Welcome to my section on probabilities in sports betting. This and racetrack betting are unique sections at the Wizard of Odds because it can not be purely analyzed with mathematics. In other words you can never know exactly what the house edge is for a certain bet because of the human factor involved in sports. However we can look at past bets available and their eventual outcome to make some pretty accurate observations. We can also assume that the bookmaker’s actions are motivated by the desire to balance the action on both sides of a bet so that he wins regardless of the outcome. In other words we can assume that on average both sides of a bet are about equal. The organization of this section will be to address various bets available and analyze their return.
Straight Bets
Straight bets are the most popular and in my opinion the best kind of bet of all sports bets. This is a simple bet on the outcome of a game, relative to a point spread. The point spread is created to add some fictional points to the underdog team. For example suppose the Baltimore Ravens are playing the New Orleans Saints and New Orleans is favored to win. The expert handicappers may determine that giving Baltimore an extra 6 points would make it a fair bet, in other words people would bet equally on both sides. The way this bet would look in the papers or in the casinos is New Orleans -6 vs. Baltimore. A way to remember what this means is that New Orleans would have a fictional negative six points to begin the game, or that New Orleans would have to overcome a six point handicap. If instead of a number there is the letter P (for “pick”) then there is no point spread at all and you simply “pick” who will win the game. The point spread is set in units of 1/2. Sometimes an apostrophe symbol is used to designate a half, for example 6′ would be a spread of 6 1/2.
When making a straight bet you must usually คาสิโนออนไลน์ wager $11 to win $10. Another way of looking at is that it is an even money bet but the loser must pay a 10% commission. For example if you wanted to win $50 you would have to bet $55, and if you bet $50 you would get $50*(10/11)=$45.45 if you won (subject to rounding). Assuming that the spread is truly fair the house edge is (.5*10 – .5*11)/11 = 4.55%. In the event that the outcome of the game is exactly on the point spread then all bets are a push. This actually happened twice in the Super Bowl recently. In 99 Saint Louis was favored by 7 over Tennessee and the score was 23-16. In 96 Green Bay was favored by 14 over New England and the score was 35-21.
Sometimes the Las Vegas sport books wills have promotional 5% straight bets. In other words the player must wager $10.50 to win $10. For example this year (2001) the Regent casino offers 5% straight bets during certain hours on Mondays to celebrate Monday Night Football. The house edge on 5% straight bets for a random picker is 2.38%, ignoring ties.
Money Lines
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 on the 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.
House Edge on 10 Cent Line Money Line Bets
Money Lines Probability
Favorite House Edge
Underdog Favorite Underdog Favorite
-105 -105 50% 2.38% 2.38%
+100 -110 51.22% 2.44% 2.22%
+105 -115 52.38% 2.38% 2.07%
+110 -120 53.49% 2.33% 1.94%
+115 -125 54.55% 2.27% 1.82%
+120 -130 55.56% 2.22% 1.71%
+125 -135 56.52% 2.17% 1.61%
+130 -140 57.45% 2.13% 1.52%
+135 -145 58.33% 2.08% 1.44%
+140 -150 59.18% 2.04% 1.36%
+145 -155 60% 2% 1.29%
+150 -160 60.78% 1.96% 1.23%
+155 -165 61.54% 1.92% 1.17%
+160 -170 62.26% 1.89% 1.11%
+165 -175 62.96% 1.85% 1.06%
+170 -180 63.64% 1.82% 1.01%
+175 -185 64.29% 1.79% 0.97%
+180 -190 64.91% 1.75% 0.92%
+185 -195 65.52% 1.72% 0.88%
+190 -200 66.1% 1.69% 0.85%
House Edge on 15 Cent Line Money Line Bets
Money Lines Probability
Favorite House Edge
Underdog Favorite Underdog Favorite
