Boule and Small Small Wheels
Di small cousins of roulette: wheel of nine numbers for French casinos, dice wey get twenty sides, pin board, wheel wey dem pair with hopper of balls, and star of lights. One rule dey price all of dem.
Boule, wey some French casinos still dey deal, get nine numbers and e dey pay 7 to 1 on one of dem: 11.11%, four times European wheel. Roulette-18 dey roll dice instead of to spin wheel and e cost 5.26%. For online, Pin Ball and Spingo cost 2% to 4.76%, and Lucky Star, light wey dey run round one star, 2.22% to 4%. Diamond Roulette drop red and black for six colours and e sell one bet at 15.79%.
One rule, small small wheels
Di rule from di page of unusual wheels dey price dis games too: count di results wey di 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 → ignore and divide am by all di results. For European wheel, 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 → na 1 pocketequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin → out of 37. For small wheel, one house pocket na bigger share, so small games dey cost more, unless dem set di payouts anoda way.
Boule: na nine numbers
Boule na di small French cousin of roulette, wey some casinos for France still dey deal; one casino booklet for Antibes describe im rules. 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 → dey settle for one of nine numbers. Four na blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin → (1, 3, 6, 8), four na redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → (2, 4, 7, 9), and di 5, wey be yellow, na di house number. One number dey pay 7 to 1. Di even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin →, red or black, odd or even, low (1 reach 4) or high (6 reach 9), all of dem dey lose when di 5 come out. Every bet cost 1/9 = 11.11%, four times European wheel. One version for Genting for Malaysia number im wheel 0 reach 9 and e dey pay 8 to 1 on one number and 2 to 1 on three: 10%.
Avions: na seventeen numbers
Epstein (2013) record anoda small wheel, Avions, wey dem deal for some time for Monte Carlo, with 17 numbers. One number dey pay 15 to 1, groups of four dey pay 3 to 1, and di even-money bets cover eight numbers each, dem leave out di 9, wey play di part of di zero. Every bet come out at 1/17 = 5.88%, small pass di American 5.26%, for wheel wey be half di size of European one.
Roulette-18: dice instead of wheel
Dem show Roulette-18 for di Global Gaming Expo for 2014 and dem deal am for some Grosvenor casinos for di United Kingdom. Dice wey get twenty sides replace di wheel, with di numbers 1 reach 18, one 0 and one 00. For 00, dem no dey settle anytin and dem go throw di dice again, so 19 faces dey count with payouts wey dem set for 18: straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → dey pay 17 to 1, splitbetSplitTwo numbers wey dey near each oda, e dey pay 17:1.Read di whole tin → 8 to 1, streetbetStreetThree numbers for one row of di layout, e dey pay 11:1. For French: transversale.Read di whole tin → 5 to 1, cornerbetCornerFour numbers wey share one corner for di layout, e dey pay 8:1.Read di whole tin → 7 to 2, line 2 to 1. Every bet cost 1/19 = 5.26%, di American price, except di even-money bets, wey dey lose only half for 0: 2.63%.
Pin Ball and Spingo: games for online
Pin Ball, from Realistic Games, dey drop ball through board of pins enter one of 25 slots, 0 reach 24. Bets dey pay as if na 24 dey: one number 23 to 1, split 11 to 1, so each one cost 1/25 = 4%, and di even-money bets dey lose only half for 0, wey bring dem to 2%. Spingo, from Microgaming, join two draws togeda: ball from hopper of 21, two each of 1 reach 10 and one 0, and wheel of 25 segments, eight each for yellow, red and blue and one green. Number dey pay 9 to 1 and e cost 4.76%; colour dey pay 2 to 1 and e cost 4%. Di longest shot for di board, number and colour togeda, dey pay 31 to 1 for chance of 16 in 525 and e cost only 2.48%: di bet wey cheap pass for di game.
Lucky Star: light for one star
Lucky Star, wey some online casinos dey offer British players, no get ball. Light dey run round star wey get five points, wey dem draw with five straight lines, and e dey stop for one of 40 spots wey dem number 0 reach 8. Di five spots where di lines cross each oda, dem number all of dem 1, and di light dey pass each of dem two times for one circuit, so one circuit get 45 stops and 1 na di result wey fit come pass, 10 stops in 45. Bets dey go on number, colour (0 and 8 na green; 1, 3 and 6 na red; 2, 4, 5 and 7 na black), odd or even, low (1–4) or high (5–8), In or Out, and on five Chinese elements, one for each line. Payouts na “for 1” and dem dey come for fractions, like 2.2 for red, and dis one make dem fit price every bet within two points of di oda ones: from 2.22% to 4%.
