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The following tables shows the house edge of most
casino games. For games partially of skill perfect play is assumed.
See below the table for a definition of the house edge.
| Game |
Bet/Rules |
House Edge |
Standard
Deviation |
| Baccarat |
Banker |
1.07% |
0.93 |
| Baccarat |
Player |
1.22% |
0.95 |
| Baccarat |
Tie |
14.05% |
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 |
| Blackjack a |
Atlantic City rules |
0.43% |
1.2 |
| Blackjack b |
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% |
1.71-55.67 |
| Let it Ride |
3.51% |
5.17 |
| Pai Gow c |
1.50% |
d |
| Pai Gow Poker c |
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 |
| Spanish 21 |
Dealer hits soft 17 |
0.76% |
d |
| Spanish 21 |
Dealer stands on soft 17 |
0.40% |
d |
| Three Card Poker |
Pairplus |
2.32% |
2.91 |
| Three Card Poker |
Ante & play |
3.37% |
d |
| Video Poker |
Jacks or better (full pay) |
0.46% |
4.42 |
| Wild Hold 'em Fold 'em |
0.46% |
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.
House Edge
The house edge is defined as the ratio of the average
loss to the initial bet. The house edge isnotthe 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.
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 Carribean 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 ignorred. 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.
| 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% |
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.
| 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 |
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.
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.
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