-105 -110 50.62% 3.59% 3.37%
+100 -115 51.81% 3.61% 3.14%
+105 -120 52.94% 3.53% 2.94%
+110 -125 54.02% 3.45% 2.76%
+115 -130 55.06% 3.37% 2.59%
+120 -135 56.04% 3.3% 2.44%
+125 -140 56.99% 3.23% 2.3%
+130 -145 57.89% 3.16% 2.18%
+135 -150 58.76% 3.09% 2.06%
+140 -155 59.6% 3.03% 1.96%
+145 -160 60.4% 2.97% 1.86%
+150 -165 61.17% 2.91% 1.77%
+155 -170 61.9% 2.86% 1.68%
+160 -175 62.62% 2.8% 1.6%
+165 -180 63.3% 2.75% 1.53%
+170 -185 63.96% 2.7% 1.46%
+175 -190 64.6% 2.65% 1.4%
+180 -195 65.22% 2.61% 1.34%
+185 -200 65.81% 2.56% 1.28%
House Edge on 20 Cent Line Money Line Bets
Money Lines Probability
Favorite House Edge
Underdog Favorite Underdog Favorite
-110 -110 50% 4.55% 4.55%
-105 -115 51.22% 4.76% 4.24%
+100 -120 52.38% 4.76% 3.97%
+105 -125 53.49% 4.65% 3.72%
+110 -130 54.55% 4.55% 3.5%
+115 -135 55.56% 4.44% 3.29%
+120 -140 56.52% 4.35% 3.11%
+125 -145 57.45% 4.26% 2.93%
+130 -150 58.33% 4.17% 2.78%
+135 -155 59.18% 4.08% 2.63%
+140 -160 60% 4% 2.5%
+145 -165 60.78% 3.92% 2.38%
+150 -170 61.54% 3.85% 2.26%
+155 -175 62.26% 3.77% 2.16%
+160 -180 62.96% 3.7% 2.06%
+165 -185 63.64% 3.64% 1.97%
+170 -190 64.29% 3.57% 1.88%
+175 -195 64.91% 3.51% 1.8%
+180 -200 65.52% 3.45% 1.72%
According to Las Vegas Sun columnist Jeff Haney casinos that offer the best 10-cent baseball line include the Las Vegas Club, Hard Rock, Club Fortune (Henderson), Cal-Neva (Lake Tahoe), Stardust, Luxor, Excalibur, Barbary Coast, Gold Coast, Suncoast, Orleans, El Cortez, Jerry’s Nugget, and the Rio. He lists some others as well that break from 10 cents early. To view his entire article click here.
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 13-5 10.00% 8.88%
3 6-1 12.50% 13.03%
4 10-1 31.25% 16.98%
5 20-1 34.38% 20.75%
6 40-1 35.94% 24.36%
The Stardust offers better returns on their parlays than the typical pay table above. Another novelty about the Stardust is that all point spreads end in a half point, so there is never a tie. Other casinos that offer the same parlay bets as the Stardust are Sam’s Town, California, Fremont, Edorado, and Jokers Wild.
Stardust Parlays
Number
of Events Pays House
Edge
3 11-2 18.75%
4 12-1 18.75%
5 25-1 18.75%
6 51-1 18.75%
7 103-1 18.75%
8 207-1 18.75%
9 419-1 17.97%
10 849-1 16.99%
Teasers
A teaser is similar to the parlay bet in that you choose multiple events and have to win them all. However the bookmaker teases the player with a specified number of extra points for each team bet on. Naturally the player pays for these extra points in the form of lower payoffs than on a parlay bet.
For example the Ravens are playing the Giants and the Ravens are favored by 3. If you bet on the Giants are part of a 6-point teaser you will win that game if the Ravens outscore the Giants by less then 9 points, or if the Giants win.
The following tables show the payoff and house edge according to the number of teaser points and number of games. Note the variation in payoffs. For example the Fiesta Casino in Las Vegas pays 8:5 for a 3 game, 6 point, teaser, while the Suncoast casino pays 9:5 for the same thing.
6 Point Teasers
Number
of Games Pays House Edge
2 10:11 9.07%
2 10:12 12.68%
3 9:5 7.96%
3 8:5 14.54%
3 7:5 21.11%
4 3:1 9.26%
4 5:2 20.6%
5 9:2 13.89%
5 4:1 21.72%
6 7:1 13.56%
6 6:1 24.37%
7 9:1 25.43%
8 10:1 43.39%
6 1/2 Point Teasers
Number
of Games Pays House Edge
2 5:6 8.84%
2 10:13 12.03%
3 8:5 8.84%
3 7:5 15.85%
3 6:5 22.87%
4 5:2 13.47%
4 2:1 25.83%
5 4:1 12.84%
5 7:2 21.55%
6 6:1 13.95%
6 5:1 26.25%
7 8:1 21.99%
8 9:1 38.88%
7 Point Teasers
Number
of Games Pays House Edge
2 5:7 11.23%
3 3:2 6.84%
3 6:5 18.02%
3 1:1 25.47%
4 2:1 19.55%
4 9:5 24.92%
5 7:2 13.16%
5 3:1 22.81%
6 5:1 16.68%
6 4:1 30.57%
7 7:1 20.06%
8 8:1 35.28%
Based on all 1975 NFL games in the 93 through 2000 seasons the following are the probability of a win, loss, and draw according to the number of teaser points.
