# The Parlay Problem

**Disclaimer : Nothing I say or write should be construed as financial or any type of advice. My posts on sports betting are exclusively for illustrating probability and statistics concepts, using examples from the real world**

I would rather just straight up write checks to a casino than play parlays

In American sports betting, a -110 means, you bet $ 110 to get a payout of $ 100, if you win the bet

We have talked quite a bit about betting $ 110 to win $ 100, simply because, it is one of the most common bet and payment structures you’ll find in online sports books. Allow me to just use that as an example throughout this series (more on the 110/100 payout structure here)

So, what are parlays ? As opposed to placing one bet, parlays cobble up a number of bets into one thing

For example, in the upcoming Super Bowl this Sunday, you can bet on two things separately: one can be Patrick Mahomes throwing for more than 250 passing yards, and another one can be Christian McCaffrey running (more like - raging !) for more than 100 yards. Those are individual bets and are not connected

A parlay however, combines both of those and gives you a higher payout (than if you bet on both, separately). The difference is : both events need to come true for you to get that payout in a parlay. If only one of those events come true, or if neither come true, you lose the $ 110

**American Odds and Decimal Odds :** There is really only one thing we need to understand, to proceed. That is - how do American odds convert to decimal odds ? Say, if you bet 110 to get a payout of 100 - that’s American odds. If you want to convert it to decimal odds, it becomes (100/110)+1 = 1.91. You can think of this 1.91 as - the total amount of money you’ll get in return, if you place a *successful* bet of $ 1

Great, now imagine you have four events, and each of those has a 1.91 payout structure

So, you need four events to happen and if we assume 1.91 for each event, then for a four leg parlay, this problem becomes : 1.91 x 1.91 x 1.91 x 1.91 = 13.3

So, if you bet $ 100, your payout (if all four events happen) is 13.3 * 100 = 1330. Deducting your initial $ 100 from $ 1330, you end up with a $ 1230 gain

So, every $ 100 of an initial bet gives you a payout of $ 1230 (this moves a little bit, so the four leg parlay card below has $ 1260)

That’s pretty much it, every $ 100 gives you 1260 in gain

Perfect. Now what ?

**Is the payout fair ? **

How would we know, if the payout from the casino is fair ? What I’m really asking is - if my payout is anywhere close to the actual payout I should have gotten ? risk should match rewards right ? even in a world filled with dice, deck and debauchery ?

Great, let’s go back to the drawing board. Rake is the cut taken by the house from each bet (more on Rake - here). You bet 110 to get a payout of 100, where as without the rake, you’d just bet 100 to gain 100 (if you win)

Let’s work with that

Without the rake, if I bet $ 1, I should have gotten a total of $ 2 back (my initial bet of $ 1 + my winnings of $ 1)- as opposed to the $ 1.91 that Vegas gives me (after taking a rake)

So, for a four leg parlay, theoretically, I should have gotten, 2 x 2 x 2 x 2 x (100) = 1600. 1600 - your initial bet of 100 = 1500

Voila !

**In theory, your $ 100 initial bet must lead to a payout of $ 1500, but Vegas only gives you $ 1260**

You can pretty much evaluate any parlay using this structure. Sometimes Vegas gives you more than the theoretical payout, in which case they probably think it is highly unlikely that all those events in that parlay will come true, and vice versa

Honestly though, who are we kidding ?

You really are gambling when you do parlays, I have a better chance of becoming Patrick Mahomes or C-MAC, or hell - Taylor Swift herself, than winning a five or six leg parlay

Parlays are how casinos pay their mortgages - they know the chances of all those four events happening are next to zero

You may as well bet on your cat to stop Christian McCaffery on Sunday - than play parlays

Source : Forbes