The Parlay Myth

I know there are a lot of people out there like me who are obsessively addicted to sports betting. One of the more intriguing options on a sports bet is to do a parlay. Parlay are often viewed as the "lottery ticket" of sports betting. The get-rich-quick scheme of the gambler. However, do they actually work? Is this a good means earning that little extra side cash in the long run? The answer really comes down to simply mathematics.

Most Vegas spread odd parlays are at payouts of a -110 line (which means for every $100 you bet you have an opportunity to win approximately $91). Since spread odds are seen as 50/50, the -110 line gives the house an edge. With these same odds in mind the typical 3 game parlay card will pay out at 6/1.

For those that may be new to sports betting I'll digress a bit into what a straight odds parlay is. You place a bet on 3 teams to all win. If you lose one or push (hit the exact number on the spread) on any game you lose the full amount. However if you win all 3 the payout is significantly larger than if you were to simply bet on each team individual (in the case of this example you would be $600 for a $100 bet).

Now the question becomes: When does it become advantageous to the gambler to use a parlay rather than making 3 separate bets? The answer lies in a gambler's winning percentage in the long run (this is assuming prior betting statistics would hold for the future).

WARNING: If algebra makes your head hurt just look at the totals I came up with and assume I know what I am talking about.

Now lets assume you want to bet on 3 teams (A, B, C) and you have $100 dollars to spend. You are equally confident in them so if you bet on them separately you will equally dispense the money.

Dartboard Strategy:
First lets assume you use the dartboard strategy and pick the three games that the darts land on first. By doing so you've given yourself a 50% shot of winning each game.

.5*.5*.5= .125
This is the likelihood you will either win all of your games or lose all of your games. You will either win $91 or lose $100.

3*.125= .375
Their are three possibilities each for making 1/3 or 2/3 correct. A could win, but B and C lose. A and C could win, but B loses. And I think you get the point. If you go 1-2, you will lose roughly $37. If you go 2-1 you will win roughly $26.

(.125)(-100)+(.375)(-37)+(.375)(26)+(.125)(91)= -7.125
So on an average $100 bet you would lose $7.13 (the house advantage rears its ugly head).

Now if you chose to parlay your dartboard picks:
(.125)(600)+(.875)(-100)= -12.5
You are losing $12.50 on your average parlay.

Well gee willickers I guess I ain't too shabby at sports betting (52% WP)
Now lets say you are better than the average joe schmoe at sports betting and your winning percentage is actually at 52%. Using the same math as our prior example:

.52*.52*.52=.1406
The odds that you win all of your games

.48*.48*.48=.1106
The odds you lose all of your games

.48*.52*.52*3=.3894
The odds you win 2 and lose 1.

.48*.48*.52*3=.3594
The odds you win 1 and lose 2.

Average payout on 3 bets:
.1406(91)+(.1106)(-100)+(.3894)(26)+(.3594)(-37)= -1.4388
Still losing money at $1.44 per bet which sucks but hey, at least we have our health (maybe?). And at least our knowledge has helped close the gap.

Parlay:
(.1406)(600)+(.8594)(-100)= -1.58
Wowzers, that winning percentage really closed the gap. Now we are only losing $1.58 per parlay, however it is still advantageous to do separate betting in terms of average return.

Broesph, I am so much better at sports betting than you.
Now lets say you are quite the above average sports better. You win 54% of the games that you pick consistently. Lets go through the math again (ugh):

.54*.54*.54= .1575
Odds you win them all

.46*.46*.46= .0973
Odds you get skunked

.46*.54*.54*3= .4024
Win 2, Lose 1

.46*.46*.54*3= .3428
Win 1, Lose 2

Straight Bets:
(.1575)(91)+(.0973)(-100)+(.4024)(26)+(.3428)(-37)= 2.3813
Hey, look at you, you finally made something. You are making $2.38 per series of bets.

Parlay:
(.1575)(600)+(.8425)(-100)= 10.25
Holy raveoli, that certainly jumped up. You are now making $10.25 per parlay. It was become advantageous to you to actually bet using a parlay rather than 3 separate games

So the conclusion would be if you can consistently win at sports betting 52.2ish% of the time, 3 game parlays would actually be a good bet in the long run. Because this article is running a little long I'll create a Part II showing my calculations for that and also the winning percentages required to win a 4-and 5-game parlay (be aware the percentages climb with the more games added).

Now the task is on you to keep track of your winning percentage and use this as a general to see if parlays are advantageous.

I apologize for the algebra lesson, I'm sure we all took enough math classes in our lives but lets move onto other criteria to consider if you choose a parlay.

First of all you must be as confident in all of your picks as you have been for your past picks. If you are simply "throwing" games into a parlay than you draw your winning percentage back down towards 50% (also a note, if you are below 50% winning percentage the less advantageous parlays become. So if you are below 50% DO NOT PARLAY and I repeat DO NOT PARLAY). Finding an amount of games within a single day can be difficult to do.

Also, parlays are much more risky and you can easily lose your money a lot quicker. You need to have a good base of money to work this strategy with, you will go through parlay droughts which will lower your account a lot quicker.

All those people that tell you parlay are sucker bets are wrong if you can meet the following criteria.

1. Is your betting winning percentage above 52.3%?
2. Can you expect to maintain this in the future in the long run?
3. Can you survive parlay droughts?
4. Are you willing to assume higher risk for a higher payout? (The higher your winning percentage, the higher the average payout, and thus the less risk you are taking on)
5. Are you as confident in all of your picks as you would be betting on them separately (remember avoid "throw in" games, they only hurt you)?

If you can answer yes to all of those then you might want to consider switching to parlays, mathematically it would help you.

This is a really simplified way of looking at everything and assumes the past will hold true in the future but a friend thought it was interesting so I thought I'd share it. Its a good measure if you expect to win as much as you are today.

In part 2 I'll show my calculation for when parlays become advantageous over odds betting for 3,4, and 5 game parlays. I will also show at what winning percentage you start making money with straight betting and with parlays.

I still would not recommend doing parlays but at least now you get to see the payouts in a mathematical format.