Probabilities in Professional Football
Number
of Events 6 points 6.5 points 7 points
Win 67.69% 69.61% 70.89%
Lose 30.39% 29.11% 27.62%
Draw 1.92% 1.28% 1.49%
Stardust Teasers
The Stardust offers a 5-point teaser where ties win. In addition they move point spreads ending with a half by a half point, so every game has the potential to end in a tie. The probability of any random pick winning is 67.1%, based on the 93 through 2000 NFL seasons. Other casinos that offer the same teaser bets as the Stardust are Sam’s Town, California, Fremont, Eldorado, and Jokers Wild.
Stardust Teasers
Number
of Games Pays House Edge
3 3-2 24.56%
4 3-1 19.04%
5 5-1 18.54%
6 7-1 27.15%
7 9-1 38.92%
8 14-1 38.55%
9 19-1 45.04%
10 29-1 44.70%
11 39-1 50.55%
12 59-1 50.24%
13 99-1 44.38%
14 149-1 44.04%
15 319-1 19.92%
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%.
Futures
Propostion bets usually pay long odds that a specified team will win the playoffs or the season championship. For example before the beginning of the 2000 baseball season a bet that the Baltimore Orioles winning the world series paid 35 to 1 odds.
To calculate the house edge on a set of futures bets follow these steps:
Convert all winning odds to a fair probability of winnings. For example if the Orioles paid 35 to 1 odds then a fair probability of winning would be 1/36. In general if the odds pay x to y then the probability of winning is y/(x+y).
Add all the probabilities form step 1. Call this total t.
The overall house edge on all futures bets is 1-(1/t).
Lets look at an example. The Suncoast casino in Las Vegas offered the following odds to win the Pontiac Excitement 400, which ran on May 5, 2001. The following table shows total probability of 155.04%. The house edge is 1-1/1.5504=0.3550, or 35.50%.
Odds to Win Pontiac Excitement 400
Driver Pays Fair Probability
Dale Jarrett 4 to 1 20.00%
Dale Earnhardt Jr. 7 to 1 12.50%
Bobby Labonte 7 to 1 12.50%
Tony Stewart 6 to 1 14.29%
Mark Martin 10 to 1 9.09%
Jeff Burton 9 to 1 10.00%
Rusty Wallace 5 to 1 16.67%
Field (all others) 3 to 2 4.00%
Total 155.04%
Using this method the following list presents the house edge on futures bets on the Superbowl XXXVI at various casinos.
House Edge on Superbowl Futures
Casino House Edge
Imperial Palace 28.09%
Palms 32.1%
Frontier 32.93%
Venetian 33.57%
Rio 33.78%
MGM Grand 34.72%
Bellagio 34.72%
Golden Nugget 34.72%
Holiday 34.72%
Stratosphere 36.64%
Arizona Charlie’s 36.64%
Aladdin 36.82%
Hard Rock 37.09%
Suncoast 38.3%
Regent 40.35%
Ballys 41.74%
Paris 41.74%
Flamingo 41.74%
Hilton 41.74%
Caesars Palace 41.74%
Mandalay Bay 42.49%
Santa Fe Station 43.66%
Plaza 53.36%
Stardust 53.57%
California 53.57%
Luxor 55.41%
Excalibur 56.74%
Monte Carlo 56.74%
Tropicana 57.1%
Gold Coast 57.33%
Circus Circus 57.54%
Harrah’s 58.41%
San Remo 59.09%
Fitzgeralds 61.2%
Lady Luck 61.2%
Binion’s Horseshoe 61.6%
Sahara 68.69%
Many groups of sportsbooks share the same odds on futures with each other. For example Ballys, the Paris, and the Flamingo Hilton all offer the same odds, which are all owned by Park Place Entertainment. There is not always an obvious connection among sportbooks. For example the futures at the Rio are much more competitive than at the Las Vegas Harrah’s, despite the Rio being owned by Harrah’s. The MGM Grand offers the same odds on futures as the Bellagio. The Monte Carlo offers the same futures as the Excalibur.
