The Art of the Parlay

Ah yes, the parlay. The most temptation of betting instruments, a way to take a series of wins and multiply them instead of adding them. It's every punter's dream lottery ticket. If it works out, woohoo! I'm rich! If it doesn't work out, eh, it was worth a beer. Every so often you hear about about some rando being eight legs in to some fuck off nine leg parlay, which if it hits is going to make them win six digits. Everyone's talking about it and the bookmakers are promoting them, so it could be you too, right?

Right!?

And indeed yes, it could be you: that's what makes it so tempting. I've touched on it in the past that different countries have different betting traditions. Whereas Irish betting is more focused around finding a small number of high edge bets, "beating the bookie" as we call it, English betting on the other hand has much more of an emphasis on accumulators (or "accas", as they call them over there). English punters love a good have a go hero who wins all ten Premier League games and has his own rags to riches story. In the USA, you have the euphoria and the glory of the parlay, one of the ultimate symbols of making it on your own dime, working smart.

Now parlays are a funny one even by betting standards. Many of you will know that if you talk to non bettors about betting (or worse, delve into the cesspit that is Reddit), you will be met with warnings of "don't gamble, it's a mug's game, my cousin's friend's brother's dog's hairdresser's uncle was a gambler and he lost it all, I wouldn't want the same to happen to you. Bookies always win!" Of course, you know that bookies misprice odds all the time, so this warning (even when it comes from a good place) doesn't phase you; and yet, you can go on to betting subreddits which are full of people who have had the exact same experience with non-bettors and know better, then some of them will say with a straight face, "Don't do parlays, it's a mug's game, you may as well just give the bookies their money back!" That's how you know you're dealing with a powerful tool that requires extra special care when wielding.

Now it would be remiss of me not to say that parlays are one of the bookies' big moneymakers. Whereas the general public chases favourites on singles while being averse to underdogs, parlays are where they're willing to take the cumulative underdog. If you're parlaying a bunch of favourites, it doesn't really feel like you're backing a loser. That's what makes it so easy to sell parlays. On every singles bet, the bookies underpay you a bit. You when compound them in a parlay, they underpay you at every leg. If you bet on a coin toss and were given odds of -105, the overround is about 2.4% so that's how much you'd be down on your stake on average. If you parlayed two coin tosses, the bookmaker would quote you at +281, which would lead to an expected loss of 4.7% on average. From a bookmaker's point of view, you lose money faster and the odds are long enough that it obscures the underpayment. I've heard it referred to a number of times that least year the bookmakers lost money on NFL straight bets but they made it up on parlays. That tells its own story.

How do we do parlays properly? Well, following on from my last paragraph, if you have an edge on every bet, parlaying them will compound the edge. If you were being quoted at +105, your edge would be around 2.4% on a single coin toss but around 4.7% on two coin tosses parlayed. This is where the average bettor fails with parlays: they don't have a consistent statistical edge to begin with, so the parlay overround just murders their account balance.

How else might we find value in the parlay? Through correlated events. The basic premise is that if you have two events that are not independent, we can quantify their dependence via the probability of event B given event A. When you parlay obviously correlated events, the bookmakers will take this into account in the quoted odds. If the bookies underestimate the correlation (or if they overestimate the anticorrelation), you can glean an edge from that, even if the bets individually do not have an edge! In a practical sense this is not something I know very much about but Will from Game On talks about this a fair bit so check him out if you'd like to learn more.

As any of you who have been following the baseball picks will know, baseball has presented a consistent edge easily beyond 95% confidence. As a result of this, I decided to backtest how profitable parlaying the baseball picks would be. In short, it was very profitable, so I started parlaying the daily picks in batches of twos and threes. There was still quite a bit of variance on this, so I decided that I would make a round robin parlay on all the picks for that day. This gave me some feast days, but without the famines that you can get if you do just enough parlays to cover each fixture once. I did round robins by twos and threes and this ensured that the compounded edge of the picks shone through because I scaled down the stake size on each parlay but compensated by the larger sample size. As a result, when three out of five bets hit, it didn't matter which ones hit because the return was similar whichever picks hit.

I haven't parlayed any of the other sporting picks so far because parlays have much less room for error than straight bets. They are a powerful tool which in the right hands will turn minor wins into home run plays but if you misjudge your edge for any reason, you'll lose money faster than if you had just played straight bets. There is always a layer of uncertainty (and hence variance) on top of the original estimation of probabilities of the events we'd like to bet on since we don't know the underlying probabilities for sure. Circumstances might change and your edge might not hold any longer. So if you're looking to play parlays, you'll want to really be careful that you know what you're doing.

One final addendum: prediction markets like Polymarket and Kalshi have begun to offer some simple parlays this year. Watch out for them, because not only can you buy them if you think you have an edge and make more than you would from a bookmaker, you can also sell them if you think they're overpriced and benefit from parlay fever. As always, stay safe this gambling season!