Payout Analyzer: True Odds vs Casino Payouts
Every casino game pays less than true mathematical odds. This fundamental discrepancy is how casinos generate profit. The Payout Analyzer helps you understand exactly how much casinos withhold by comparing what a bet should pay based on probability versus what it actually pays.
Understanding this gap between true odds and casino payouts is essential for anyone studying gambling mathematics. It reveals why no betting system can overcome the house advantage and why casinos remain profitable businesses despite individual players occasionally winning.
Select a Common Casino Bet
Choose from popular casino bets to see the payout analysis. Click any bet to view detailed true odds versus actual payout comparison.
Roulette: Single Number
American Roulette straight-up bet on any single number
Roulette: Red/Black
Even money bet on red or black in American Roulette
Baccarat: Tie Bet
Side bet on Player and Banker having equal totals
Craps: Any Seven
One-roll bet that the next roll will total 7
Craps: Hard 8 (4-4)
Bet that an 8 will be rolled as 4-4 before a 7 or easy 8
Keno: 1-Spot Game
Matching one number out of 80 with 20 drawn
Slots: Major Jackpot
Typical 3-reel slot machine top prize combination
Blackjack: Insurance
Side bet when dealer shows Ace, pays if dealer has blackjack
Custom Payout Analysis
Enter your own probability and payout values to calculate the house edge and see how much the casino withholds.
Compare Multiple Bets
See how different casino bets compare in terms of true odds versus payouts. This table reveals which bets have the largest discrepancies.
| Bet | Win Probability | True Odds | Fair Payout | Actual Payout | House Edge |
|---|---|---|---|---|---|
| Blackjack (Basic) | 49.71% | 1.01:1 | 1.01:1 | 1:1 | 0.50% |
| Baccarat Banker | 45.86% | 1.18:1 | 1.18:1 | 0.95:1 | 1.06% |
| Craps Pass Line | 49.29% | 1.03:1 | 1.03:1 | 1:1 | 1.41% |
| European Roulette (Red) | 48.65% | 1.06:1 | 1.06:1 | 1:1 | 2.70% |
| American Roulette (Red) | 47.37% | 1.11:1 | 1.11:1 | 1:1 | 5.26% |
| American Roulette (Single) | 2.63% | 37:1 | 37:1 | 35:1 | 5.26% |
| Craps Any Seven | 16.67% | 5:1 | 5:1 | 4:1 | 16.67% |
| Baccarat Tie | 9.52% | 9.47:1 | 9.47:1 | 8:1 | 14.36% |
| Blackjack Insurance | 30.77% | 2.25:1 | 2.25:1 | 2:1 | 7.69% |
| Keno (Match 1 of 1) | 25.00% | 3:1 | 3:1 | 2:1 | 25.00% |
| Big Six Wheel ($1) | 44.44% | 1.25:1 | 1.25:1 | 1:1 | 11.11% |
Reading the Table
Highlighted rows show bets with particularly large payout discrepancies or high house edges. Notice how bets that appear attractive due to big payouts (like the Baccarat Tie at 8:1) often have the largest gaps between fair and actual payouts.
The house edge represents what percentage of each bet the casino expects to keep over time. A 5.26% house edge means for every $100 wagered, the casino expects to profit $5.26 on average.
Understanding True Odds vs Payout Odds
The difference between true odds and payout odds is the foundation of casino profitability. True odds represent the actual mathematical probability of an event occurring, expressed as a ratio. Payout odds are what the casino actually pays when you win. The gap between these two numbers is where the house edge comes from.
According to Encyclopedia Britannica's coverage of probability theory, true odds can be calculated directly from the number of ways to win versus the number of ways to lose. For example, in American roulette with 38 numbers, the true odds of hitting any single number are 37:1 (37 ways to lose, 1 way to win). However, the casino only pays 35:1, keeping the 2-unit difference as profit margin.
True Odds = (Total Outcomes - Winning Outcomes) : Winning Outcomes
Fair Payout = True Odds (what you should receive to break even)
House Edge = (Fair Payout - Actual Payout) / (Actual Payout + 1) × 100%
Expected Value = (Win Prob × Payout) - (Loss Prob × Bet)
The Mathematics of Casino Profit
Casinos don't need to cheat or manipulate games. Their profit comes from systematically paying less than true odds on every winning bet. As explained by the UNLV International Gaming Institute, this mathematical edge ensures long-term profitability regardless of short-term player wins.
