Bonus-Round Wheels
Wheels that pay extra when a bonus lights up: random Bonus numbers on a four-zero wheel, a wide pocket that hands out free spins, a second wheel of multipliers. The bonus is real, and so is the bill for it.
A bonus has to be paid for, by extra house pockets or by a cut somewhere else. Fast Action Roulette pays for its Bonus numbers with four zeros, and its straight up costs 6.65%. Double Bonus Spin adds a wide Bonus pocket that gives free spins and, by our calculation, makes its standard bets cheaper than a plain American wheel. The extra bets built around the bonus are where the cost is: 13% to 25%. Deal or No Deal Roulette cannot be priced at all, because it does not say how often its bonus starts.
Paying for a bonus
On an ordinary wheel the house edgemathHouse edgeThe share of each stake the casino keeps on average: 2.70% in European roulette.Read full → is the share of pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full → the payoutsmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → ignore: 1 in 37, 2 in 38. A bonus breaks that rule, because some results pay more than the rule allows. The money has to come from somewhere, and the first three wheels on this page find it in three ways: more house pockets, a separate bet on the bonus itself, or both. The fourth does not say what its bonus costs.
Fast Action Roulette
Fast Action Roulette opened at Marina Bay Sands in Singapore in 2020. Its wheel has 40 pockets: 1 to 36, 0, 00, an S and the casino’s logo, so four pockets that the payouts ignore. On the rule alone that would cost 10% on every bet. On every spin, 10 of the 40 spaces on the layoutequipmentLayoutThe printed betting grid on the table. Also: table, felt, cloth.Read full → light up at random as Bonus spaces. The layout has 10 rows of 4, and only four bets are allowed.
How the single number gets to 6.65%
Three times in four your number is not a Bonus number and pays the usual 35 to 1. About one time in four it is, and pays 40 to 1. One time in 435 its whole row is lit and it pays 80 to 1. Averaged, a winning straight upbetStraight upA single number, pays 35:1.Read full → pays about 36.3 to 1. True oddsmathTrue oddsThe payout that would make a bet fair: losing outcomes divided by winning ones. A straight up on 37 pockets has true odds of 36 to 1.Read full → on 40 pockets are 39 to 1, so the plain 35 to 1 falls four unitsmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full → short; the bonuses make up about a third of that, and the bet costs 6.65% instead of 10%: more than an American wheel, less than a plain four-zerowheelZeroThe single green pocket that no even-money, dozen or column bet covers; the source of the house edge. Also: single zero, 0.Read full → one.
Designing a split
The game offers no splitbetSplitTwo adjacent numbers, pays 17:1.Read full →. Bollman asks what a split should pay if it used the same Bonus idea: 17 to 1 normally, more if one or both of its numbers are Bonus. For two given spaces, neither is Bonus 29 times in 52, one is 20 times in 52 and both are 3 times in 52. Keeping the edge between the American 5.26% and the triple-zero 7.69% leaves a narrow choice. The simplest design leaves the one-Bonus case alone and pays 30 to 1 when both are Bonus: 6.25%.
Double Bonus Spin
IGT’s Double Bonus Spin keeps the American wheel and adds a yellow Bonus pocket one and a half pockets wide, so the wheel counts 39.5 pocket widths. Without free spins that extra width would simply belong to the house: 3.5 house pockets’ worth out of 39.5, an edge of 8.86% on every bet. When the ballequipmentBallThe small ball launched along the track against the rotor. Modern balls are ivorine or Teflon, 18–21 mm.Read full → lands in the Bonus pocket, every bet on the layout stays up for two free spins, shown as one ball on two rings. You lose your chipmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → only if both free spins miss, and win once or twice if one or both hit. That makes this the rare wheel where the cost depends on how many numbers a bet covers: the free spins are worth most to a bet on few numbers.
The yellow bets
The cost of Double Bonus Spin sits in its yellow bets, which you place on the Bonus pocket itself. A straight yellow bet pays 12 to 1 if the ball lands in the Bonus pocket and then multiplies its prize by 10 if one free spin hits it again, by 100 if both do. Split and trio versions add 00, or 0 and 00, at 6 to 1 and 4 to 1, but a ball in 0 or 00 pays without starting the bonus round.
A second wheel of multipliers
In August 2025 the Palazzo on the Las Vegas Strip put out Interblock’s Bonus Wheel Roulette. Four colored gem pockets take the place of the zeros, and a ball that lands on a gem starts a second wheel with multipliers of up to 500×. A Las Vegas news report, citing Vegas Advantage, gave a house edge of 10% on the numbers and 9.25% on the gems. Ten percent is what four house pockets cost on a 40-pocket wheel, the same base as Fast Action, before any bonus is given back. We have not seen the full pay tablemoneyPay tableThe list of what each bet or result pays. On machines and side bets, it is where the house edge is set.Read full →, so these are the reported figures.
