Di house edge inna roulette
Di part a each stake weh di casino keep, pon average.
European roulette: 2.70% pon evry standard bet, cause di payout dem work out like seh 36 pocket deh pon di wheel, but 37 deh deh.
Weh it come fram
Fair odds fi a straight upbet demStraight upOne single numba, pay 35:1.Read di whole ting → woulda be 36 to 1, cause 36 way deh fi lose fi evry one way fi win. Di casino pay 35 to 1. Di unitmoney mattaUnitDi base stake weh a system or a playa work wid. Dem describe progression inna unit suh dem work at any table.Read di whole ting → weh missin, spread ova 37 result weh all have di same chance, a 1/37 = 2.70% a di stake evry spin. Di same short show up inna evry payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting →, cause evry payout use di 36/n − 1 rule: a splitbet demSplitTwo numba weh deh side by side, pay 17:1.Read di whole ting → pay 17 instead a 17.5, a dozenbet demDozen1–12, 13–24 or 25–36, pay 2:1.Read di whole ting → pay 2 instead a 2.083, redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → pay 1 instead a 1.056. Di gap always a 1/n unit pon evry win, an n/37 win come evry spin, suh it always a 1/37 evry spin.
Edge an hold, nuh di same ting
Edge a di expected lossmathsExpected lossExpected value times all di money yuh bet; di average amount yuh lose ova a session or a period (di loss yuh fi expec pon average).Read di whole ting → pon evry unit yuh bet: 2.70% evry spin. Holdmoney mattaHoldDi part a di money weh playa bring to di table weh di casino really keep (di part weh di house keep). It higher dan di house edge cause people bet di winnins again.Read di whole ting → a wah di casino really keep outta di money yuh bring come a di table, an it much higher cause yuh bet back yuh winnins. A $100 buy-inpon di tableBuy-inFi change cash fi chip at di table. Yuh do it between spin, an yuh put di cash pon di betting layout, yuh nuh hand it to di dealer.Read di whole ting → weh yuh bet $10 at a time ova 200 spin done turn ova $2,000 an pay bout $54 inna edge; di hold pon dat buy-in a 54%. Casino report di hold; playa fi tink inna edge.
Wah mek evry bet have di same edge
Dem design it suh; it nuh happen by chance. Di 36/n − 1 rule set inna di 18th century, an later dem tek out di double zeroversionDouble zeroDi 00 pocket pon di American wheel. Because it deh deh, di house edge go up fram 2.70% to 5.26%.Read di whole ting → an neva touch di payout dem. If di payout dem did fair fi 37 pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting →, di straight up woulda pay 36 to 1 an di casino wudda nuh mek nuh money. Di same edge pon evry bet mek tings easy: no roulette bet a “sucker bet” nex to anodda one, only exception a di American five-numba bet at 7.89%.
Wah di roulette edge nuh mean
It nuh di probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → fi lose a session; most short session a variancemathsVarianceA measure a ow wide di result dem spread roun di expected value. High fi straight up, low fi even-money bet.Read di whole ting → decide dem, an bout 42% a 100-spin even-money session end up ahead. It nuh a fee fi each session; it grow wid turnovermoney mattaTurnoverAll di money yuh bet ova a session or a period, countin di winnins yuh bet again (all di money yuh bet, roun afta roun). Nex name: handle, action.Read di whole ting →, suh a progressionstrategy demProgressionAny rule weh change di stake based pon di result dem weh pass. Negative progression raise it afta loss, positive progression afta win.Read di whole ting → weh bet more pay more. No bet pattern cyaan water it dung, cause di edge dem a bet weh yuh put dung same time add up by di size a dem stake.
