House Edge for Roulette
Di part of every stake wey di casino dey keep for average.
European roulette: 2.70% for every standard bet, becos dem calculate payouts as if na 36 pockets dey, but na 37 dey.
How E Take Come
Fair odds for straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → go be 36 to 1, becos 36 ways dey to lose for every one way to win. Di casino dey pay 35 to 1. Di unitmoniUnitDi base stake wey system or player dey work with. Dem dey describe progressions in units so dat dem go fit work for any table.Read di whole tin → wey miss, wey dem spread over 37 outcomes wey get di same chance, na 1/37 = 2.70% of di stake for every spin. Di same shortfall dey show for every payoutmoniPayoutWetin bet wey win dey return, wey dem dey quote as “X to 1” on top di stake wey dem return.Read di whole tin → becos every payout dey use di 36/n − 1 rule: splitbetSplitTwo numbers wey dey near each oda, e dey pay 17:1.Read di whole tin → dey pay 17 instead of 17.5, dozenbetDozen1–12, 13–24 or 25–36, e dey pay 2:1.Read di whole tin → 2 instead of 2.083, redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → 1 instead of 1.056. Di gap na always 1/n units for every win, and n/37 wins for every spin, so na always 1/37 for every spin.
Edge Compared to Hold
Edge na di expected lossmathsExpected lossExpected value times di total moni wey you bet; di average amount wey you go lose for one session or one period.Read di whole tin → for every unit wey you bet: 2.70% for every spin. HoldmoniHoldDi part of di moni wey players bring come di table wey di casino keep for real. E high pass di house edge becos players dey bet dia winnings again.Read di whole tin → na wetin di casino really keep from di moni wey you bring come di table, and e high well well pass, becos you dey bet your winnings again. $100 buy-intableBuy-inTo change cash to chips for di table. You go do am between spins, and you go put di cash on top di layout, you no go hand am give di dealer.Read di whole tin → wey you bet $10 at a time across 200 spins don turn over $2,000 and pay about $54 for edge; di hold on dat buy-in na 54%. Casinos dey report hold; players suppose think for edge.
Why Every Bet Get Di Same Edge
Na design choice, no be coincidence. Dem fix di 36/n − 1 rule for di 18th century, and dem remove di double zerotype of rouletteDouble zeroDi 00 pocket of di American wheel. Becos e dey there, di house edge go up from 2.70% to 5.26%.Read di whole tin → later without to touch di payouts. If di payouts dey fair for 37 pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →, straight up go pay 36 to 1 and di casino no go get income. Di edge wey be di same everywhere dey convenient: no roulette bet na “sucker bet” compared to anoda, except only di American five-number bet for 7.89%.
Wetin Di Roulette Edge No Be
E no be di probabilitymathsProbabilityDi chance of one outcome, from 0 to 1 or from 0% to 100%. One number: 1/37 = 2.70%.Read di whole tin → sey you go lose one session; na variancemathsVarianceOne measure of how wide di results dey spread around di expected value. E high for straight up, e low for even-money bets.Read di whole tin → dey decide most short sessions, and about 42% of even-money sessions of 100 spins dey end for profit. E no be fee for every session; e dey grow with turnovermoniTurnoverDi total moni wey you bet for one session or one period, including winnings wey you bet again. Dem also dey call am: handle, action.Read di whole tin →, so progressionstrategyProgressionAny rule wey dey change di stake based on di results wey don pass. Negative progressions dey raise am afta losses, positive ones afta wins.Read di whole tin → wey dey bet more dey pay more. E no be tin wey bet pattern fit dilute, becos di edges of bets wey you put di same time dey add up according to dia stakes.
