Casino, Sports Betting, and
Lottery - A Comparison of the House Edge
by: Melkam Dirset
The house edge, which is the commission that a
gambling agent such as a casino, a sportsbook
(bookmaker), or a lottery administrator charges, is
a yardstick that measures how a specific gambling
game is fair and reasonable. It is one of the most
important factors that every player should consider
whenever he/she is engaged in any type of gambling,
inasmuch as it indicates how much of the money
wagered goes to the gambling agent's pocket and how
much is redistributed to the winners.
Indeed, a house edge cannot be zero since
casinos, sportsbooks, and lottery administrators
have to make some money in order to cover their
expenses, and to make some profit as well. Yet, a
high house edge simply means that the players are
unecessarily being ripped-off, and as a result, any
gambling game with a high house edge should
certainly be avoided by a knowledgeable gambler.
In this article, we shall compare, in the
simplest way possible, the house edges of a
roulette, an evens-odd betting, and a Cash 3 lottery
game as representatives of the three major gambling
categories.
The Equation
The easiest way to compute a house edge is to
compare the actual winnings that are paid by the
respective agents to the winnings that would be paid
in a fair game or bet. A fair game or a fair bet is
one in which no commission is involved; an obvious
model is a game between friends. Therefore, in
percentage form, the house edge is obtained by
subtracting an actual game winning from a fair game
winning and dividing the result by the fair game
winning, finally multiplying by 100. Thus,
House Edge = [ (fair game winning - actual game
winning) / fair game winning ] * 100
Roulette
Because of its simplicity and popularity, we
shall consider the roulette as a representative
casino game. A European roulette wheel has grooves
marked by the numbers 0 to 36; the American wheel
(also called Las Vegas wheel) has an additional
groove marked as '00'. So, the European wheel has a
total of 37 numbers, while the American wheel has
38. Internet casinos usually make available the
option to select the type of wheel the customer
prefers, but the brick and mortar casinos normally
offer only one type. The winning number in a
roulette game is the number corresponding to the
groove where a spinning ball lands.
Now, consider a fair game in which 38 friends are
playing the roulette at home, and each one selects a
number and places a $1 bet on the number (no two or
more players wagering on the same number). When the
ball is spun and lands in a groove, the number
marking that groove will be the winning number. The
person who has selected this winning number collects
all the money on the table thus making him win $37.
On the other hand, if the game were conducted in a
casino, the winner would be paid only $35. The
difference between the two winnings applied in the
above equation gives us the house edge of a roulette
game as
( 37 - 35 ) / 37 * 100 = 2 / 37 * 100 = 5.4%
This means that every time you spend a $100 on an
offline or online casino roulette, $5.40 goes to the
casino and the rest is redistributed to the winners.
Evidently, there are quite a number of casino games
and the house edge varies from game to game, many of
them having a house edge less than that of the
roulette. For obvious reasons, a good gambler always
prefers games that have low house edges, while the
casino itself loves those games with high house
edges. For example, the house edge of craps is 1.4%
which makes it one of the most preferred casino
games by the players.
Even-odds Sports Betting
Again, because of its simplicity, we shall
consider an even-odds betting as a representative of
this category of gambling. By even-odds we mean that
the event (usually a sports game) has equal chances
of going either way. An example is a tennis match
between two competitive players each of which has an
equal chance of winning the match.
A fair bet, in this case, is just a simple bet
between two friends who just pick one of the tennis
player as winner. If these two friends wager $1
each, the winner will collect $2, thus winning $1.
If instead the bets are placed through a sportsbook,
the winner will collect only $1.91, since the odds
of an evens game at most bookies and online
sportsbooks is 1.91. If you are not familiar with
the decimal representation of odds, 1.91 is the same
as 10/11 in UK notation and -110 in US odds
notation. Odds of 10/11 mean that you'll win $10
when you wager $11; and odds of -110 mean that you
have to wager $110 in order to win $100. Anyway,
since the winnings paid by a sportsbook is only
$0.91, the house edge of an even-odds betting will
therefore be
( 1 - 0.91 ) / 1 * 100 = 0.09 * 100 = 9%
So, this is how sportsbooks make a living. Since
several internet sportsbooks offer odds higher than
1.91 in order to lure bettors, the house edge could
be smaller than 9%, which is one of the things that
the bettor should be looking for when searching for
a sportsbook. On the other hand, if the bettor is
wagering on parlays the house edge would be
significantly higher than 9%; for big parlays, it
could go as high as 40%.
