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Introduction
This name goes by various names: Big Six, Wheel of Fortune, Money Wheel, Big Wheel, and Lucky Wheel. Whatever the name, it is a big vertical wheel where the player bets on the number it will stop on. The odds are conveniently the same as the number. For example, a bet on 5 will pay 5 to 1.
The odds are pretty bad but at least you can count it usually being staffed by the front door with an attractive well-endowed dealer. Just one of those Vegas traditions.
Las Vegas Rules
The following table shows the betting options, payout odds, number on wheel, and the house edge under the Las Vegas rules Big Six rules.
Las Vegas Rules
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| $1 | 1 | 24 | 44.44% | 11.11% |
| $2 | 2 | 15 | 27.78% | 16.67% |
| $5 | 5 | 7 | 12.96% | 22.22% |
| $10 | 10 | 4 | 7.41% | 18.52% |
| $20 | 20 | 2 | 3.70% | 22.22% |
| Logo #1 | 40 | 1 | 1.85% | 24.07% |
| Logo #2 | 40 | 1 | 1.85% | 24.07% |
Atlantic City Rules
The Atlantic City is the same as the Las Vegas one, except they change one $1 position to $5, and the pay 45 instead of 40 on the two logos.
Atlantic City Rules
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| $1 | 1 | 23 | 42.59% | 14.81% |
| $2 | 2 | 15 | 27.78% | 16.67% |
| $5 | 5 | 8 | 14.81% | 11.11% |
| $10 | 10 | 4 | 7.41% | 18.52% |
| $20 | 20 | 2 | 3.70% | 22.22% |
| Logo #1 | 45 | 1 | 1.85% | 14.81% |
| Logo #2 | 45 | 1 | 1.85% | 14.81% |
Charles Town Rules
The Hollywood Casino in Charles Town, West Virginia, follows the Atlantic City rules, except pays only 40 on the two logos.
Big Six — Charles Town WV Rules
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| $1 | 1 | 23 | 42.59% | 14.81% |
| $2 | 2 | 15 | 27.78% | 16.67% |
| $5 | 5 | 8 | 14.81% | 11.11% |
| $10 | 10 | 4 | 7.41% | 18.52% |
| $20 | 20 | 2 | 3.70% | 22.22% |
| Logo #1 | 40 | 1 | 1.85% | 24.07% |
| Logo #2 | 40 | 1 | 1.85% | 24.07% |
Macau Rules
In Macau there is a similar game. One or two wheels each can be found in the larger casinos. It does not seem to be a popular game there. The game wheel is the same size, but instead of dollars, it has colors. The table below shows the number of stops on the wheel, probability, and return for each bet. The table shows the best bet is tied for orange, purple, and green, at 7.69% each.
Big Six — Macau Rules
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| Orange | 1 | 24 | 46.15% | 7.69% |
| Purple | 3 | 12 | 23.08% | 7.69% |
| Green | 5 | 8 | 15.38% | 7.69% |
| Blue | 10 | 4 | 7.69% | 15.38% |
| Yellow | 20 | 2 | 3.85% | 19.23% |
| Logo 1 | 45 | 1 | 1.92% | 11.54% |
| Logo 2 | 45 | 1 | 1.92% | 11.54% |
Australia Rules
The Star City casino in Sydney has a similar game, called the 'Big Wheel.' Instead of money, it uses native Australian animals. As the following table shows, the house edge is the same on all bets at 7.69%.
Big Six — Australia Rules
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| Koala | 1 | 24 | 46.15% | 7.69% |
| Kookaburra | 3 | 12 | 23.08% | 7.69% |
| Lizard | 5 | 8 | 15.38% | 7.69% |
| Echidna | 11 | 4 | 7.69% | 7.69% |
| Platypus | 23 | 2 | 3.85% | 7.69% |
| Emu | 47 | 1 | 1.92% | 7.69% |
| Kangaroo | 47 | 1 | 1.92% | 7.69% |
Aruze & Interblock Lucky Big Wheel
Aruze and Interblock are makers of electronic table games. They both make a Big Six wheel that are mathematically equivalent. The following tables show the bets available, the number of stops for each one, the probability of winning, and house edge.
Aruze and Interblock Big Six Wheel
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| $1 | 1 | 26 | 48.15% | 3.70% |
| $3 | 3 | 13 | 24.07% | 3.70% |
| $6 | 6 | 7 | 12.96% | 9.26% |
| $12 | 12 | 4 | 7.41% | 3.70% |
| $25 | 25 | 2 | 3.70% | 3.70% |
| Flag | 50 | 1 | 1.85% | 5.56% |
| Joker | 50 | 1 | 1.85% | 5.56% |
| Total | 54 | 100.00% |
In addition, Aruze makes another version with a $6.50 symbol instead of $6 and the Joker and Flag bets pay 52 instead of 50. This more liberal wheel I've seen at the Star City casino in Sydney, Australia. The full odds are below.
