House Edge on Money Line Bets
Money lines are another popular way to bet on sports. This is a simple bet on the true winner of a sporting event without any point spread. Naturally one team will be favored most of the time so if you want to bet on the favorite you must bet more than you stand to win (laying odds). If you bet on the underdog you stand to win more than your bet (taking odds). Let's use the Baltimore/New Orleans from the previous section as an example again. The money line would look something like this: New Orleans (-210) vs. Baltimore (+170). This means that if you prefer to bet on the favorite, New Orleans, you must wager $210 for every $100 you win if New Orleans wins. If you prefer to bet on the underdog, Baltimore, you win $170 for every $100 you wager if Baltimore wins.
The way a money line is established is first the bookmaker uses his best judgment to determine the probability that the favorite will win. For example let's assume 60%. He then converts this to a fair money line with no house edge. If the probability is p then the money lines are +/- 100*p/(1-p). If p is 60% then the fair money lines would be +150 and -150. Then the bookmaker will take a constant and add it to the amount the favorite better must bet and subtract is from the amount the underdog better can win. A common constant is 10 points. In this example the bookmaker would adjust the money lines to +140 and -160. This is referred to as a 20 cent line, referring the total line movement from the theoretical fair line. For games with a strong favorite the numbers of points will increase.
If the two money lines are x and y (for example x=+140 and y=-160) then the house edge taking odds (or betting on the underdog) is (x+y)/(200+x-y). The house edge on the laying odds (or betting on the favorite) is -100*(x/y+1)/(200+x-y). In the +140/-160 example the house edge on the taking odds is 4.00% and laying odds is 2.50%. If the player must lay odds on either team (for example x=-105 and y=-115) then the house edge on x is ((20000/x)+x-y+200)/(x-y+400) and on y is ((100/y)*(x-y+200)+200)/(x-y+400). In this example the house edge on x is 4.76% and on y is 4.24%.
The following tables show the house edge according to the kind of money line (10, 15, or 20 cents) and specific money lines.