Deal or No Deal Roulette: a price nobody publishes
An online single-zero game, offered mainly to British players, adds a ring outside the numbers. It is mostly blank, with one redbetRedEven-money bet on the 18 red numbers. French: rouge.Read full → box and one blackbetBlackEven-money bet on the 18 black numbers. French: noir.Read full → telephone. The main bets are ordinary European roulettevariantEuropean rouletteSingle-zero wheel, 37 pockets, house edge 2.70%. The canonical model on this site.Read full →. An optional Bonus Bet wins if the ball stops beside one of the two symbols. Beside the box you play the television show: 22 boxes hold 3 to 151 times the bet, you keep one and open the others in rounds of six, five, five and four, and after each round a banker offers about 96% of the average still unopened. The 22 prizes average 1,027/22 = 46.68 times the bet, so refusing every offer is worth slightly more on average than taking one. Beside the telephone you open one of three boxes, which caps a prize wheel at 50, 80 or 100 times the bet, and spin it up to three times. The Wizard of Odds works out that taking 35 or more on the first spin and 27 or more on the second averages 40.42 times the bet.
What the game leaves out
The help screen gives the prizes but not how often the ball stops beside a symbol. If it were 1 spin in 37 for each, the bonus bet would return 46.68/37 + 40.42/37, about 235% of what is staked: a bet that favored the player more than two to one. The Wizard of Odds reckons the symbols come up far less often than that, and without the frequency the bet cannot be priced. A pay table with no chances beside it is not a price.
What to take from it
A bonus does not make a wheel cheaper unless the casino gives back more than the bonus costs it, and only one of the three priced here does.
- Count the house pockets first. Four of them start at 10%, whatever lights up.
- The bets on the bonus itself are the dearest on the layout: 13% to 25% here.
- Double Bonus Spin’s standard bets are the exception, at under 3% by our calculation, if the game pays as described.
- Read the help screen: “for 1” or “to 1”, and what a bonus multiplies.
Questions
Its straight up, at 6.65%, costs more than an American wheel and much more than a European one. Its three bonus bets cost 13% to 25%.
Because the two free spins are worth more than the extra pocket and a half costs, for every standard bet. That is our calculation from the rules as Bollman describes them; check the game’s own pay table.
Four gem pockets that the payouts treat as house pockets, which is the same thing for the price: 10% before the bonus wheel.
Fun with Math
Try these yourself first. Each solution is folded; open it when you are ready.
On Fast Action Roulette, 10 of the 40 spaces on the layoutequipmentLayoutThe printed betting grid on the table. Also: table, felt, cloth.Read full → light up as Bonus spaces on every spin, chosen at random. The layout has 10 rows of 4. How often is exactly one whole row lit? How often are two?
Show the solution
Answer One whole row: about 2.3% of spins, 1 in 44. Two whole rows: about 1 spin in 38,000.
There are 847,660,528 ways to pick 10 spaces out of 40, all equally likely.
Two whole rows: choose the two rows (45 ways), then the last 2 Bonus spaces from the other 32 (496 ways). Two spaces cannot complete a third row, so that is 22,320 ways: 1 in about 37,978.
Exactly one whole row: choose the row (10 ways) and the other 6 spaces from the remaining 36 (1,947,792 ways), then remove the choices that complete a second row (9 rows × 496 = 4,464). That leaves 10 × 1,943,328 = 19,433,280 ways, 2.29%. Bollman’s answer key prints 0.0203, which looks like a slip for 0.0230: one given row is full 2.30% of the time, and there are ten rows.
Double Bonus Spin keeps the American layout, including the five-number basketbetBasketOn a single-zero wheel: 0, 1, 2, 3 with one chip, pays 8:1. Also: first four, quatre premiers.Read full →, which pays 6 to 1. Its yellow Bonus pocketequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full → is one and a half pockets wide, and a ballequipmentBallThe small ball launched along the track against the rotor. Modern balls are ivorine or Teflon, 18–21 mm.Read full → that lands there gives every bet two free spins. Bollman leaves the basket’s cost as an exercise. What is it?
Show the solution
Answer About 4.72%, against 7.89% for the same bet on a plain American wheel.
Count the wheel in pocket widths: 38 ordinary pockets and 1.5 for the Bonus, 39.5 in all. On a normal spin the basket wins with chance 5/39.5 and pays 6, and loses with chance 33/39.5.
In the bonus round each free spin hits one of your five numbers with chance 5/39.5. You lose your chipmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → only if both miss, (34.5/39.5)² = 76.3% of the time; one hit pays 6, two hits pay 12. On average the round is worth +0.756 unitsmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full →.
Put together, per spin: (5 × 6 − 33 + 1.5 × 0.756)/39.5 = −0.0472. The free spins save the basket from about two fifths of its usual cost. The answer is our calculation; Bollman sets the question without one.
Comic relief
Count the house pockets before the lights.
Sources
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- “Uh-Oh! Quadruple Zero Roulette Hits Las Vegas Strip.” Bonus Wheel Roulette at the Palazzo.
- Wizard of Odds. “Deal or No Deal Roulette.”