Ever wonder why casinos always come out ahead? The answer is in casino mathematics — the simple, powerful ideas behind every game on the floor. With a few core concepts, you can read the odds, estimate your hourly cost of play, and make smarter decisions before you sit down.
In this guide, you’ll learn how house edge works, what expected value means for your wallet, how variance drives winning and losing streaks, and how to compare games like blackjack, roulette, craps, baccarat, slots, sports betting, and poker.

Casino Mathematics Basics: The House Always Has a Plan

Casinos don’t need luck. They rely on rules and payouts that create a built-in advantage called the house edge. Over the long run, this edge guarantees profit for the house and a predictable average cost for players.

Expected Value (EV) Made Simple

Expected value is the average amount you’ll win or lose on a bet if you could repeat it millions of times. Positive EV favors you; negative EV favors the house.

  • EV = (Probability of win × Win amount) − (Probability of loss × Loss amount).
  • House edge is the EV expressed as a percentage of your bet.

Variance, Volatility, and Why Streaks Happen

Variance measures how widely results can swing around the average. High-variance games (like many slots) deliver bigger swings; low-variance games (like baccarat banker bets) are steadier.

Variance explains why you can win in the short term even with a negative EV. Over enough trials, results trend toward the mathematical average.

Casino Mathematics in Action: Game-by-Game

Let’s translate the theory into numbers you can use at the table or machine.

Blackjack (with Basic Strategy)

  • Typical house edge: about 0.5% with good rules and perfect basic strategy.
  • Hourly decisions: roughly 60–100 hands per hour at full tables; faster heads-up.
  • Key idea: Using correct strategy matters more than “hunches.”

Example: $10 average bet × 80 hands × 0.5% ≈ $4 expected loss per hour (before comps).

Roulette

  • American roulette (0 and 00): house edge ≈ 5.26% on most bets.
  • European roulette (single zero): house edge ≈ 2.70%.
  • All standard bets on the same wheel share the same edge; only volatility differs.

Example (American): $10 per spin × 50 spins × 5.26% ≈ $26.30 expected loss per hour.

Craps

  • Pass Line: ≈ 1.41% house edge; Don’t Pass: ≈ 1.36%.
  • Free Odds bets have 0% house edge but require a Pass/Don’t Pass base bet.
  • Proposition bets often carry double-digit edges—avoid them.

Example: $10 Pass × 40 decisions × 1.41% ≈ $5.64 expected loss per hour (before odds).

Baccarat

  • Banker bet: ≈ 1.06% house edge (with standard 5% commission).
  • Player bet: ≈ 1.24%; Tie bet: often ≈ 14.36% (best avoided).

Example: $25 per hand × 60 hands × 1.06% ≈ $15.90 expected loss per hour on Banker.

Slots

  • Return to Player (RTP) commonly spans roughly 85–96% depending on jurisdiction and denomination.
  • High volatility means longer droughts and occasional big hits; budget accordingly.

Example: $1.50 spin × 500 spins × 8% edge (92% RTP) ≈ $60 expected loss per hour.

Sports Betting and Poker

  • Sportsbook “vig”: On -110 lines, expected loss is ≈ 4.54% if your true win rate is 50%.
  • Poker isn’t house-edge; the room takes “rake.” Your skill must beat opponents plus rake.

These markets illustrate statistical edge: you win long-term only if your predictions or decisions are stronger than the field plus fees.

Step-by-Step: How to Evaluate Any Bet

  1. Identify rules and payouts. Small rule changes (e.g., 6:5 blackjack) can double the edge against you.
  2. Find the house edge or RTP from reliable sources (game rules, regulators, reputable math sites).
  3. Estimate decisions per hour (hands/spins/rolls).
  4. Calculate expected hourly loss: Average bet × Decisions per hour × House edge.
  5. Account for variance: Higher volatility needs a larger bankroll to survive swings.

When in doubt, assume a slightly worse edge than advertised to stay conservative.

Real-Life Example: Maya’s $10 Blackjack Plan

Maya plays $10 blackjack with decent rules and uses basic strategy. She logs 10,000 hands over several months (about 125 hours at 80 hands/hour).

  • Expected loss = 0.5% × $10 × 10,000 = $500.
  • Standard deviation per hand ≈ 1.15 bets. Over 10,000 hands: 1.15 × $10 × √10,000 = $1,150.
  • Approximate 95% range: -$500 ± $2,300 → from about -$2,800 to +$1,800.

What happened? She finished down $900—well within the expected range. This is why short winning streaks don’t prove a system, and losing streaks don’t mean the game is “due.” It’s just variance doing what variance does.

Common Myths Debunked by Casino Probability

  • Myth: “Roulette is due for red.” Reality: Spins are independent; casino probability doesn’t keep score.
  • Myth: “Betting systems beat the table.” Reality: Progressions can’t overcome negative EV.
  • Myth: “Slots warm up.” Reality: Results are driven by RNG and programmed paytables.
  • Myth: “Tables are rigged at night.” Reality: Edges come from rules and payouts, not time of day.

Finding or Avoiding a Statistical Edge

Casinos design games so the house has the edge. Players only gain a statistical edge in rare, specific cases: perfect promotions, favorable video poker paytables, expert card counting with ideal conditions, or skilled sports/poker play. These demand knowledge, discipline, and often carry heat or limits.

Smart Bankroll and Responsible Play

  • Set a session budget you can comfortably lose.
  • Choose low-edge games with clear rules.
  • Slow your pace to reduce hourly cost.
  • Use basic strategy cards where allowed.
  • Take breaks; avoid chasing losses.
  • If gambling stops being fun, step away and seek help.

Conclusion

You don’t need to memorize formulas to benefit from casino mathematics. Know the house edge, estimate your hourly cost, respect variance, and pick bets that match your goals and budget. That’s how you keep the game fun—and under control.