Inna money
Fi evry $1,000 yuh bet, di expected loss a $27.03 inna European rouletteversionEuropean rouletteSingle-zero wheel, 37 pocket, house edge a 2.70%. Di main model pon dis site.Read di whole ting →, $52.63 inna American, $13.51 pon even-money betbet demEven-money betRed/black, odd/even, high/low. 18 numba, pay 1:1.Read di whole ting → wid la partagerule demLa partageFrench rule: wen zero hit, half a di even-money stake come back. It cut di house edge pon dem bet deh inna half, to 1.35%.Read di whole ting →. A regula weh bet $500 a evenin, two time a week, fi a year done turn ova $52,000 an pay bout $1,400 inna edge pon a European wheel. Di figure small evry spin, but it nuh let up evry year.
Evry spin or evry bet weh settle
Almost evry roulette bet settle inna one spin, suh di edge evry spin an di edge evry bet a di same numba. A bet weh can push an stay pon di betting layoutgearBetting layoutDi bettin grid weh print pon di table. Nex name: table, felt, cloth.Read di whole ting → have two. Di teal bet inna Riverboat Roulette cover 3 numba pon a American wheel, win at 2 to 1 if one a dem come up bifo one a 8 White numba, an push pon evryting else. Fi evry bet weh settle, it lose 2/11 a di stake, 18.18%. Fi evry spin it lose 2/38, 5.26%, cause pon average a bet stay up fi 38/11 spin, bout 3.5. Both figure correct. Di figure fi each spin line up di bet wid di res a di table an show wah a hour cost; di figure fi each settle bet show ow much a each stake come back wen di bet finally settle.
Wen a casino get di price wrong
Evry edge pon dis page come fram arithmetic weh casino normally get right. Sometime dem nuh get it right. Inna October 1994 di Grand Casino inna Biloxi, Mississippi, did offa 80 to 1 pon tree dice weh add up to 4, an di same pon 17. Tree dice can fall 216 way an only 3 a dem add up to 4, suh di bet give back 81 × 3/216 = 1.125 fi evry unit yuh stake: a 12.5% edge fi di playa. Playa dem notice. Di casino lose bout $180,000 inna one day, close di bet, an open it back at 60 to 1, an dat turn di same 3 chance outta 216 inna a 15.3% edge fi di house. Hunacek (2025), weh quote Bollman, tell di story. Di standard roulette payout dem too simple fi get wrong dis way; a di odd side betbet demSide betA extra bet weh yuh nuh haffi mek, weh hook on to di main game, usually pon a run, a bonus ting or a jackpot. Almos always it cost more dan di standard bet dem.Read di whole ting → dem weh di arithmetic worth fi check.
Side bet inna di odda table game dem
Bollman (2021) put di main bet dem a blackjack, baccarat, craps an roulette side by side wid normal side bet pon di same table dem. Inna di fus tree game, di side bet cost more dan di main bet, nuff time plenty more. Di exception a di las game inna di table: di edge a American rouletteversionAmerican rouletteWheel wid 0 an 00, 38 pocket, house edge a 5.26%. It nuh di main model pon dis site.Read di whole ting → a 5.26% pon di main bet dem, high enough dat a side bet like Colors or WINGO can come cheaper.
Formula
Question dem
No. It a 2.70% a wah yuh bet. If yuh bet back di same money, yuh a bet it again.
No. It a proportion. Di expected loss inna dollar grow wid di stake.
If yuh measure by di edge, all standard European bet equal; dem only different inna ow often dem win an ow much dem pay. Wid la partage, di even-money bet dem edge a half a di odda dem.
Fun wid maths
Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.
Pon a European wheel, a straight upbet demStraight upOne single numba, pay 35:1.Read di whole ting → an a bet pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → both cost 2.70%, even though one cover jus one numba an di odda one cover eighteen. Wah mek evry bet have di same house edgemathsHouse edgeDi part a evry stake weh di casino keep pon average: 2.70% inna European roulette.Read di whole ting →?
Show di ansa
Ansa Evry payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting → set like di zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting → neva deh deh, suh evry bet lose one unitmoney mattaUnitDi base stake weh a system or a playa work wid. Dem describe progression inna unit suh dem work at any table.Read di whole ting → inna 37 spin, nuh mind wah it cover.
