True Odds vs Casino Odds Converter

Every casino bet has two sets of odds: the true odds (what probability actually dictates) and the casino odds (what the casino pays). The difference between them is where the house edge lives. This tool reveals exactly how much casinos shave off every winning bet.

How True Odds Work

Every gambling outcome has a mathematical probability. A fair coin has a 50% chance of heads. A single number on an American roulette wheel has a 1-in-38 (2.63%) chance of hitting. These are true odds—the actual mathematical reality of the bet.

In a truly fair game, payouts would match these probabilities exactly. A 50/50 bet would pay 1:1 (even money). A 2.63% chance bet would pay 37:1. But casinos don't operate fair games—they operate profitable ones.

Classic Examples: The Math Behind Common Bets

Understanding this concept is easier with real examples. According to the UNLV Center for Gaming Research, these are among the most widely-analyzed casino bets:

Notice how the "Any Seven" bet in craps pays 4:1 when fair odds would be 5:1. That missing unit per win is the casino's profit margin. As the American Gaming Association explains, this mathematical structure is what allows casinos to operate—and why they've been profitable businesses for centuries.

Why Casinos Use the Payout Gap

Casinos could theoretically charge an entry fee and run fair games. Instead, they hide their profit margin inside the payout structure. There are several reasons for this approach:

• Psychological invisibility: Players focus on the payout (35:1 sounds impressive!) rather than comparing it to true odds (37:1 would be fair)
• Automatic extraction: The house edge applies to every bet without additional transactions
• Scalability: Larger bets and more bets automatically generate proportionally larger profits
• Player acceptance: "Even money" and round-number payouts are easier to understand than fair-odds payouts like 1.11:1

This is explored in depth in our article on casino design psychology—the gap between true odds and casino payouts is just one of many ways gambling environments are optimized for profit.

The Law of Large Numbers in Action

Individual gambling sessions can go either way—you might win big or lose everything in a single night. But the casino isn't playing one session. According to probability theory documented by Britannica, as the number of bets increases, actual results converge toward expected value.

For casinos handling millions of bets per month, the law of large numbers is essentially a guarantee. That 5.26% house edge on roulette isn't a hoped-for outcome—it's a mathematical certainty over sufficient volume. This is why casino whales receive such lavish treatment: their larger bets generate proportionally larger guaranteed profits.

Understanding Implied Probability

Professional gamblers and sports bettors often work backwards from payouts to calculate implied probability. If a casino pays 4:1 on a bet, the implied probability is:

Implied Probability = 1 / (Payout + 1) × 100

4:1 payout → 1/5 → 20% implied probability — Standard Probability Calculation

If you believe the true probability is higher than the implied probability (e.g., you think the bet wins 25% of the time but the payout implies 20%), then the bet has "positive expected value" from your perspective. This is the foundation of advantage play and why casinos ban card counters—they find bets where true odds exceed implied odds.

The True Cost of Playing

Many players think of house edge as "what I might lose." But it's more accurate to think of it as a fee for entertainment—paid automatically on every dollar wagered.

If you bet $100 on roulette 100 times at $1 each (total wagered: $100), the expected cost is roughly $5.26. If you bet the same $100 a thousand times by recycling wins (total wagered: potentially $10,000+), the expected cost grows proportionally. This is why session length matters as much as bet size, as we explain in the Session Outcome Calculator.

Comparing Edges Across Games

Not all casino games extract the same percentage. The Nevada Gaming Control Board publishes detailed statistics showing how different games perform. Generally:

• Best odds: Blackjack with basic strategy (0.5%), Craps Pass Line (1.41%), Baccarat Banker (1.06%)
• Moderate odds: Roulette (2.7% EU, 5.26% US), Pai Gow Poker (~2.5%)
• Worst odds: Slot machines (2-15%), Keno (25-40%), Big Six Wheel (11-24%)

This variance in house edge is why experienced players gravitate toward table games and why slot machine psychology must work harder to retain players despite worse mathematical expectations.

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