Economics says don’t bet on parlays.
Parlays (known as accumulators or bet builders in UK and Ireland) involve combining multiple bets. If your first bet wins, your return rolls on to your second pick and if that wins your money is placed on the third pick and so on.
There is an obvious reason why parlays are generally bad bets. Bookmakers earn profits, so the expected return from a one unit bet is 1-m where m represents the bookmaker’s margin. The expected return on an N-leg accumulator is (1-m)N and that falls as N gets bigger. So the more legs you add, the more you lose.
This is well known in the betting industry and reports from US states have shown average loss rates on parlays are about four times larger than on regular bets.
But that’s not why this paper says parlays are bad. What if you had an edge so the expected value of your one unit bet was greater than one? This paper shows that – even in this situation – if you want to maximize expected utility, you should not play long-legged parlays.
The paper builds on the literature on the Kelly criterion, showing that the higher variance of parlays bets often offsets the higher expected return you get from cumulating your edge. Maximization of subjective expected utility requires placing separate bets when per-leg win probabilities are below one-third, and combining at most two legs for probabilities between one-third and one-half. Surprisingly, these thresholds are largely independent of the bettor’s level of risk aversion and or the size of their edge.
Since most component bets in parlays have probabilities of one-half or below (well below in the case of most player prop bets), the typical 5-leg parlays that people play can’t be justified by having an edge.
Key research finding: The optimal parlay length for bettors with an edge is largely independent or risk aversion or the size of the edge, and points to placing bets separately or at most a two-leg parlay as the best options.
Practical advice: Parlays\accumulators\bet builders are really bad bets if you don’t have an edge. But even if you do have an edge, economic theory says the extra risk is typically not worth the higher returns, so you should not play long-legged parlays.