Diamond Roulette: six colours and no red
Diamond Roulette show for Atlantic City for 2008 for double-zero wheel wey get di numbers for six colours of six numbers each, and no red or black bet. One colour dey pay 5 to 1: 5.26%, di normal American price, or 2.70% for single-zero wheel. Di trap na colour wey dem add 0 and 00 join: eight numbers at 3 to 1, where di rule ask for 3¾ to 1. E cost 15.79%. To round payout down by small part of 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 → fit make one bet cost three times di oda ones.
Wetin di small wheels show
Di device dey change; di arithmetic no dey change.
- One house number out of nine cost 11.11%; one out of 37 cost 2.70%. Di fewer di numbers, di more zero dey cost.
- Dice, pin board or hopper no dey change anytin: di price dey inside di count of results and di payouts.
- Half wey come back for zero, like for Pin Ball and Roulette-18, dey cut di even-money edge into half, like 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 → dey do.
- Payouts for fractions, like for Lucky Star, dey allow designer price every bet within one or two points of di oda ones.
- Look for di bet wey dem round im payout down: di 3 to 1 of Diamond instead of 3¾.
Questions wey pipo dey ask
No. At 11.11%, e cost four times European wheel. E still dey becos e quick and e simple, no be becos e cheap.
Some French casinos still dey deal boule. Dem deal Roulette-18 for British casinos for di 2010s. Pin Ball, Spingo and Lucky Star na online games, and Diamond Roulette don comot from Atlantic City.
Becos im payout of 31 to 1 near fair, 31.8 to 1, pass how di payouts of di single bets near am. Dem dey price each bet on im own.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
Spingo dey draw 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 → from hopper of 21 (two each of 1 reach 10, one 0) and e dey spin wheel of 25 segments (eight each of three colours, one green). One number dey pay 9 to 1, one colour 2 to 1, and number and colour togeda 31 to 1. Price all three.
Show di solution
Answer Number 4.76%, colour 4.00%, number and colour 2.48%: di bet wey hard pass to win na im cheap pass.
One number: 2 balls for 21. $1 wey win dey bring back $10, so di bet dey return 2/21 × 10 = 20/21: edge of 1/21 = 4.76%.
One colour: 8 segments for 25, wey dey bring back $3: 24/25, edge of 4%.
Both togeda: di ball and di wheel na separate draws, so di chances dey multiply: 2/21 × 8/25 = 16/525. Winner dey bring back $32, so di bet dey return 16 × 32 = 512 for 525 wey you stake: edge of 13/525 = 2.48%.
Fair 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 → go be 509/16, about 31.8 to 1, so 31 to 1 no reach am, but di gap no reach 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 thirty-two. Dem dey price each bet for di board by imself, and di long shots no always be di ones wey cost pass.
For Roulette-18, bet on redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → dey cover 9 out of di 19 live faces of di dice, e dey pay even money and e dey lose only half when di 0 come out. How much e dey cost?
Show di solution
Answer 1/38, wey be about 2.63%.
Throw di dice 19 times, without di 00s wey dem dey throw again. For average, red dey come 9 times (+9), blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin → 9 times (−9) and di 0 once, wey dey carry half of di stake (−½).
Net: −½ for 19 throws, wey be 1/38 = 2.63%.
Without di half wey come back, e go be −1 for 19, 5.26%, di price of every oda bet for di dice. To give back half for 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 → dey cut di edge into half, like 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 → dey do for French table.
Multicolore, wey pipo play for Monte Carlo for di 1950s, dey spin ball go 25 sectorswheelSectorPockets wey follow each oda for one arc of di wheel, no be group for di layout.Read di whole tin →: six each of green, red, white and yellow, and one blue. Dem dey pay bet on one colour for di odds wey dem print for di sector where di ball stop: 4, 3, 3, 3, 2 and 2 to 1 for di six sectors of each colour, and 24 to 1 for di blue. How much each bet dey cost?
Show di solution
Answer Blue na fair bet and e no dey cost anytin. Every oda colour dey cost 8%.
Imagine 25 spins where every sector come out once. $1 bet on green dey win for im six sectors, 4 + 3 + 3 + 3 + 2 + 2 = $17, and e dey lose $1 for di oda 19: −$2 for 25 spins, 8%.
Blue dey win $24 once and lose $1 for di oda 24 sectors: e dey exactly even.
Casino game wey get fair bet inside dey rare. Compared with di 11.11% of boule, di blue na di one bet for di room wey worth to make. Bollman (2024) give di game as exercise.
Small laugh
One house number out of nine na 11.11%.
Sources
- Wizard of Odds. “Boule”, “Roulette-18”, “Pin Ball”, “Spingo”, “Lucky Star” and “Diamond Roulette”.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.