Consider American roulette's single number bet: the true probability of winning is 1/38 (2.63%), which translates to true odds of 37:1. A fair game would pay 37:1, meaning if you bet $1 and won, you'd receive $37 plus your original $1 back ($38 total). Instead, casinos pay only 35:1 ($36 total return). Over 38 spins at $1 each, a player betting on one number expects to win once and lose 37 times. With fair odds, they'd break even ($38 spent, $38 won). With casino odds, they spend $38 and receive only $36 on their one win—a 5.26% loss.
Why Payout Discrepancies Matter
Understanding payout discrepancies is crucial for making informed decisions about gambling. The National Council on Problem Gambling emphasizes that recognizing the mathematical certainty of player losses over time is essential for responsible gambling education.
The payout gap explains several important realities:
- No betting system can overcome the house edge. Whether you bet big or small, change patterns, or use progressive systems, every bet carries the same negative expected value.
- High payouts often mask higher house edges. Bets offering 8:1 or 35:1 payouts appear lucrative but typically have larger discrepancies from true odds.
- Time is the casino's ally. The more bets placed, the more actual results converge toward mathematical expectation, ensuring casino profit.
- Short-term wins are expected but temporary. Variance allows some players to win, but extended play trends toward the house edge.
Application to Korean Gambling Context
At Kangwon Land, South Korea's only legal casino for Korean citizens, all games operate with standard payout discrepancies that comply with international gaming regulations. Understanding these payout structures helps explain why the casino generated over ₩1.36 trillion (approximately $950 million USD) in gross gaming revenue in 2024.
South Korea's strict gambling laws partly reflect governmental understanding that payout discrepancies create systematic wealth extraction. When you know that every bet has a negative expected value, you can make clearer decisions about whether gambling entertainment is worth its mathematical cost.
Identifying Sucker Bets
Some casino bets have dramatically larger gaps between true odds and payouts. These are often called "sucker bets" because they offer the illusion of value while delivering exceptionally poor expected returns. According to Stanford Encyclopedia of Philosophy's coverage of decision theory, rational decision-making requires understanding the true expected value of choices.
Common sucker bets include:
- Baccarat Tie Bet: True odds of 9.47:1, pays only 8:1 (14.36% house edge)
- Keno: House edges typically range from 25-40%
- Big Six Wheel: House edges from 11-24% depending on the bet
- Craps Proposition Bets: House edges from 9-17%
- Blackjack Insurance: True odds 2.25:1, pays only 2:1 (7.69% house edge)
Use our Bet Comparator tool to see these differences side by side, or try our House Edge Calculator to see how these percentages translate to expected losses over time.
Educational Resources
For deeper understanding of gambling mathematics and probability theory, explore these resources on our site:
- Probability Calculator - Calculate true odds, expected value, and multi-trial probabilities
- Risk of Ruin Calculator - Understand bankroll survival probability
- Session Simulator - Visualize how gambling sessions unfold over time
- Fallacy Analyzer - Identify cognitive biases that distort perception of odds
- Responsible Gambling Resources - Support and prevention information
Educational Purpose Only
This tool is designed solely for educational purposes to help users understand gambling mathematics. It demonstrates why casino gambling has a negative expected value and should not be considered a viable income source. All forms of gambling carry risk of financial loss.
If you or someone you know has a gambling problem, please seek professional help. Visit our responsible gambling resources page for support organizations and treatment options available in South Korea and internationally.
Connection to Regulatory Understanding
Gaming regulators worldwide use these mathematical principles to ensure fair play within established parameters. While individual spins or hands are random, the aggregate outcome over millions of wagers is mathematically predictable. This predictability allows casinos to operate as stable businesses and governments to estimate tax revenues.
South Korea's enforcement of gambling laws recognizes that even mathematically fair games (those with disclosed house edges) systematically extract money from players. The prohibition of most gambling activities reflects a policy judgment that the social costs of widespread gambling outweigh potential economic benefits, even when games operate with standard, regulated payout structures.