House Edge and RTP Explained: The Math Behind Every Bet
A clear, example-driven explanation of house edge and Return to Player — what they mean, how they are calculated, and why they guarantee the house wins over time no matter what you do.
Every casino game — crypto or traditional, provably fair or not — is built on a single foundation: the house expects to keep a predictable percentage of every dollar wagered over time. This is the house edge. Understanding it precisely, not vaguely, is the most important piece of financial literacy a gambler can have, because it determines whether you are making an informed decision or a mathematically uninformed one.
This article builds from first principles. No hand-waving, no “it’s complicated.” The maths here is secondary-school level and worth following carefully.
What House Edge Actually Means
The house edge is the casino’s expected profit expressed as a percentage of each bet, averaged across an infinite number of rounds.
Consider a coin-flip game where heads pays 1.8x your stake (you win 0.8 units for every 1 unit bet) and tails loses your stake. A fair coin flip has a 50% chance of each outcome.
Expected value per $1 bet:
- Win: 0.50 × $0.80 = $0.40
- Lose: 0.50 × (−$1.00) = −$0.50
- Net: −$0.10
The house edge is 10%. For every $1 you bet on this game in the long run, you expect to lose $0.10.
RTP (Return to Player) is simply 100% minus the house edge. In this example: 100% − 10% = 90% RTP. Over time, players collectively get back 90 cents of every dollar they wager.
A Worked Example: European Roulette
European roulette has 37 numbered pockets (0 through 36). A single-number bet pays 35:1.
Probability of winning: 1/37 ≈ 2.703% Probability of losing: 36/37 ≈ 97.297%
Expected value per $1 bet:
- Win: (1/37) × $35 = $0.9459
- Lose: (36/37) × (−$1) = −$0.9730
- Net: −$0.0270
House edge: 2.70%. RTP: 97.30%.
This is one of the better edges in any casino. Yet even here, if you make 1,000 bets of $10 each ($10,000 wagered total), you expect to lose roughly $270. The longer you play, the closer your actual result converges on that expectation.
Typical House Edges by Game Type
The table below shows approximate house edges under standard rules. Specific variants and strategy choices affect the exact figure.
| Game | Approximate House Edge | Notes |
|---|---|---|
| European Roulette | 2.7% | Single-zero wheel |
| American Roulette | 5.26% | Double-zero adds one bad pocket |
| Blackjack (basic strategy) | 0.5% – 1% | Varies by rule set; strategy matters |
| Baccarat (banker bet) | 1.06% | After 5% commission on banker wins |
| Video Poker (full-pay) | 0.5% – 1% | Optimal play required |
| Slots (online) | 3% – 15% | RTP is set in software; varies widely |
| Crash (typical crypto) | 1% – 4% | Depends on operator setting |
| Dice (typical crypto) | 1% – 2% | Often adjustable within limits |
| Sports betting (vig) | 4% – 10% | Built into the odds spread |
Why the House Edge is Inescapable
Some players believe that betting systems — Martingale, Fibonacci, Kelly — can overcome the house edge. They cannot. Here is why.
Every bet you place has a negative expected value. Changing the size or sequence of bets does not change the per-bet expected value. The Martingale system (doubling after each loss) is often presented as a guaranteed recovery mechanism. In reality:
- It does produce frequent small wins.
- It eventually hits a losing streak that either breaches the table maximum bet limit or exhausts the player’s bankroll.
- When that happens, the loss wipes out all previous small wins and more.
The expected outcome of any betting system, over enough bets, converges on: total wagered × house edge × (−1).
How Volume Amplifies the Edge
Here is the most counterintuitive point about the house edge: it compounds with volume.
If you bet $10 per spin on a slot with a 4% house edge, you lose an expected $0.40 per spin. At 300 spins per hour, that is $120 of expected loss per hour. The machine’s entertainment looks cheap per spin and catastrophically expensive per session once volume is understood.
Expected loss = stake × house edge × number of bets
| Sessions | Bets | Total Wagered | Expected Loss (4% edge) |
|---|---|---|---|
| 1 session | 300 | $3,000 | $120 |
| 1 week (5 sessions) | 1,500 | $15,000 | $600 |
| 1 month (20 sessions) | 6,000 | $60,000 | $2,400 |
These are expectations, not certainties. Variance means you may be ahead after one month. But variance shrinks relative to the expected loss as bets accumulate — the “law of large numbers” means your result approaches the expectation with more bets, not fewer.
Crypto-Specific Considerations
Crypto casinos often advertise lower house edges than traditional operators, and some do offer competitive RTPs — particularly on in-house games like dice. However, two factors specific to crypto gambling complicate the picture:
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Asset volatility. If you deposit ETH and its price falls 20% during your session, your losses in fiat terms include both the house edge and the price movement. You can be an “above-average” gambler in crypto units and still lose significantly in real purchasing power.
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Token-based rewards. Many crypto casinos offer rakeback or staking rewards in their own native token. These tokens are speculative assets whose value can collapse. Including them in an RTP calculation inflates the apparent return.
For a detailed look at how casinos structure these revenue streams, see how crypto casinos make money.
What RTP Does and Does Not Tell You
RTP is useful for comparing games and making an informed choice about which game is least costly to play for entertainment. It does not tell you:
- What your individual session result will be
- How long your bankroll will last (that depends on variance)
- Whether a casino is operating fairly (a rigged RNG can produce any advertised RTP figure in theory)
For RTP figures to be trustworthy, they need to come from either a certified independent audit (traditional casinos) or a verifiable provably fair system (some crypto casinos). See provably fair explained for how that verification works.
The house edge and RTP are the single most important numbers to understand before placing any bet. Every other feature of a gambling platform — bonuses, design, game variety, payout speed — is secondary. For further context on where the house edge sits within a casino’s full business model, continue to how crypto casinos make money.