It should be apparent by now that the gambler is
better off with casino games than sports betting. It
should also be noted that while the house edge could
be a major factor to consider while selecting a
gambling game, it is by no means the only one. For
instance, one should consider the fact that casino
games are mostly games of chance, while sports
betting also involves a learned decision in
selecting a pick, consequently leading to a higher
probability of winning a bet.
Cash 3
Depending on the state you are in, this lottery
game may be known by a different name such as Pick
3, Play 3, Daily 3, etc. In this game, the player
selects a three-digit number from 000 to 999, and
plays the number as a straight or as a box. A
straight play is a prediction that the number will
come exactly as selected while a box is a prediction
for the number to come in any order. For instance,
if a player selects the number 672 and plays it
straight, he/she will win if the number drawn is
exactly 672. Instead, if the player plays 672 as a
box, he/she will win as long as the drawn number
contains a 6, a 7 and a 2, in any order (276, for
example). Obviously, a straight game pays much more
than a box game for the same amount wagered.
Now consider 1000 friends (maybe in a club)
selecting a number as a straight, each for $1, so
that all the 1000 possible numbers are covered. When
the winning number is drawn, the person who has
selected that lucky number will be deemed a winner
and will cash in all the $1000 collected, so making
him win $999. This is a fair game. In the case of
state lotteries, however, the winner will be paid
only $500 in most states. Some states may pay a
little bit less, others may pay a little bit more,
but $500 is more or less the standard. The winner
therefore wins $499. The house edge for a Cash 3
game will therefore be
( 999 - 499 ) / 999 * 100 = 500 / 999 * 100 = 50%
This house edge applies not only to the Cash 3
game but also to all state lottery games such as
Play 4, Cash 5, Mega, Fantasy 5, Lotto, Power Ball,
etc. So, whenever you are playing the state lottery,
remember that you are wagering only half of your
money on the actual lottery; the other half, you are
just giving it away. Where this other half goes is
not the gambler's concern, since his/her main
objective is to win some money in order to pay the
ever present bills, or to get out of a miserable
life, or to change his/her 20-year-old car. As
regards contributing to education and other noble
causes, there are other means of collecting money
called taxes and charities.
Unfortunately, many states do not allow casino
games, and furthermore, sports betting is illegal in
the United States. The player is therefore left with
no choice but to cross state borders in search of a
casino, or more recently, to engage in online sports
betting through the several offshore internet
sportsbooks. Nowadays, there is a plethora of
trustworthy online casinos and sportsbooks operating
from Canada, the UK, Antigua, Costa Rica, and so on.
The Conclusion
As far as the house edge is concerned, it has
been shown that casino games are the best choice for
the gambler. On the other end, any state lottery is
a pretty miserable game to play. Nevertheless,
besides the house edge, there is also the
possibility of winning to consider.
Casino games, like lotteries are mostly games of
chance; the player just selects a number or numbers
and waits to see what luck brings him/her. There is
absolutely no basis to prefer one number to others.
Some people try to analyze previously drawn numbers
in order to see the trend and predict the next
numbers. This strategy may work a few times, but not
always. Keep in mind that it is the players, and not
the machines, who remember the previous numbers. In
short, the possibility of winning a roulette or the
lottery entirely depends on luck.
While there is little or nothing that a roulette
or a lotto player can do to initially select a
possible winning number, the situation could be
quite different in the case of betting. With a lot
of information and some assistance from sports
handicappers, it is possible to predict the outcome
of a sports event with more certainty than
predicting a Cash 3 number.
