The Good and Bad of Parlays

# The Good and Bad of Parlays

Jason Scavone
Odds Explained
April 17, 2023

At some point in your life, you may have considered the possibility and concluded with great certainty: “I’d like to invest a tiny bit of money and get back, in return, Scrooge McDuck money.” Maybe that led you to the stock market or Bitcoin or Powerball or fancy digital basketball cards or running Fyre Festival. We all have our paths. But there’s a decent chance that thought led you to parlays.

Because we’re talking about sports betting in the year of our lord 2023, we know you’ve listened to plenty of people planning their parlay. Dissecting their parlay. And, eventually, following you around, telling you about how they just missed on the last leg of their parlay.

They’re the worst, granted. Still, that doesn’t necessarily make parlays a bad play. Or a good one. They can certainly be tempting for some bettors. Dangerous, too.

There are times to deploy parlays, and a time to keep your powder dry.

## Parlay basics

We assume you already know what a parlay is. The math behind them is relatively straightforward.

There are a couple of ways to calculate the payouts, to help see what’s going on under the hood.

You could convert each leg to decimal odds, multiply those values together, then convert back to American odds.

Leg 1 (American): -110

Leg 2 (American): -110

Leg 1 (Decimal): 1.91

Leg 2 (Decimal): 1.91

1.91 x 1.91 = 3.65

3.65 = +265

Another way to calculate the payout is to convert the American odds to their implied probabilities. From there, multiply them all together, and convert back to odds.

Leg 1 (American): -110

Leg 2 (American): -110

Leg 1 (Implied): 52.4 percent

Leg 2 (Implied): 52.4 percent

0.524 * 0.524 = .2746

27.64 percent = +264 (The difference is in the rounding.)

## What’s happening inside a parlay?

There are two ways to look at how a parlay works. In The Logic of Sports Betting, Ed Miller and Matthew Davidow advance the idea that a parlay should be treated like a series of successive bets of increasing stake.

The example they use is a three-leg \$10 parlay. Each leg is -110, and the total play pays +600. If you win the first leg, now you have \$19.09 (your \$10 initial stake plus \$9.09 in winnings). That becomes your stake. If you win the second leg, you’re betting \$36.44 on the third leg. The total volume you’re putting in on the play is \$65.53, not \$10.

There are eight possible outcome for a three-leg parlay (loss-loss-loss, loss-win-loss, etc.). That means the average volume for each outcome is \$28.65.

Miller and Davidow write:

Over the course of the eight bets, you haven’t bet just \$80. You’ve actually bet \$229.24. And of that \$229.24 total bet, you lose \$10.

Which works out to a 4.4% hold. Which is roughly the same old hold we’re always looking at on straight bets.

Parlays don’t hold more. They make you bet more money.

And if you look at it that way, the math doesn’t lie. The \$10 you’d lose divided by \$229.24 (the \$28.65 average volume multiplied by eight) is 4.39 percent.

### Viewing the Stake as the Stake

Then again, there’s another way to look at these bets. Likely, it’s the way most bettors do. Not as discrete bets of \$10, \$19 and \$36, but as a whole. As a bet where at the end of the day, their bankroll either shrinks by \$10 or swells by \$60.

And in that view of a parlay, you’re looking at the house edge relative to the amount you’ve risked. Of the eight ways the three -110 leg parlay bet can resolve, seven times you lose \$10 and the eighth you win \$60. The house holds 12.5 percent.

The house edge compounds over the span of the bet.

If you’re compounding interest, a \$100 investment at 5 percent leaves you with \$105 after the first month. After the second month, you earn 5 percent on \$105. Now you have \$110.25. After three months it’s \$115.76. You have a 401k. You get it. It’s beautiful financial magic.

It works the same way with edge. The house edge compounds to nibble away at your stake.

If you make a \$10 bet at -110 you’d collect \$19.09. Roll that over at -110, it’s betting \$19.09 to win \$17.35. Then it’s \$36.44 at -110 to win \$33.13. The total payout is \$69.58. You hit at +596 and your winnings are \$59.58.

But if you had made the first two \$10 bets independently at -110, you’d have had \$38.18. Bet that at -110 and you’d stand to win \$34.71.

Looking at it another way, if you bet \$38.18 at -121, it would net \$31.55. You’d collect \$69.73.

### Don’t Compound Minus-EV Spots

In other words, you can look at it like your original stake is your total stake, or your original stake gets added onto with each bet. Though as a practical matter, you arrive at the same end point.

By that same practical measure, for recreational bettors and bettors who are less sure about their edges, they can start drowning one leg at a time.

“The typical bettor is betting into negative-EV situations, and they are compounding that edge and making it harder for themselves to win in the long run,” Captain Jack Andrews said. “If the odds of you winning get more and more minuscule, you’re going to grind through your bankroll. There’s a psychological effect when you’re winning so infrequently.”

## Compounding Plus-EV

Yes, it does work the other way. If you have multiple plus-EV legs that you can string together, you will compound your edge that way.

But parlays, by their nature, hit less often than straight bets. The breakeven percentage of a two-leg parlay where each leg is -110 is 27.4 percent. It’s 14.4 percent when you add a third leg. Playing parlays means assuming loads of variance.

“You don’t have this infinite supply of positive-EV plays,” Andrews said. “Maybe if you’re an avid Unabated user, you do. For the most part, you see an edge, you grab that edge, and that edge isn’t coming back anytime soon. If you put in a six-team parlay and hit five out of six legs, that makes you feel like you just blew through six positive-EV plays and got \$0 out of it.

“Your EV was very strong though, and for the right kind of sports bettor – the one that thinks the long term – they’re willing to say, yes, I banked a lot of EV and maybe next time I’ll manifest it. Trouble is you’re always wondering if there will be a next time.”

## The Art of Parlays

There is room for the parlay in the sharp bettor’s repertoire. Beyond those situations where you can compound edge with a series of plus-EV legs, there’s a benefit in helping keep a step ahead of the sportsbooks, too.

“Sports books by default, love parlays,” Andrews said. “They think parlays are a sucker bet. If you walk in the door and you’re betting a lot of parlays, they just assume you’re a sucker. If you parlay positive-EV plays together, you’re not a sucker and they think you are. You can slip a few positive-EV parlays in there and disrupt their profiling.”