Quantifying True Odds on Parlay Bets

Written By @Hookslide23

It was another week living on the razor’s edge in the land of NFL betting, but I’m happy to report that I survived another gauntlet and came out on top, thanks to Aaron Rodgers and the Packers.  (The previous sentence has been brought to you by NFL bettors since the last decade.)  I would have been even further ahead, but I decided to get fancy for the sake of this column.  More on that in a moment.

I took the Bills +140, the Seahawks at +108, and the Packers +115.  The Seahawks and Packers both won, and there was loud and necessary rejoicing.  This strategy of taking “coin flip” bets and investing on the underdog money line continues to be profitable, even if it is turning into a bit of a grind.  (Should I give myself a “bye week?” Perhaps, by which I mean, “No!”)

Now, about that whole “I decided to get fancy” thing …

Winning two out of three underdog bets like I did this week is awesome.  If you can do that on a regular basis, you’re going to make a lot of money.  You will still make money when you “break even” on underdog wins and losses (such as a few weeks ago when I went 2-2), but it’s obviously less money, because your wins are barely covering your losses.

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Not only did I place those three underdog bets last week, I also (drum roll) bet a parlay.  For those who don’t know what a parlay is, here’s a brief and informative FAQ:

What is a parlay?

Please refer to this FAQ.

Is it true that with a parlay, you can make insane amounts of money on very small bets?

Absolutely you can!  Just not you, specifically.

How does it work?

Instead of placing your $100 bet on a single team for a modest payout, you place that $100 on multiple teams, and if all of those teams win, you can make six, seven, even ten times as much as your original bet.  Again, this does not apply to you, personally.  You will lose these bets every time.

Why do so many people lose these bets?

Because people think they can easily pick three or four winners and cash in, but they don’t understand how math works.  In my case, I picked my three teams and came up with my true odds for each team: the Dolphins were 59%, the Seahawks 55%, and the Lions 63%, so you would think my overall chances of winning the parlay would be fantastic!

Thing again! They are not!

To get the true odds on my parlay, I have to multiply all three of those true odds by each other: 0.59 x 0.55 x 0.63 = 0.20

Those are my true odds to win the parlay: 20%

Those are terrible odds.  Why would you place that bet?

Because the voices in my head are very loud.  And also because the numbers support making this bet.

This is about to get very nerdy, isn’t it?

Yes.  Strap in.

I’ve just explained how to calculate the true odds of winning the parlay.  The next step is to calculate the minimum payout necessary to make this bet profitable. It’s very simple: one divided by the true odds, or in this case:

1/0.20 = 5

The minimum payout I’m looking for is 5-to-1.  Obviously, I’ll take a payout better than that, but it’s got to be at least 5-to-1 for me to even consider it.

How do you calculate the payout?

You have two options here.  The first way is the hard way: calculate the payout percentage on each individual bet, multiply those payouts by the amount you want to bet, subtract your original investment, then divide by your original investment.

Example: the Dolphins were +105, the Seahawks were +100, and the Lions were -128.

+105 = 105/100 = 105% + 100% (my original bet) = 205% payout (2.05)

+100 = 100/100 = 100% + 100% (my original bet) = 200% payout (2.00)

-128 = 100/128 = 78% + 100% (my original bet) = 178% payout (1.78)

My bet ($100) x Payout 1 (2.05) x Payout 2 (2.00) x Payout 3 (1.78) = 729.80

Subtract my $100 bet = 629.80

Divide by my $100 bet = 6.29 (round-up to 6.3)

My parlay payout for these three games is 6.3-to-1, and that is indeed better than the minimum 5-to-1 break-even payout I needed.

What was the easy way to do this?

Tell BetOnline.AG which teams you want to bet and how much you’re betting, and they’ll just tell you what the total payout is.

So how did it go?

All of my teams won except the Lions, because that’s Murphy’s Law: the team I had pegged with the highest chances of winning is the one that lost.  So I lost my bet, because that’s what usually happens with a parlay.  I could have prevented all this torture if I listened to Bet The Board Podcast last week and bet the Bengals and stayed far away from the Lions.  You should do that every week.  I got busy and didn’t last week.  I’m dumb.

Then why keep betting parlays?

It’s all about expected value over the long haul, as always.  I had a 20% chance of a winning parlay for a 630% return on my investment.  If I lose that parlay eight out of ten times like I’m supposed to, I lose $800.  But the two times I expect to win, I’m making $630 each time, which more than covers my losses.  It’s a plus-EV play.  That’s how you stay profitable.  And despite what the internet tells you, parlays can be profitable if they’re executed properly.

You’re saying you want to go get a beer and look at this week’s parlay options?

Absolutely.  “Bartender, Corona with lime, please!”