Gambling, honestly: the math the casino hopes you skip
Free education on odds, expected value, and the house edge — plus calculators, downloadable worksheets, and real lottery odds. No sign-up, nothing to bet.
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Expected value, house edge per game, odds conversion, parlays, bankroll/Kelly, and lottery EV — all run in your browser.
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House-edge-by-game table, an odds-conversion sheet, and an EV/bankroll worksheet as CSV spreadsheets.
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Powerball, Mega Millions and friends — the real 1-in-hundreds-of-millions numbers and what a ticket is actually worth.
House edge & RTP — what every game keeps
The house edge is the casino's expected hold, as a percentage of your wager. Lower is better for you; none of these are zero or negative for the player. The two roulette rows below are computed live from our §4.7 odds engine: an American (double-zero) wheel keeps 5.26% and a European (single-zero) wheel keeps 2.70%.
| Game / bet | House edge | Return to player (RTP) | Notes |
|---|---|---|---|
| Video poker — 9/6 Jacks or Better (optimal play) | 0.46–5% | 99.54% | Best-paying paytable + perfect strategy. Worse paytables and misplays raise the edge sharply. |
| Blackjack (basic strategy) | 0.5% | 99.50% | Edge depends heavily on rules (decks, dealer hits/stands soft 17, double/split, surrender) and on the player using correct basic strategy. Card counting is a separate, advantage-play topic. |
| Baccarat — Banker (5% commission) | 1.06% | 98.94% | The single best bet at the baccarat table. |
| Baccarat — Player | 1.24–1.36% | 98.76% | Close behind the Banker bet. |
| Craps — Don't Pass | 1.36% | 98.64% | Don't Pass / Don't Come; marginally lower edge than the Pass line. |
| Craps — Pass Line | 1.41% | 98.59% | Pass / Come line. Backing it with free odds dilutes the overall edge toward 0. |
| Roulette (European, single 0) | 2.7% | 97.30% | Single-zero wheel; "la partage"/"en prison" rules can halve the edge on even-money bets. |
| Roulette (American, 0 and 00) | 5.26% | 94.74% | Double-zero wheel; every bet (except the 5-number) carries the same 5.26% edge. |
| Craps — Field (2 & 12 pay double) | 5.56% | 94.44% | One-roll bet; edge drops to 2.78% if the 12 (or 2) pays triple. |
| Slot machines (typical) | 2–15% | 94.00% | RTP is set by the operator and usually undisclosed; casino slots commonly hold 4–10%. |
| Sic Bo (varies by bet) | 2.78–30% | 92.00% | Small/Big ~2.78%; specific triples can exceed 16–30%. |
| Baccarat — Tie (8:1) | 4.8–14.4% | 85.60% | A sucker bet; ~14.4% at 8:1 (about 4.8% at 9:1). |
| Big Six / Money Wheel | 11–24% | 85.00% | One of the worst bets on the floor. |
| Keno | 25–35% | 73.00% | Lottery-like odds on the casino floor — among the highest edges anywhere. |
| State lottery / Powerball (draw games) | 30–55% | 50.00% | RTP is roughly ~50% — you keep about half of what is wagered, in aggregate, before taxes. |
RTP = 1 − house edge = the share of each dollar wagered that comes back to players in aggregate, over the very long run. It is not a promise for any single session; variance dominates the short run.
Implied probability & the vig (overround)
Odds are just a probability in disguise. A decimal price d implies a win probability of
1 / d. Bookmakers shade every price a little short, so the implied probabilities across a
market add up to more than 100%. That excess is the vig (a.k.a. juice / overround) — the
slice the book keeps no matter who wins.
Classic example: a sportsbook posts both sides of a game at −110. Each side implies 52.38%, so the two sides sum to 104.76% — an overround of 4.76%. The "fair" no-vig probability of each side is 50.00%. You are paying that 4.76% margin on every bet.
Expected value: +EV vs −EV
Expected value (EV) is the average result of a bet if you could repeat it forever:
EV = (Ptrue × payout) − (1 − Ptrue)
where payout is the net profit per unit staked on a win (decimal odds − 1). If your honest
probability estimate beats the price offered, EV is positive (+EV) — rare, and usually
competed away. If the price is worse than fair — the normal case, because of the vig and the house edge —
EV is negative (−EV) and you lose over time.
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Variance & bankroll
A negative expectation does not mean you lose every session — variance means short runs swing wildly, and that swing is exactly what keeps people playing. The longer you play a −EV game, the more the average asserts itself and the closer your results track the house edge. Sensible bankroll rules (only stake money you can lose, size bets as a small fraction of your bankroll, set loss limits and walk away) reduce the chance of ruin — they do not turn a −EV game positive.
The gambler's fallacy
Independent random events have no memory. After red hits five times on a fair roulette wheel, black is not "due" — the next spin is still 18/37 either way. Believing otherwise (the gambler's fallacy) is one of the most expensive mistakes in gambling. Related trap: the "hot hand" — assuming a streak will continue. Neither the wheel, the dice, nor the RNG knows what came before.
The one honest takeaway
There is no system, pattern, or trick that changes the house edge of a negative-EV game. Anyone selling you one is selling you the fallacy above. The realistic goals are: understand the true cost, treat it strictly as paid entertainment with money you can afford to lose, and know where the exit is. Want to play for fun with zero real money at risk? See the free, provably-fair, non-cashable KULA Arcade play-token games — entertainment only, with no real-money stake and no payout.