The following are payouts for the various PrizePicks offerings:

Let’s start with calculating the per-leg odds for a simpler case, a Power Play. We will calculate the 4-Pick Power Play per leg odds. Let p be the probability of a single leg hitting. These are each independent events and only one way for this to happen (all 4 hit), so its simply:

If we bet $1 with 10X payout, we need $1 to break-even, so:

Solving for p:

This means that each leg must have a 56.23% chance of hitting to break-even on the payout, which is equal to American odds of about -128.

Now lets take the more complex cases into account, the Flex Plays. We will model the 5-Pick Flex Play. We have 3 different potential payout scenarios. Lets start with the simplest, all 5 legs hitting. There is only one way for this to happen as well, every leg hits. So for this component of the payout, the math is again simple:

The next scenario is when exactly 4 legs hit. Here the math becomes a little more complex, as there are multiple ways this could happen (5 ways to be exact). To calculate this, we need to use Binomial Distribution Formula, which reads as follows:

Where P is the binomial probability, x the specific successful outcomes, {n \choose x} the number of combinations, p the probability of success (same definition as p before), q the probability of failure, and n the total number of trials. Breaking this down once more, our total combinations (known as the binomial coefficient) is:

There are no pushes on these bets, so the probability of losing a leg (q) is simply 1 - p. Plugging in all our numbers:

We can simplify this a bit to:

Finally, we can do the same exercise for 3 legs to hit in a 5-Pick Flex play:

Which we can simplify to:

Finally, lets take our payouts (10X, 2X, and 0.4X) and model a break-even where we bet $1:

Expanding (1-p)^2 to p^2-2p + 1:

The real solution to this is approximately:

This means that each leg must have a 54.25\% chance of hitting to break-even on the payout, which is equal to American odds of about -119.