Casino House Edge Explained
The house edge is defined as the ratio of the average loss to the initial bet. 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. Casino House Edge - How to Play Craps Pt. 6 You need to understand which bets have the lowest house edge, If you want to win more at the game of craps.
If you spend any time at all reading about online casino games and gambling in casinos, you’ll encounter an expression—“the house edge.”
You’ll see writers explain that blackjack house edge is the lowest in the casino, and that the slots have the worst.
You’ll see them mention that some of the bets at the craps table have a house edge of less than 2%, while other bets at the craps table have a house edge of more than 16%.
But what is the house edge in a casino game and how does it work?
This site covers some similar concepts as they relate to the math of sports betting, but the casinos’ house edge works slightly differently.
Some Probability Background that Matters
You can’t understand the house edge if you don’t understand some of the basics of probability.
Probability is just a mathematical way to measure how likely something is to happen.
When a weatherman says there’s a 50% chance of rain, he’s using probability (as well as meteorology) to express that likelihood.
And most people have an intuitive understand of probability when it’s stated as a percentage, because we use it all the time.
If you paid attention in 8th grade math, you probably already know that a percentage is just another way of expressing a fraction, and that’s all a probability is—a fraction.
To determine the probability of something happening, you just look at the number of ways it could happen and divide it by the total number of possible events.
You’re rolling a 6-sided die, and you want to know what the probability of rolling a 6 is. A 6-sided die has 6 sides numbered 1 through 6. There’s only a single 6.
Since there are 6 possible outcomes, and since only one of those outcomes is a 6, the probability of rolling a 6 is 1/6.
You can convert that to a percentage of 16.67%.
You can also convert it to “odds format,” which just compares the number of ways it can’t happen with the number of ways it can. The odds of rolling a 6 on a 6-sided die are 5 to 1.
Once you have a basic understanding of probability, you can move on to the next step, which is determining the house edge of a bet.
What Is the House Edge and Why Does It Matter?
Every bet has a payout if you win and an amount you lose if you lose. This is often the same amount, or even money.
If you’re playing blackjack, you bet one unit, and most of the time, if you win, you win one unit. If you lose, you just lose that one unit.
In other words, if you bet $100 on a hand of blackjack and win, you usually win $100.
If you lose, you usually lose $100.
That’s called even money.
(And some bets in blackjack result in bigger winnings, and you sometimes have the option of surrendering, which means you only lose half your stake. But that’s a complication that doesn’t help you understand the house edge, so I’m going to save that discussion for another blog post.)
A bet’s payout can also be expressed using odds, though.
An even-money bet pays off at 1 to 1.
A bet that pays off at 5 to 1 is also possible—if you win, you get 5 units, but if you lose, you only lose 1 unit.
In the die-rolling probability example I used above, if you have a payout of 5 to 1, you’re playing a game with no house edge.
That’s because in the long run, you’ll win as much money as you lose.
But suppose I reduced the payout for rolling a 6 to 4 to 1?
You can use statistics to determine an average amount you’ll lose per bet in this situation.
You assume 6 statistically perfect rolls of the die. This means you’ll win once and lose 5 times.
If you’re betting $100 every time, you’ll have a single win of $400 along with 5 losses of $100 each, or a $500 total loss.
Your net loss after that is $100.
Since that’s a net loss of $100 over 6 bets, you’ve lost an average of $16.67 per bet.
That’s the same thing as lose 16.67% of each bet, and that percentage is the house edge.
There are other ways to arrive at that number, but that’s the easiest method I’ve seen used.
With every online casino game you play, the house pays off your bets at odds lower than the odds of winning. This results in a mathematical edge for the house.
That’s why casinos are profitable in the long run, even though every, a percentage of their customers go home with winnings in their pockets.
Probabilities—and the house edge—are always long-term phenomena. In the short run, anything can happen.
Casino House Edge Explained Game
Individual online casino gamblers are always playing in the short term.
Online casinos are always playing in the long term.
If the House Has an Edge, Why Do People Still Play Casino Games?
So if, in the long run, the house can’t lose because of the math behind the games, why do people still play?
The answer is simpler than you think:
I have a friend who visits the casino at least once a week. He loses money on 4 out of 5 visits to the casino, but on one of those 5 visits every month, he comes home a winner.
