[Ganchrow]

Originally Posted by rjp

If you're betting a Kelly fraction then parlays can fit in nicely.

Let's say you find two 55% bets against -110 odds (a 0.1033% expected bankroll growth), which is worth roughly 2.7502% at half Kelly.

Now these figure to both happen 30.25% of the time, and you're going to get paid out at +260, so for this two team parlay your expected bankroll growth is now 0.1130%, which is slightly better than each individually.

Assuming half Kelly, what you do is bet 1.7115% on the parlay, and then spread out the rest of the remaining worth on each individually. Let's say you've got a 10k bankroll: individually you would want to wager $275.02 on each, but instead you should wager $171.15 on the parlay, and then you should wager $103.87 on each straight bet ($275.02 - $171.15 = $103.87).

I'd like to hear what Ganchrow thinks of this, but based on everything I've read from him and others about Kelly this would be the appropriate way to get the best of what's available.

Well your numbers are slightly off, but you've got the right idea.

Given a $10,000 bankroll at half Kelly, two independent events priced at -110, each occurring with 55% likelihood, the Kelly optimal allocation is $267.94 on each single bet and $7.59 on the (true odds) parlay, yielding expected bankroll growth of 0.2070%.

Note however, that these numbers only hold if the parlay pays out at true parlay odds. If the parlay instead were only to pay out at +260, then the Kelly optimal allocation would be $275.34 per single with nothing on the parlay. This would yield expected bankroll growth of 0.2068%.

Check out Simultaneous-bet Kelly staking -- the simplest case where I explain the math in the unconstrained case (post #9), and its implementation in my Multivariable Kelly Calculator.