Aruze Lucky Big Wheel — Australian Version
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| 1 | 1 | 26 | 48.15% | 3.70% |
| 3 | 3 | 13 | 24.07% | 3.70% |
| 6.5 | 6.5 | 7 | 12.96% | 2.78% |
| 12 | 12 | 4 | 7.41% | 3.70% |
| 25 | 25 | 2 | 3.70% | 3.70% |
| Joker | 52 | 1 | 1.85% | 1.85% |
| Flag | 52 | 1 | 1.85% | 1.85% |
| Total | 54 | 100.00% |
Number Game Ma
The house edge on both versions of the Aruze game is significantly less than standard Big Six, with a live dealer.
Gamesys
Internet casinos using Gamesys software have two wheel of fortune games. Both have a 49-stop wheel with prizes of $1, $3, $7, $15, $23, and $47. The following table shows the number of stops of each win, what it pays, probability of winning, and house edge. As you can see, every bet has a house edge of 2.04%. That is the best Big Six/Wheel of Fortune game I've ever seen, by far.
Gamesys Version
| Bet | Pays | Number on Wheel | Probability | House Edge |
|---|---|---|---|---|
| 1 | 1 | 24 | 0.489796 | 0.020408 |
| 3 | 3 | 12 | 0.244898 | 0.020408 |
| 7 | 7 | 6 | 0.122449 | 0.020408 |
| 15 | 15 | 3 | 0.061224 | 0.020408 |
| 23 | 23 | 2 | 0.040816 | 0.020408 |
| Logo | 47 | 1 | 0.020408 | 0.020408 |
| Joker | 47 | 1 | 0.020408 | 0.020408 |
| Total | 49 | 1.000000 |
The also have a 'zero house edge' version. In that game the rules are the same, except:
- If the wheel stops on the Logo, then any bet besides the Logo shall push, instead of lose.
- If the wheel stops on the Joker, then any bet on the Logo shall push, instead of lose.
By changing one stop from a loss to a push on all bets, that does indeed make the house edge exactly 0.00%. However, there is a catch. The player must pay a 10% commission on any net win per 'gambling session.' Any break between bets of an hour or more shall end a session and no session may last over 24 hours.
KGM
I saw this machine at the 2018 Global Gaming Expo. The Bonus issues prizes on a separate prize wheel of 5, 20, 50, 100, 250, and 100. I have no idea how they are weighted, so am leaving the return on that one a question mark.
Aruze Lucky Big Wheel — American Version
| Bet | Number on Wheel | Probability | House Edge |
|---|---|---|---|
| $2 | 24 | 46.15% | 7.69% |
| $4 | 12 | 23.08% | 7.69% |
| $6 | 8 | 15.38% | 7.69% |
| $16 | 3 | 5.77% | 7.69% |
| $24 | 2 | 3.85% | 7.69% |
| $48 | 1 | 1.92% | 7.69% |
| Bonus | 2 | 3.85% | ? |
| Total | 52 | 100.00% |
Interblock Big Six
Yet another Interblock product is titled 'Big Six.' It follows the same rules as the Australian version, except adds two more slices to the wheel titled 'Super Spin.' If the player bets on Super Spin and the wheel lands in one of those two slices on the wheel, then an electronic wheel in the middle of the big wheel will spin to determine the win. Possible wins are 20, 50, 75, 100, 500, and 1000. I do not know how this inner wheel is weighted. Company literature I obtained at the 2019 Global Gaming Expo indicated there are five different pay tables for the Super Spin Feature. Since then, I saw the game at the Resorts World casino in New York City.
The following table shows the return of each bet. Wins are on a 'to one' basis. The table shows a return of 88.89% on all bets (or 11.11% house edge) except the Super Spin, which I can't quantify without knowing the wheel weightings.
Interblock Big Six
| Bet | Pays | Number on Wheel | Probability | Return |
|---|---|---|---|---|
| 1 | 1 | 24 | 44.44% | 88.89% |
| 3 | 3 | 12 | 22.22% | 88.89% |
| 5 | 5 | 8 | 14.81% | 88.89% |
| 11 | 11 | 4 | 7.41% | 88.89% |
| 23 | 23 | 2 | 3.70% | 88.89% |
| Red Diamond | 47 | 1 | 1.85% | 88.89% |
| Yellow Diamond | 47 | 1 | 1.85% | 88.89% |
| Super Spin | ? | 2 | 3.70% | ? |
| Total | 54 | 100.00% |
Other Wheel Games
- Money Wheel is a similar game to Big Six, but involves multipliers and extra spins.
- Wheel looks like Big Six but plays more like roulette on a wheel with 19 possible outcomes. It is a live dealer game by BetGames.tv.
