12.03.2021

Chances Casinos

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

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GameBet/RulesHouse EdgeStandard
Deviation
BaccaratBanker1.06%0.93
Player1.24%0.95
Tie14.36%2.64
Big Six$111.11%0.99
$216.67%1.34
$522.22%2.02
$1018.52%2.88
$2022.22%3.97
Joker/Logo24.07%5.35
Bonus SixNo insurance10.42%5.79
With insurance23.83%6.51
BlackjackaLiberal Vegas rules0.28%1.15
Caribbean Stud Poker5.22%2.24
Casino WarGo to war on ties2.88%1.05
Surrender on ties3.70%0.94
Bet on tie18.65%8.32
Catch a Wave0.50%d
CrapsPass/Come1.41%1.00
Don't pass/don't come1.36%0.99
Odds — 4 or 100.00%1.41
Odds — 5 or 90.00%1.22
Odds — 6 or 80.00%1.10
Field (2:1 on 12)5.56%1.08
Field (3:1 on 12)2.78%1.14
Any craps11.11%2.51
Big 6,89.09%1.00
Hard 4,1011.11%2.51
Hard 6,89.09%2.87
Place 6,81.52%1.08
Place 5,94.00%1.18
Place 4,106.67%1.32
Place (to lose) 4,103.03%0.69
2, 12, & all hard hops13.89%5.09
3, 11, & all easy hops11.11%3.66
Any seven16.67%1.86
Crazy 4 PokerAnte3.42%*3.13*
Double Down Stud2.67%2.97
Heads Up Hold 'EmBlind pay table #1 (500-50-10-8-5)2.36%4.56
Keno25%-29%1.30-46.04
Let it Ride3.51%5.17
Pai Gowc1.50%0.75
Pai Gow Pokerc1.46%0.75
Pick ’em Poker0% - 10%3.87
Red DogSix decks2.80%1.60
RouletteSingle Zero2.70%e
Double Zero5.26%e
Sic-Bo2.78%-33.33%e
Slot Machines2%-15%f8.74g
Spanish 21Dealer hits soft 170.76%d
Dealer stands on soft 170.40%d
Super Fun 210.94%d
Three Card PokerPairplus7.28%2.85
Ante & play3.37%1.64
Ultimate Texas Hold 'EmAnte2.19%4.94
Video PokerJacks or Better (Full Pay)0.46%4.42
Wild Hold ’em Fold ’em6.86%d

Notes

aLiberal Vegas Strip rules: Dealer stands on soft 17, player may double on any two cards, player may double after splitting, resplit aces, late surrender.
bLas 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.
cAssuming player plays the house way, playing one on one against dealer, and half of bets made are as banker.
dYet to be determined.
eStandard deviation depends on bet made.
fSlot machine range is based on available returns from a major manufacturer
gSlot 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. Good casino games. 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

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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

GameBetHouse EdgeElement
of Risk
BlackjackAtlantic City rules0.43%0.38%
Bonus 6No insurance10.42%5.41%
Bonus 6With insurance23.83%6.42%
Caribbean Stud Poker5.22%2.56%
Casino WarGo to war on ties2.88%2.68%
Crazy 4 PokerStandard rules3.42%*1.09%
Heads Up Hold 'EmPay Table #1 (500-50-10-8-5)2.36%0.64%
Double Down Stud2.67%2.13%
Let it Ride3.51%2.85%
Spanish 21Dealer hits soft 170.76%0.65%
Spanish 21Dealer stands on soft 170.40%0.30%
Three Card PokerAnte & play3.37%2.01%
Ultimate Texas Hold 'Em2.19%*0.53%
Wild Hold ’em Fold ’em6.86%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

NumberProbability
0.250.1974
0.500.3830
0.750.5468
1.000.6826
1.250.7888
1.500.8664
1.750.9198
2.000.9546
2.250.9756
2.500.9876
2.750.9940
3.000.9974
3.250.9988
3.500.9996
3.750.9998

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

GamesHands/HourHouse Edge
Baccarat721.2%
Blackjack700.75%
Big Six1015.53%
Craps481.58%
Car. Stud501.46%
Let It Ride522.4%
Mini-Baccarat721.2%
Midi-Baccarat721.2%
Pai Gow301.65%
Pai Pow Poker341.96%
Roulette385.26%
Single 0 Roulette352.59%
Casino War652.87%
Spanish 21752.2%
Sic Bo458%
3 Way Action702.2%

Footnotes

* — 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

A Spanish translation of this page is available at www.eldropbox.com.


Written by: Michael Shackleford

Casino Details

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