% chance of winning.

At a standard 7:1 payout, Wizard of Odds calculates a house edge of 11.11%.

Meanwhile, a Place 6 bet has a very different structure. It wins when 6 appears before 7, so the relevant comparison is five combinations for 6 against six for 7. The usual 7:6 payout creates a house edge of about 1.52% per resolved wager.

Same dice, very diffrent mathematics.

Baccarat Requires Counting Card Combinations

Baccarat looks simple because most players choose among Banker, Player, and Tie.

Calculating the probabilities behind those wagers is much more involved.

Cards can produce many possible hand sequences under baccarat’s fixed drawing rules. Analysts therefore calculate the frequency of each final outcome across all relevant combinations.

For a standard eight-deck game, Wizard of Odds calculates approximately:

Banker wins: 45.86%
Player wins: 44.62%
Tie: 9.52%

Because a standard Banker win pays 0.95:1 after the usual 5% commission, its house edge is approximately 1.06%. The Player bet has an edge of about 1.24%.

The common Tie bet illustrates why payout alone can be misleading.

A traditional 8:1 Tie payment sounds much larger than the main wagers, yet Wizard of Odds calculates a house edge around 14.36% on that paytable.

A large payout often exists because the event itself is less frequent.

Slot Odds Come From Reel Mathematics and Paytables

Modern slots work differently from physical wheels and dice games.

Their theoretical return is determined by the probability assigned to possible outcomes and the amount each winning combination pays.

A simple hypothetical slot might have a 10% chance of paying 2x, a 1% chance of paying 20x, and many losing outcomes. Developers can combine all those probabilities and payouts to calculate theoretical RTP.

In modern digital games, the visible reels do not necessarily tell you the true frequency of every symbol. Software and virtual reel structures can allow different symbols or combinations to have different underlying probabilities.

The UK Gambling Commission requires relevant gaming machines in Great Britain to display their theoretical target RTP, and certain machine categories have that value verified by the manufacturer or an accredited test house.

If the designed RTP is 96%, the theoretical difference of 4% represents the long-term amount not returned to players, although actual results can vary substantially during short sessions.

That variation is often described through volatility.

RTP and House Edge Are Closely Related

RTP and house edge often express the same underlying mathematical relationship from opposite viewpoints.

If a game returns a theoretical 97% of stakes over the long run, the corresponding house advantage is roughly 3%, provided both figures are calculated on a comparable basis.

So:

RTP ≈ 100% − House Edge

A 96% RTP corresponds approximately to a 4% edge.

But care is needed when making comparisons.

Wizard of Odds notes that house edge is conventionally based on the initial wager, which can become tricky in games where additional money may enter play later.

Craps creates another complication because some bets can remain unresolved across several rolls. Wizard of Odds therefore provides house-edge figures per bet made, per bet resolved, and per roll for certain wagers.

The numbers only make sense when you know exactly how they were defined.

Why a 10:1 Payout Does Not Mean a 1-in-10 Chance

Payout language can easily create misunderstandings.

If something pays 10:1, that does not automatically mean it happens once in every 10 attempts.

A fair 10:1 payout would correspond to odds against the event of 10 to 1, meaning one winning outcome for every ten losing outcomes. That is a probability of:

1 ÷ 11 = 9.09%

Notice the denominator is 11, not 10.

A casino may also offer a payout below the true odds. If an event with fair odds of 10:1 pays only 8:1, the difference contributes to the house advantage.

This is why payout ratios and probability should always be considered together.

Looking at either number alone gives an incomplete comparision.

House Edge Does Not Tell You Session Volatility

Imagine two games that both have a 3% theoretical house edge.

One might produce frequent small wins and losses. The other could generate long losing periods interrupted by rare large payouts.

Their expected long-term loss rate may be similar, but the experience can feel completely different.

That difference is related to variance or volatility.

The UK Gambling Commission explains that actual RTP can move above or below theoretical RTP over shorter samples, with volatility affecting the acceptable range of variation. As play volume grows, actual results should generally move closer toward the designed theoretical return.

So house edge answers one question: what is the expected long-run mathematical advantage?

Volatility answers another: how unevenly might results arrive?

Confusing the two can make a high-volatility game seem “worse” simply because short-term swings are larger.

Odds Describe the Game, Not the Next Outcome

Even perfectly calculated casino odds cannot predict an individual result.

If a double-zero roulette wheel gives red a probability of 18/38, that probability does not mean a red result must arrive after several black spins.

Likewise, an RTP of 96% does not mean a slot must return $96 after exactly $100 of play.

The UK Gambling Commission states that on random gaming machines, the odds of winning the current game remain constant and are not affected by previous wins or losses.

Probabilities describe repeated outcomes across large samples.

They are extremely useful for comparing games, understanding payout structures, and calculating expected value – but they are not a timetable for future wins.

Learning How Casino Odds Are Calculated shows why every game needs its own mathematical model.

Roulette uses wheel pockets, craps uses dice combinations, baccarat and blackjack involve card probabilities, while slots combine programmed outcome frequencies with paytables.

Before comparing two wagers, look at both the chance of winning and the payout offered. House edge and RTP can then show how those numbers translate into long-term expected value.