Roulette Wheels Wey No Common
Wheels wey get 18, 25, 26, 31, 40, 49, 62, 73 or 105 pockets. One rule dey price almost all of dem: di share of pockets wey di payouts ignore.
When dem set payouts as if di house pockets no dey dia, di house edgemathsHouse edgeDi part of each stake wey di casino dey keep for average: 2.70% for European roulette.Read di whole tin → na house pockets divide by all di pockets, no matter how big di wheel be. Most unusual wheels dey follow dat rule. Di interesting ones na di ones wey break am: payout wey dem round, bonus round, or bet wey dey stay up for plenty spins.
One rule for all di wheels
European roulettetype of rouletteEuropean rouletteSingle-zero wheel, 37 pockets, house edge 2.70%. Na di main model for dis site.Read di whole tin → dey pay 35 to 1 as if di wheel get 36 pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →. E get 37, and di pocket wey miss na di 2.70% edge. Di same rule dey work for any wheel: with N numbers and Z house pockets, bet on n numbers wey dey pay (N − n)/n to 1 get edge of Z/(N + Z). Pipo don build or propose wheels of every size on top dis rule, and di table arrange dem by price. Im rows still give di basics of how to play Royal Roulette, di Australian game: im numbers na di cards 2 reach king, im two house pockets na di ace and di joker, and one card dey pay 47 to 1.
Bigger fit cheap pass
Players dey see 62-pocket wheel as longer shot and dem dey think sey di game worse. Di edge depend only on di share of house pockets. Super 62 get two zeroswheelZeroDi 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 →, like di American wheel, but dem be 2 out of 62 pockets, no be 2 out of 38, so e cost 3.23% against 5.26%. Roulette 73, wey get 72 numbers and one zero, for cost 1.37%, almost di same as French even money. Di rule dey work di oda way for small wheel. Bollman describe one old wheel of 18 pockets, 1 reach 16 plus 0 and 00. By di rule, every bet for cost 2/18, 11.11%: two house pockets na big share of small wheel.
Where di rule break: rounding
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 → must be 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 → amount wey make sense, and when di rule give fraction, di casino dey round am down. Di Avenue bet of 100 To 1 Roulette cover 15 pockets and e suppose pay 5⅔ to 1; e dey pay 11 to 2, and dis one raise im edge from 4.76% to 7.14%. For Super 62, seven numbers get di digit 6 (6, 16, 26, 36, 46, 56, 60) and di bet on dat digit dey pay 7 to 1, wey make am 9.68%, three times di rest of di layoutequipmentLayoutDi betting grid wey dem print for di table. Dem also dey call am: table, felt, cloth.Read di whole tin →. Di White bet of Riverboat Roulette cover 8 numbers at 7 to 2; for table wey no get 50-cent chips, $5 winner dey collect $17 instead of $17.50, and dis one raise di edge from 5.26% to 7.37%. Di American five-number bet, at 7.89%, na di case wey pipo sabi of di same tin.
Where di rule break: bonuses
Fast Action Roulette, wey dem launch for Marina Bay Sands for 2020, dey run real wheel wey get four zeros, wey for cost 10% on im own. Ten Bonus numbers dey light up anyhow for every spin. Straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → dey pay 35 to 1, 40 to 1 if im number na Bonus number, and 80 to 1 if im whole row of four na Bonus, and dis one bring am to 6.65%. Di oda three bets of di game cost far more. Double Bonus Spin from IGT dey add yellow Bonus pocket, one and half pockets wide, join American wheel; when di ballequipmentBallDi small ball wey dem dey throw for di track against di rotor. Modern balls na ivorine or Teflon, 18–21 mm.Read di whole tin → land dia, every bet go get two free spins. By our calculation, dat one reduce di edge to between 1.94% (straight up) and 2.73% (even money), below di plain American wheel. Bollman (2021) print 3% to 16% for dis game; im simplified formula get algebra mistake, and for even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin → e mean sey di free spins dey lose pass di stake, and dat one no fit happen.
Where di rule break: bets wey dey stay up
Riverboat Roulette (2012) give 32 numbers of American wheel second colour. White mark di four pockets wey surround each zero (1, 2, 9, 10, 13, 14, 27, 28). Bet on one colour group dey win if one of im numbers come out before one of di eight White numbers. White number na “White Out” wey clear every colour bet. Every oda number na push: di bet go stay up, and between spins you fit remove am or raise am. Teal cover three numbers and e dey pay 2 to 1. For each bet wey settle, e dey lose 2/11 of di stake, 18.18%. For each spin, e dey lose 2/38, di 5.26% wey pipo sabi, becos for average di bet dey stay up 38/11, about 3.5 spins.
