For those who love to Gamble, maybe you shouldn't....
HOUSE EDGE & STD DEV.
The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wagered. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk.
The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wagered. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk.
The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.
| Game | Bet/Rules | House Edge | Standard Deviation |
| Baccarat | Banker | 1.06% | 0.93 |
| Baccarat | Player | 1.24% | 0.95 |
| Baccarat | Tie | 14.36% | 2.64 |
| Big Six | $1 | 11.11% | 0.99 |
| Big Six | $2 | 16.67% | 1.34 |
| Big Six | $5 | 22.22% | 2.02 |
| Big Six | $10 | 18.52% | 2.88 |
| Big Six | $20 | 22.22% | 3.97 |
| Big Six | Joker/Logo | 24.07% | 5.35 |
| Bonus Six | No insurance | 10.42% | 5.79 |
| Bonus Six | With insurance | 23.83% | 6.51 |
| Blackjacka | Atlantic City rules | 0.43% | 1.2 |
| Blackjackb | Las Vegas single deck | 0.18% | 1.2 |
| Caribbean Stud Poker | 5.22% | 2.24 | |
| Casino War | Go to war on ties | 2.88% | 1.05 |
| Casino War | Surrender on ties | 3.70% | 0.94 |
| Casino War | Bet on tie | 18.65% | 8.32 |
| Catch a Wave | 0.50% | d | |
| Craps | Pass/Come | 1.41% | 1.00 |
| Craps | Don't pass/don't come | 1.36% | 0.99 |
| Craps | Field (2:1 on 12) | 5.56% | 1.08 |
| Craps | Field (3:1 on 12) | 2.78% | 1.14 |
| Craps | Any craps | 11.11% | 2.51 |
| Craps | Big 6,8 | 9.09% | 1.00 |
| Craps | Hard 4,10 | 11.11% | 2.51 |
| Craps | Hard 6,8 | 9.09% | 2.87 |
| Craps | Place 6,8 | 1.52% | 1.08 |
| Craps | Place 5,9 | 4.00% | 1.18 |
| Craps | Place 4,10 | 6.67% | 1.32 |
| Craps | Place (to lose) 4,10 | 3.03% | 0.69 |
| Craps | Proposition 2,12 | 13.89% | 5.09 |
| Craps | Proposition 3,11 | 11.11% | 3.66 |
| Craps | Proposition 7 | 16.67% | 1.86 |
| Double Down Stud | 2.67% | 2.97 | |
| Keno | 25%-29% | 1.30-46.04 | |
| Let it Ride | 3.51% | 5.17 | |
| Pai Gowc | 1.50% | d | |
| Pai Gow Pokerc | 1.46% | 0.75 | |
| Red Dog | Six decks | 2.80% | d |
| Roulette (single zero) | 2.70% | e | |
| Roulette (double zero) | 5.26% | e | |
| Sic-Bo | 2.78%-33.33% | e | |
| Slot Machines | 2%-15%f | 8.74g | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | d |
| Spanish 21 | Dealer stands on soft 17 | 0.40% | d |
| Super Fun 21 | 0.94% | d | |
| Three Card Poker | Pairplus | 2.32% | 2.91 |
| Three Card Poker | Ante & play | 3.37% | 1.64 |
| Video Poker | Jacks or better (full pay) | 0.46% | 4.42 |
| Wild Hold 'em Fold 'em | 6.86% | d | |
Notes:
- a Atlantic City rules are 8 decks, dealer stands on soft 17, player may double on any two cards, player may double after splitting, one card to split aces, no surrender.
b Las Vegas single deck rules are dealer hits on soft 17, player may double on any two cards, player may not double after splitting, one card to split aces, no surrender.
c Assuming player plays the house way, playing one on one against dealer, and half of bets made are as banker.
d Yet to be determined.
e Standard deviation depends on bet made.- f Slot machine range is based on available returns from a major manufacturer
- g Slot machine standard deviation based on just one machine. While this can vary, the standard deviation on slot machines are very high.
ELEMENT OF RISK
For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the "element of risk." This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.
| Game | Bet | House Edge | Element of Risk |
| Blackjack | Atlantic City rules | 0.43% | 0.38% |
| Bonus 6 | No insurance | 10.42% | 5.41% |
| Bonus 6 | With insurance | 23.83% | 6.42% |
| Caribbean Stud Poker | 5.22% | 2.56% | |
| Casino War | Go to war on ties | 2.88% | 2.68% |
| Double Down Stud | 2.67% | 2.13% | |
| Let it Ride | 3.51% | 2.85% | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | 0.65% |
| Spanish 21 | Dealer stands on soft 17 | 0.40% | 0.30% |
| Three Card Poker | Ante & play | 3.37% | 2.01% |
| Wild Hold 'em Fold 'em | 6.86% | 3.23% | |
- HOLD
The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.
posted by Mix at 12:36 PM
1 Comments:
Yea, that's one of the first things you learn in a stats class. Gambling doesn't pay off. Neither does buying lottery tickets etc.
One thing I discovered the other day, while sifting through a travel book, was the little country of Bhutan (East of Nepal). The king of Bhutan said "I am not as much concerned about the Gross National Product as I am about the Gross National Happiness." Also in their Manual for Teachers of Mathematics the first rule is "Always remember that you are a human being as well as a teacher, and that your students are also human beings, and that you are here because you have something important to give them that they need." Thimpu, the capital of Bhutan, is the only world capital without traffic lights. One set was installed, but the residents complained that it was too impersonal.
Bhutan is now officially my favorite country.
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