|
House
Edge on Point Spread, Total, and Money Lines
Point Spread Bets: Almost always the bettor must lay $11 to win
$10. Assuming the probability of winning is 50% then the player's
expected return on an $11 bet is 0.5*$10 + 0.5*-$11 = -$0.50. So
an expected loss of 50 cents on an $11 bet means the house edge
is 0.5/11 = 1/22 = 4.55%.
Sometimes a casino has a promotion in which players only need to
add 5%, instead of 10%, against the spread. In this example the
player would bet $105 to win $100, or $21 to win $10. The house
edge having to lay 105 is 2.38%. Also, sometimes when a point spread
is at or close to 3 or 7 and the casino wishes to make a small adjustment
they will change how much one must lay, or get, on a point spread.
For example suppose in the above game the casino wanted to encourage
more people to bet on New York without going as far as moving the
point spread to -3. They might let the New York Bettor have even
money, while making the Buffalo bettor lay $120 to win $100.
Total Bets: Like point spread bets total
bets have a 50% chance of winning if picking randomly and the bettor
must usually bet $11 to win $10. So the house edge is the same as
point spread bets, 4.55%.
Money Line Bets: It is my understanding that when
setting money line bets the odds makers first determine a fair money
line with no house edge. For example the odds makers in the New
York/Buffalo game may have felt the probability of New York winning
was 60.78%. A fair set of money lines would be +/- 100*.6078/(1-.6078)=
+/- 155. Then the actual money lines are moved apart by an equal
number in both directions, in this case +145 and -165. This degree
of movement will get larger as the fair money line number increases.
In closely matched games both money lines may be negative. For example
if the true lines were +/- 102 and the casino moved the actual lines
10 points each the actual money lines would be -112 on the underdog
and -108 on the favorite.
To determine the house edge on money line bets let me define these
variables:
u = money line on underdog
f = money line on favorite
If u is positive then the house edge on the underdog is (u+f)/(f-u-200)
If u is positive then the house edge on the favorite is 100*(1+(u/f))/(200+u-f)
If u is negative then the house edge on the underdog is 1+(200*(100-u)/(400+u-f))/u
If u is negative then the house edge on the favorite is 1-((200+u-f)*(f-100)/(400+u-f))/f
In the New York/Buffalo game for example the house edge on Buffalo
is 3.92% and on New York is 2.38%.
Parlays
The Parlay is a way to bet on multiple sporting events with hope
for a big payoff if all of them win. All picks are relative to the
same point spread as in straight bets. If just one event doesn't
win or draw then you lose the entire bet. If one or more event is
a draw then those events are ignored. If you win all the other events
you get paid according to the number of events that you did win.
In the event all games bet on result in a push except one or none
then the entire bet becomes a push. The following table shows the
payoff according to the number of events bet on and the corresponding
house edge, assuming that the probability of winning any given event
is 50%. In addition the table presents the house edge of making
the same number of straight bets and letting the winnings ride every
time. Note that the house edge is less on the three team parlay.
House Edge on Parlay and Consecutive Straight Bets
Number of Events Pays House
Edge
(Parlay Bets) House
Edge
(Straight Bets)
2 13 to 5 10.00% 8.88%
3 6 to 1 12.50% 13.03%
4 10 to 1 31.25% 16.98%
5 20 to 1 34.38% 20.75%
6 40 to 1 35.94% 24.36%
Teasers
Teasers are similar to parlays except the point spread on each game
moves 6, 6.5, or 7 points in the player's favor. The player pays
for this in the form of much lower winnings. For example assume
Baltimore is an 8 point favorite over San Francisco. If you tease
Baltimore on a 6-point teaser they will only have to beat San Francisco
by more than 2 points.
I have more about NFL teasers in my sports betting appendix 4.
Buying Half a Point
The straight bet player has the option to move the point spread
1/2 point to his advantage. The cost of this half point is laying
120, as opposed to 110. The most oportune time to buy a half point
is when one team is favored by 2.5, 3, 6.5, or 7. This is because
many games end in a 3 or 7 point difference and the extra half point
can either turn a loss into a draw or a draw into a win. However
many sportbooks do not allow purchasing a 1/2 point on these spreads
for exactly this reason. Over 1975 games during the 1993 to 2000
seasons the overall house edge by purchasing the extra half point
is 4.13%.
|