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.