Wheel wey Thorp fit predict: Big Six
Di Big Six, or wheel of fortune, na big wheel wey stand up and get 54 slots: 24 dey pay 1 to 1, 15 dey pay 2 to 1, seven 5 to 1, four 10 to 1, two 20 to 1, and two logo slots dey pay 40 to 1. Zero no dey; di house dey take im share by paying short, and di edge run from 11.1% for di slots wey dey pay 1 to 1 reach 24.1% for di logos. For 1961, Thorp build predictor wey small like matchbox for am, wey toe switch dey work am, and for 1981, as e use wristwatch time one turn of casino wheel, e find sey most times e fit name where di wheel go stop within five slots. If you bet only di slots wey dey pay high near di prediction, e for return about +211%, if dem accept bets afta di wheel don spin. Dem no dey accept am, and di wheel dey turn slowly where everybody fit see, so late bet go show clear; Thorp write sey di game no get enough action to hide one.
Why only few dey catch on
Professional wheel cost thousands of dollars, and wheel wey get unusual number of pockets, dem must make am to order. So most new roulette games dey keep di standard wheel and add bets, and na why di side-bet page long pass dis one. Di 31-pocket eagle wheel of America for di 19th century, at 12.90% for one number and 9.68% for everytin else, die becos of im own price. Di idea of third house pocket come back for 2016 for 39-pocket wheel, where e cost 7.69%.
Questions wey pipo dey ask
No be by im size alone. Di edge na di share of house pockets: 1 in 73 cheap pass 1 in 37.
Roulette 73, at 1.37%, but na design wey dem publish, no be table wey you fit find easily. Among wheels wey dem don offer players, Super 62 at 3.23% dey follow afta European and French.
Somebody must pay for bonus, usually by cut for di base payout or by separate bet wey get high edge.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
Royal Roulette, wey dem develop for Australia, get 50 pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →: di 48 cards from 2 reach king, plus one ace and one joker. One card dey pay 47 to 1, two cards 23 to 1, three 15 to 1, four 11 to 1, six 7 to 1, eight 5 to 1, twelve 3 to 1, sixteen 2 to 1 and twenty-four 1 to 1. Which rule dey make dis payoutsmoniPayoutWetin bet wey win dey return, wey dem dey quote as “X to 1” on top di stake wey dem return.Read di whole tin →, and how much every bet dey cost?
Show di solution
Answer Each bet on n cards dey pay (48 − n)/n to 1, so every bet dey cost 2/50 = 4%.
Try di rule for some bets: 47/1 = 47, 36/12 = 3, 32/16 = 2, 24/24 = 1. E fit all nine. Di rule dey price di wheel as if e get 48 pockets, so di ace and di joker na di two house pockets, exactly like 0 and 00 for American wheel.
Two house pockets out of 50 dey give edge of 4%. “European” version dey remove di joker and keep di payouts: one house pocket for 49, edge of 2.04%.
Super 62 get one bet sey one digit wey you choose go show for di number wey win. Design di same bet for normal American wheel. How many of di numbers 1 to 36 get each digit, and which payouts go keep di usual 5.26%?
Show di solution
Answer Na only digits wey get 3 or 4 numbers go get clean payouts (11 to 1 and 8 to 1). Dem no fit pay di digits 1, 2 and 3 fairly with whole chipsmoniChipToken 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 →.
Count di numbers. Digit 1 dey inside 1, 10 to 19, 21 and 31: 13 numbers. Digit 2 dey also inside 13 numbers and digit 3 inside 10. Di digits 4, 5 and 6 dey inside four numbers each (4, 14, 24, 34), and 7, 8 and 9 inside three each.
Bet on n numbers dey keep di American edge if e pay (36 − n)/n to 1. Dat one dey give 8 to 1 for four numbers and 11 to 1 for three, both na whole numbers. For 13 numbers e dey give 23/13, about 1.77 to 1, and for 10 numbers 2.6 to 1. Round 1.77 down to 7 to 4 and di bet go cost 5.92%; round am up to 2 to 1 and di player go get 2.63% edge. If you round 2.6 down to 5 to 2, e go be 7.89%.
Di digit 0 na choice: 10, 20 and 30 alone dey pay 11 to 1 for 5.26%; add 0 and 00 and e go be five-number bet, 6 to 1 for 7.89%, like di basketbetBasketFor single-zero wheel: 0, 1, 2, 3 with one chip, e dey pay 8:1. Dem also dey call am: first four, quatre premiers.Read di whole tin →.
digitnumberswetin di rule tokwetin e fit payhouse edge1, 2131.77 to 17 to 45.92%3102.6 to 15 to 27.89%4, 5, 648 to 18 to 15.26%7, 8, 9311 to 111 to 15.26%100 To 1 Roulette dey pay (100 − n)/n to 1 for most bets, for wheel of 100 numbers and 5 house symbols. Im bets dey cover 1, 2, 3, 4, 5, 10, 15, 20 or 50 pockets and dem dey pay 100, 49, 32, 24, 19, 9, 11 to 2, 4 and 1 to 1. Di straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → and di Avenue of 15 pockets dey break di rule. Which oda bet dey break am, and how much e dey cost?
Show di solution
Answer Di bet on three pockets: di rule tok 32⅓ to 1, e dey pay 32 to 1, and e dey cost 5.71% instead of 4.76%.