Tek a bet pon n numba. It pay (36 − n)/n to 1. Ova 37 spin it win n time pon average, an lose 37 − n time.
Di win dem bring in n × (36 − n)/n = 36 − n unit. Di loss dem cost 37 − n unit. Di difference a −1 unit evry 37 spin, an di n cancel out: di result a di same fi a straight up, a cornerbet demCornerFour numba weh share a corner pon di betting layout, pay 8:1.Read di whole ting → or a dozenbet demDozen1–12, 13–24 or 25–36, pay 2:1.Read di whole ting →. One unit lose outta 37 a 2.70%.
Pon a wheel wid N pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting →, di same sum gi yuh (36 − N)/N, suh −2/38 = 5.26% pon a American wheel. Di one bet weh bruk di pattern a di American five-numba bet: di rule seh it fi pay 6.2 to 1, it pay 6, an it cost 7.89%.
Keno, di lottery-style game, keep 25% or more a wah people bet. If a casino did add zero dem to a roulette wheel an lef di payout dem same way, ow much zero it woulda tek fi mek roulette cost as much as keno?
Show di ansa
Ansa Twelve zero: a 48-pocket wheel.
Wid z zero, di wheel have 36 + z pocket, an di payout dem still a count pon 36. By di rule inna di puzzle up top, evry bet lose z unit inna 36 + z spin, suh di house edge a z/(36 + z).
Set dat equal to one quarter: 4z = 36 + z, suh z = 12. Twelve zero pon a 48-pocket wheel woulda cost 25%.
Di triple-zero wheel pon di Las Vegas Strip, di dearest roulette most playa wi meet, have one quarter a dat much.
zeropockethouse edge1372.70%2385.26%3397.69%44010.00%124825.00%Di Massachusetts Lottery start a wheel inna 2023 wid 36 numba an nuh zero. One numba pay 25 fi 1, an red, blackbet demBlackEven-money bet pon di 18 black numba. Inna French: noir.Read di whole ting →, odd or even pay 3 fi 2. Wid nuh zero, it cheaper dan roulette?
Show di ansa
Ansa No, it dear bad: 30.56% pon a numba an 25% pon red or black, gainst 2.70% pon a European wheel.
“Fi” include di stake. A $1 numba bet gi back $25 one time inna 36 draw pon average: $25 back fi $36 weh yuh put dung, a loss a $11 inna 36, 30.56%.
A $2 bet pon red gi back $3 half di time: $3 back fi evry $4 weh yuh put dung, a loss a 25%.
A zero a jus one way fi set a price. Roulette pay like it have 36 pocket an den add a 37th; dis wheel have 36 pocket an jus pay less. Bollman (2024) set it as a exercise.
A casino waan a new bet pon di eleven prime numbamathsPrime numbaA whole numba ova 1 weh only 1 an itself divide exact: 2, 3, 5, 7, 11, 13 an suh on.Read di whole ting → fram 1 to 36: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 an 31. Wah it fi pay fi cost di same 2.70% as evry odda bet pon a European wheel? Wah it woulda cost at 2 to 1?
Show di ansa
Ansa 25 to 11, bout 2.27 to 1. At 2 to 1 it woulda cost 10.81%.
Use di rule fram di fus puzzle: a bet pon n numba pay (36 − n)/n to 1. Wid n = 11 dat a 25/11 to 1, a awkward payout, cause a $10 chipmoney mattaChipA token weh stand fi a fix amount, weh yuh put pon di betting layout fi mek a bet. Nex name: check.Read di whole ting → woulda win $22.73.
At 2 to 1, a $1 bet win $2 pon 11 spin outta 37 an lose $1 pon di odda 26: 22 − 26 = −4 unit evry 37 spin, 10.81%.
Dat a why roulette sell bet pon 1, 2, 3, 4, 6, 12 an 18 numba: 36 divide by evry one a dem, suh di fair payout a whole numba. Taylor (2021) set di exercise wid ten prime; but it have eleven.
Sumting fi laugh
1/37 a evry stake, pon evry bet, evry spin.
Source dem
- 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.