- Dream Catcher, by Evolution Gaming, plays like Big Six, but offers 2x and 7x multipliers.
Written by:Michael Shackleford
Games available in most casinos are commonly called casino games. In a casino game, the players gamble cash or casino chips on various possible random outcomes or combinations of outcomes. Casino games are also available in online casinos, where permitted by law. Casino games can also be played outside casinos for entertainment purposes like in parties or in school competitions, some on machines that simulate gambling.
Categories[edit]
There are three general categories of casino games: gaming machines, table games, and random number games. Gaming machines, such as slot machines and pachinko, are usually played by one player at a time and do not require the involvement of casino employees to play. Tables games, such as blackjack or craps, involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as croupiers or dealers. Random number games are based upon the selection of random numbers, either from a computerized random number generator or from other gaming equipment. Random number games may be played at a table or through the purchase of paper tickets or cards, such as keno or bingo.
Some casino games combine multiple of the above aspects; for example, roulette is a table game conducted by a dealer, which involves random numbers. Casinos may also offer other type of gaming, such as hosting poker games or tournaments, where players compete against each other.
Common casino games[edit]
Notable games that are commonly found at casinos include:
Table games[edit]
| Gaming machines[edit] | Random numbers[edit] |
House advantage[edit]
Casino games typically provide a predictable long-term advantage to the casino, or 'house', while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players possessing sufficient skills to eliminate the inherent long-term disadvantage (the house edge or vigorish) in a casino game are referred to as advantage players.
The players' disadvantage is a result of the casino not paying winning wagers according to the game's 'true odds', which are the payouts that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that the player gets the original amount wagered back. However, the casino may only pay 4 times the amount wagered for a winning wager.
The house edge or vigorish is defined as the casino profit expressed as the percentage of the player's original bet. (In games such as blackjack or Spanish 21, the final bet may be several times the original bet, if the player double and splits.)
In American roulette, there are two 'zeroes' (0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared to European roulette. The chances of a player, who bets 1 unit on red, winning is 18/38 and his chances of losing 1 unit is 20/38. The player's expected value is EV = (18/38 × 1) + (20/38 × (−1)) = 18/38 − 20/38 = −2/38 = −5.26%. Therefore, the house edge is 5.26%. After 10 spins, betting 1 unit per spin, the average house profit will be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one 'zero' and therefore the house advantage (ignoring the en prison rule) is equal to 1/37 = 2.7%.
The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%. Keno can have house edges up to 25%, slot machines having up to 15%.
The calculation of the roulette house edge is a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation is necessary to complete the task.
In games which have a skill element, such as blackjack or Spanish 21, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting), on the first hand of the shoe (the container that holds the cards). The set of the optimal plays for all possible hands is known as 'basic strategy' and is highly dependent on the specific rules and even the number of decks used. Good blackjack and Spanish 21 games have house edges below 0.5%.
Traditionally, the majority of casinos have refused to reveal the house edge information for their slots games and due to the unknown number of symbols and weightings of the reels, in most cases it is much more difficult to calculate the house edge than that in other casino games. However, due to some online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing.[1]
In games where players are not competing against the house, such as poker, the casino usually earns money via a commission, known as a 'rake'.
Standard deviation[edit]
The luck factor in a casino game is quantified using standard deviations (SD).[2] The standard deviation of a simple game like roulette can be calculated using the binomial distribution. In the binomial distribution, SD = √npq, where n = number of rounds played, p = probability of winning, and q = probability of losing. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than −1 units for a loss, which doubles the range of possible outcomes. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.[3]
- SD (roulette, even-money bet) = 2b√npq, where b = flat bet per round, n = number of rounds, p = 18/38, and q = 20/38.
For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 × 1 × √10 × 18/38 × 20/38 = 3.16 units. After 10 rounds, the expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss.[4]
The standard deviation for pai gow poker is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.
Casino Number Game
As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is impossible for a gambler to win in the long term. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win.
It is important for a casino to know both the house edge and variance for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the variance tells them how much they need in the way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so outsource their requirements to experts in the gaming analysis field.
See also[edit]
References[edit]
- ^'Michael Shackleford is the wizard of odds'. Observer. Retrieved 13 October 2015.
- ^Hagan, general editor, Julian Harris, Harris (2012). Gaming law : jurisdictional comparisons (1st ed.). London: European Lawyer Reference Series/Thomson Reuters. ISBN978-0414024861.
- ^Gao, J.Z.; Fong, D.; Liu, X. (April 2011). 'Mathematical analyses of casino rebate systems for VIP gambling'. International Gambling Studies. 11 (1): 93–106. doi:10.1080/14459795.2011.552575. S2CID144540412.
- ^Andrew, Siegel (2011). Practical Business Statistics. Academic Press. ISBN978-0123877178. Retrieved 13 October 2015.