For Moni
For every $1,000 wey you bet, di expected loss na $27.03 for European roulettetype of rouletteEuropean rouletteSingle-zero wheel, 37 pockets, house edge 2.70%. Na di main model for dis site.Read di whole tin →, $52.63 for American, $13.51 for even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin → with la partageruleLa partageFrench rule: when zero come out, dem go return half of even-money stake. E dey cut di house edge for dose bets into half, to 1.35%.Read di whole tin →. Regular player wey dey bet $500 every evening, two times every week, for one year don turn over $52,000 and pay about $1,400 for edge for European wheel. Di figure small for every spin, but e no dey stop for di whole year.
For Every Spin or for Every Bet Wey Settle
Almost every roulette bet dey settle with one spin, so im edge for every spin and im edge for every bet na di same number. Bet wey fit push and stay for di layoutequipmentLayoutDi betting grid wey dem print for di table. Dem also dey call am: table, felt, cloth.Read di whole tin → get two. Di teal bet of Riverboat Roulette dey cover 3 numbers of American wheel, e dey win for 2 to 1 if one of dem show before one of 8 White numbers, and e dey push for everytin else. For every bet wey settle, e dey lose 2/11 of di stake, 18.18%. For every spin e dey lose 2/38, 5.26%, becos for average one bet dey stay for 38/11 spins, about 3.5. Both figures correct. Di per-spin figure dey compare di bet with di rest of di table and set wetin one hour go cost; di per-settled figure dey tell how much of every stake go come back when di bet finally settle.
When Casino Price Am Wrong
Every edge for dis page dey come from arithmetic wey casinos dey normally get correct. Sometimes dem no get am correct. For October 1994, di Grand Casino for Biloxi, Mississippi, offer 80 to 1 for three dice wey total 4, and di same for 17. Three dice dey fall 216 ways and only 3 of dem dey total 4, so di bet return 81 × 3/216 = 1.125 for every unit wey you stake: edge of 12.5% for di player side. Players notice. Di casino lose about $180,000 for one day, close di bet, and open am again for 60 to 1, wey turn di same 3 chances out of 216 to edge of 15.3% for di house. Hunacek (2025), wey cite Bollman, tell di story. Di standard payouts of roulette simple too much to get wrong like dis; im unusual side betsbetSide betExtra bet wey you fit choose wey dem join to di main game, usually on streak, bonus event or jackpot. E dey almost always cost pass di standard bets.Read di whole tin → na where e worth to check di arithmetic.
Side Bets for Di Oda Table Games
Bollman (2021) put di main bets of blackjack, baccarat, craps and roulette side by side with di usual side bets for di same tables. For di first three games, di side bet dey cost more pass di main bet, often many times more. Di exception na di last game for di table: di edge of American roulettetype of rouletteAmerican rouletteWheel wey get 0 and 00, 38 pockets, house edge 5.26%. E no be di main model wey dis site dey use.Read di whole tin → na 5.26% for di main bets, high reach di level wey side bet like Colors or WINGO fit come cheaper.
Formula
Questions wey pipo dey ask
No. Na 2.70% of wetin you bet. If you bet di same moni again, you don bet am again.
No. Na proportion. Di expected loss for dollars dey grow with di stake.
If you measure am by di edge, all standard European bets dey equal; dem different only for how often dem dey win and how much dem dey pay. With la partage, even-money bets na half of di oda ones.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
For European wheel, straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → and bet on redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → dey both cost 2.70%, even though one dey cover only one number and di oda one dey cover eighteen. Why every bet get di same house edgemathsHouse edgeDi part of each stake wey di casino dey keep for average: 2.70% for European roulette.Read di whole tin →?
Show di solution
Answer Dem set every payoutmoniPayoutWetin bet wey win dey return, wey dem dey quote as “X to 1” on top di stake wey dem return.Read di whole tin → as if di zerowheelZeroDi one green pocket wey no even-money, dozen or column bet dey cover; na im be di source of di house edge. Dem also dey call am: single zero, 0.Read di whole tin → no dey there, so every bet dey lose one unitmoniUnitDi base stake wey system or player dey work with. Dem dey describe progressions in units so dat dem go fit work for any table.Read di whole tin → for 37 spins, no matter wetin e cover.