He doesn’t care that he’s losing money hand over fist in the long run. He just wants to keep getting that buzz from his occasional wins.
The human brain is irrational, especially when it comes to gambling.
How the House Edge for Various Casino Games Compare
The house edge is only one factor that affects how much you’re going to lose when you’re gambling on online casino games. Other factors include how many bets you place per hour and how much you’re betting every time you place a wager.
That being said, if everything else is equal, you should play the casino games with the lowest house edge.
Keep in mind, too, that game conditions affect the house edge, too.
In some blackjack games, a natural pays off at 6 to 5 odds instead of 3 to 2 odds. The house edge on such a blackjack game is higher.
And, in fact, blackjack is a good place to start a discussion of the house edge for various casino games. It’s widely known that the house edge for blackjack is between 0.5% and 1%, but that number assumes that you’re making the optimal move in every situation. The average blackjack player is probably giving up 2% or so in mistakes.
Craps is a game where different bets have a different house edge. If you stick with the basic bets, pass and come, you face a house edge of 1.41%, which is relatively low. The more “exciting” wagers on the craps table come with a higher house edge.
Roulette comes in 2 main versions—single zero and double zero. The double zero version of roulette is predominant in the United States, and the roulette house edge for that game is 5.26%. By removing one of the zeroes, the online casino reduces the house edge to 2.70%.
Slot machines have a house edge that varies based on the PAR sheet for the game. (That’s the logic behind the game which determines the probability of getting various combinations of symbols and the payouts for those combinations.) You can find slot machines with a house as high as 35% or as low as 5%, but you never know what the number is.
Video poker machines look like slot machines, but they offer a better house edge—if you play the hands optimally. Depending on the pay table, the house edge for video poker can be as low as 0.5% or as high as 5% or 6%.
Conclusion
And those are the basics of the house edge as it pertains to casino games.
Now that you have an understanding of the probability behind casino games and how it affects your winnings and losses, are you going to be more or less likely to play casino games?
Are you going to change the amounts you bet or the games you play?
Let me know in the comments.
Introduction
The house edge is defined as the ratio of the average loss to the initial bet. 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. For games like Ultimate Texas Hold 'Em and Crazy 4 Poker, where there are two required initial wagers, the house edge is based on one of them only. House edge figures are based on optimal or near-optimal player strategy.
The table below shows the house edge of most popular casino games and bets.
Casino Game House Edge
| Game | Bet/Rules | House Edge | Standard Deviation |
|---|---|---|---|
| Baccarat | Banker | 1.06% | 0.93 |
| Player | 1.24% | 0.95 | |
| Tie | 14.36% | 2.64 | |
| Big Six | $1 | 11.11% | 0.99 |
| $2 | 16.67% | 1.34 | |
| $5 | 22.22% | 2.02 | |
| $10 | 18.52% | 2.88 | |
| $20 | 22.22% | 3.97 | |
| Joker/Logo | 24.07% | 5.35 | |
| Bonus Six | No insurance | 10.42% | 5.79 |
| With insurance | 23.83% | 6.51 | |
| Blackjacka | Liberal Vegas rules | 0.28% | 1.15 |
| Caribbean Stud Poker | 5.22% | 2.24 | |
| Casino War | Go to war on ties | 2.88% | 1.05 |
| Surrender on ties | 3.70% | 0.94 | |
| Bet on tie | 18.65% | 8.32 | |
| Catch a Wave | 0.50% | d | |
| Craps | Pass/Come | 1.41% | 1.00 |
| Don't pass/don't come | 1.36% | 0.99 | |
| Odds — 4 or 10 | 0.00% | 1.41 | |
| Odds — 5 or 9 | 0.00% | 1.22 | |
| Odds — 6 or 8 | 0.00% | 1.10 | |
| Field (2:1 on 12) | 5.56% | 1.08 | |
| Field (3:1 on 12) | 2.78% | 1.14 | |
| Any craps | 11.11% | 2.51 | |
| Big 6,8 | 9.09% | 1.00 | |
| Hard 4,10 | 11.11% | 2.51 | |
| Hard 6,8 | 9.09% | 2.87 | |