Check each payout against di rule: 98/2 = 49, 96/4 = 24, 95/5 = 19, 90/10 = 9, 80/20 = 4 and 50/50 = 1 all fit. For three pockets di rule dey give 97/3 = 32⅓, wey no chip fit pay, so dem round am down to 32.
Di bet dey win 3 times for 105 spins and e dey return 33 unitsmoniUnitDi 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 → including di stake: 3 × 33 = 99 units come back for every 105 wey you stake, loss of 6/105 = 5.71%.
Roulette 73, one design wey dem publish, get 72 numbers and one 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 →, and every bet dey pay (72 − n)/n to 1. You fit cover im 24 gray numbers with 14 chips: 4 straight ups and 10 splitsbetSplitTwo numbers wey dey near each oda, e dey pay 17:1.Read di whole tin →. How much dat bet of 14 chips dey cost?
Show di solution
Answer 1.37% of di 14 chips, like every oda bet for dat wheel.
Di long way: straight up dey pay 71 to 1 and split dey pay 35 to 1. If one of di 4 straight-up numbers come out, you win 71 and lose di oda 13 chips: +58. If one of di 20 split numbers come out: +35 − 13 = +22. For di oda 49 pockets you lose all 14. For average over 73 spins: 4 × 58 + 20 × 22 − 49 × 14 = 232 + 440 − 686 = −14 units, wey be 1/73 of each chip.
Di short way: expected valuesmathsExpected valueDi average result for each bet for di long run. −1/37 of di stake for every standard European bet.Read di whole tin → dey add up. Each chip na normal bet wey dey lose 1/73 of imself, so 14 chips dey lose 14/73. To combine bets dey change how di results spread, e no dey ever change wetin dem cost.
Super 62 get 60 numbers, 0 and 00, and e dey pay (60 − n)/n to 1. Di pipo wey design am also draw am with one, three and four house pockets. Alphabetic Roulette dey pay (24 − n)/n to 1 for 25 pockets, and e get one type where Y and Z get dia own pockets. Price all five.
Show di solution
Answer With one reach four zeros: 1.64%, 3.23%, 4.76% and 6.25%. Alphabetic with Y and Z separate: 7.69%.
Each of dem dey keep im payouts and e dey change only di number of house pockets, so di edge na house pockets ÷ all di pockets.
One zero, 61 pockets: 1/61 = 1.64%. Two, 62 pockets: 2/62 = 3.23%. Three, 63 pockets: 3/63 = 4.76%. Four, 64 pockets: 4/64 = 6.25%. Each zero wey dem add dey cost about one point and half.
Alphabetic dey pay as if e get 24 letters. When Y and Z dey share one pocket, di house get 1 for 25, 4%. When Y and Z dey separate, e get 2 for 26, 7.69%, reach di level of triple-zero wheel. To split one pocket into two almost double di price.
wheelpocketshouse pocketshouse edge60 numbers, one zero6111.64%Super 626223.23%60 numbers, three zeros6334.76%Super 646446.25%Alphabetic2514.00%Alphabetic, Y and Z separate2627.69%One old wheel get 18 pockets: 1 to 16, 0 and 00. Odd numbers and 0 na redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin →, even numbers and 00 na blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin →, and di 16 numbers sit for layoutequipmentLayoutDi betting grid wey dem print for di table. Dem also dey call am: table, felt, cloth.Read di whole tin → of 4 by 4. Design pay tablemoniPay tableDi list of wetin each bet or each result dey pay. For machines and side bets, na there dem dey set di house edge.Read di whole tin → wey go give every bet di same edge. And why 0 must lose bet on red, even though e be red?
Show di solution
Answer Pay (16 − n)/n to 1: 15 to 1 for one number, 7 for two, 3 for four, 1 for eight. Every bet dey cost 11.11%. If 0 win di red bet, red go be fair bet.
Price di wheel as if 0 and 00 no dey there. Bet on n numbers dey win n times for 18 and e dey pay (16 − n)/n to 1, so e dey bring back 16 units, stake inside, for every 18 wey you stake. Every bet dey cost 2/18, 11.11%.
Di natural bets of di layout dey come out whole: one number 15 to 1, two wey dey side by side 7 to 1, one row or one columnbetColumnTwelve numbers for one column of di layout wey stand from up to down, e dey pay 2:1.Read di whole tin → of four 3 to 1, and two rows, or di odd, even, low or high eight, 1 to 1. Bet on three numbers go need 4⅓ to 1; if dem round am down to 4 to 1, e go cost 16.67%.
Red dey cover di eight odd numbers. If 0, wey be red, also win di red bet, red go cover 9 out of di 18 pockets for 1 to 1: fair gamemathsFair gameGame where no side get edge: every bet get expected value of zero.Read di whole tin → wey no get edge at all. Di house pockets dey get dia edge only by losing every bet except bet on dem.
Small laugh
Count di house pockets, then look for di rounding.
Sources
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”