Take one bet on n numbers. E dey pay (36 − n)/n to 1. For 37 spins, e go win n times for average and e go lose 37 − n times.
Di wins dey bring n × (36 − n)/n = 36 − n units. Di losses dey cost 37 − n units. Di difference na −1 unit every 37 spins, and n don cancel: di result na di same for straight up, cornerbetCornerFour numbers wey share one corner for di layout, e dey pay 8:1.Read di whole tin → or dozenbetDozen1–12, 13–24 or 25–36, e dey pay 2:1.Read di whole tin →. One unit wey you lose for 37 na 2.70%.
For wheel wey get N pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →, di same sum dey give (36 − N)/N, so −2/38 = 5.26% for American wheel. Di one bet wey break di pattern na di American five-number bet: di rule tok sey e suppose pay 6.2 to 1, e dey pay 6, and e dey cost 7.89%.
Keno, di game wey be like lottery, dey keep 25% or more of wetin pipo bet. If casino add zeros to roulette wheel and leave di payouts as dem be, how many zeros e go take to make roulette cost reach keno?
Show di solution
Answer Twelve zeros: wheel wey get 48 pockets.
With z zeros, di wheel get 36 + z pockets, and di payouts still assume 36. By di rule for di puzzle wey dey up, every bet dey lose z units for 36 + z spins, so di house edge na z/(36 + z).
Make am equal one quarter: 4z = 36 + z, so z = 12. Twelve zeros for wheel of 48 pockets go cost 25%.
Di triple-zero wheel for di Las Vegas Strip, di roulette wey cost pass wey most players go see, get only one quarter of dat number of zeros.
zerospocketshouse edge1372.70%2385.26%3397.69%44010.00%124825.00%Di Massachusetts Lottery launch one wheel for 2023 wey get 36 numbers and no zero. One number dey pay 25 for 1, and red, blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin →, odd or even dey pay 3 for 2. Since zero no dey, e cheap pass roulette?
Show di solution
Answer No, e cost pass well well: 30.56% for one number and 25% for red or black, against 2.70% for European wheel.
“For” dey include di stake. $1 bet on one number dey return $25 once for 36 draws for average: $25 come back for $36 wey you stake, loss of $11 for 36, 30.56%.
$2 bet on red dey return $3 half of di time: $3 come back for every $4 wey you stake, loss of 25%.
Zero na only one way to set price. Roulette dey pay as if 36 pockets dey and e add di 37th; dis wheel get 36 pockets and e just dey pay less. Bollman (2024) give am as exercise.
One casino wan create new bet on di eleven prime numbersmathsPrime numberWhole number wey pass 1 wey only 1 and imself fit divide exactly: 2, 3, 5, 7, 11, 13 and so on.Read di whole tin → from 1 to 36: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31. Wetin e suppose pay make e cost di same 2.70% as every oda bet for European wheel? How much e go cost for 2 to 1?
Show di solution
Answer 25 to 11, about 2.27 to 1. For 2 to 1, e go cost 10.81%.
Use di rule from di first puzzle: bet on n numbers dey pay (36 − n)/n to 1. With n = 11, na 25/11 to 1, payout wey no easy, becos $10 chipmoniChipToken wey stand for one fixed amount, wey you put on top di layout to make bet. Dem also dey call am: check.Read di whole tin → go win $22.73.
For 2 to 1, $1 bet dey win $2 for 11 spins out of 37 and e dey lose $1 for di oda 26: 22 − 26 = −4 units every 37 spins, 10.81%.
Na why roulette dey sell bets on 1, 2, 3, 4, 6, 12 and 18 numbers: 36 fit divide by each of dem, so di fair payout na whole number. Taylor (2021) give di exercise with ten primes; na eleven dey.
Small laugh
1/37 of every stake, for every bet, every spin.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Hunacek, M. Quantitative Literacy Through Games and Gambling.