| Place 6,8 | 1.52% | 1.08 | |
| Place 5,9 | 4.00% | 1.18 | |
| Place 4,10 | 6.67% | 1.32 | |
| Place (to lose) 4,10 | 3.03% | 0.69 | |
| 2, 12, & all hard hops | 13.89% | 5.09 | |
| 3, 11, & all easy hops | 11.11% | 3.66 | |
| Any seven | 16.67% | 1.86 | |
| Crazy 4 Poker | Ante | 3.42%* | 3.13* |
| Double Down Stud | 2.67% | 2.97 | |
| Heads Up Hold 'Em | Blind pay table #1 (500-50-10-8-5) | 2.36% | 4.56 |
| Keno | 25%-29% | 1.30-46.04 | |
| Let it Ride | 3.51% | 5.17 | |
| Pai Gowc | 1.50% | 0.75 | |
| Pai Gow Pokerc | 1.46% | 0.75 | |
| Pick ’em Poker | 0% - 10% | 3.87 | |
| Red Dog | Six decks | 2.80% | 1.60 |
| Roulette | Single Zero | 2.70% | e |
| 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 |
| Dealer stands on soft 17 | 0.40% | d | |
| Super Fun 21 | 0.94% | d | |
| Three Card Poker | Pairplus | 7.28% | 2.85 |
| Ante & play | 3.37% | 1.64 | |
| Ultimate Texas Hold 'Em | Ante | 2.19% | 4.94 |
| Video Poker | Jacks or Better (Full Pay) | 0.46% | 4.42 |
| Wild Hold ’em Fold ’em | 6.86% | d |
Notes
| a | Liberal Vegas Strip rules: Dealer stands on soft 17, player may double on any two cards, player may double after splitting, resplit aces, late 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. |
Guide to House Edge
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.
The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Caribbean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of money lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette.
Many other sources do not count ties in the house edge calculation, especially for the Don’t Pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn’t resolved then it should be ignored. I personally opt to include ties although I respect the other definition.
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.
Element of Risk
| 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% |
| Crazy 4 Poker | Standard rules | 3.42%* | 1.09% |
| Heads Up Hold 'Em | Pay Table #1 (500-50-10-8-5) | 2.36% | 0.64% |
| 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% |
| Ultimate Texas Hold 'Em | 2.19%* | 0.53% | |
| Wild Hold ’em Fold ’em | 6.86% | 3.23% |
Standard Deviation
The standard deviation is a measure of how volatile your bankroll will be playing a given game. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds.
The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.
I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.
Standard Deviation
| Number | Probability |
|---|---|
| 0.25 | 0.1974 |
| 0.50 | 0.3830 |
| 0.75 | 0.5468 |
| 1.00 | 0.6826 |
| 1.25 | 0.7888 |
| 1.50 | 0.8664 |
| 1.75 | 0.9198 |
| 2.00 | 0.9546 |
| 2.25 | 0.9756 |
| 2.50 | 0.9876 |
| 2.75 | 0.9940 |
| 3.00 | 0.9974 |
| 3.25 | 0.9988 |
| 3.50 | 0.9996 |
| 3.75 | 0.9998 |
Hold
Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. 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.
Hands per Hour, House Edge for Comp Purposes
The following table shows the average hands per hour and the house edge for comp purposes various games. The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made. This table was given to me anonymously by an executive with a major Strip casino and is used for rating players.
Hands per Hour and Average House Edge
| Games | Hands/Hour | House Edge |
|---|---|---|
| Baccarat | 72 | 1.2% |
| Blackjack | 70 | 0.75% |
| Big Six | 10 | 15.53% |
| Craps | 48 | 1.58% |
| Car. Stud | 50 | 1.46% |
| Let It Ride | 52 | 2.4% |
| Mini-Baccarat | 72 | 1.2% |
| Midi-Baccarat | 72 | 1.2% |
| Pai Gow | 30 | 1.65% |
| Pai Pow Poker | 34 | 1.96% |
| Roulette | 38 | 5.26% |
| Single 0 Roulette | 35 | 2.59% |
| Casino War | 65 | 2.87% |
| Spanish 21 | 75 | 2.2% |
| Sic Bo | 45 | 8% |
| 3 Way Action | 70 | 2.2% |
Footnotes
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* — House edge based on Ante bet only as opposed to all mandatory wagers (for example the Blind in Ultimate Texas Hold 'Em and the Super Bonus in Crazy 4 Poker.
Translation
Casino House Edge Explained Youtube
A Spanish translation of this page is available at www.eldropbox.com.