X to win out of N

Understanding X to win out of N

Before applying this to betting, it helps to understand the general idea behind it, working out the chance that at least a certain number of things happen, out of a group of things that could happen.

Start with the simplest version "at least 1"

Imagine you flip 3 coins, each with its own separate chance of landing heads. You want to know, what's the chance that at least 1 of the 3 coins lands heads?

The easiest way to work this out isn't to add up the 3 individual chances. It's to flip the question around and ask, what's the chance that none of them land heads? If you know the chance each coin lands tails, and you multiply those chances together, you get the chance that all 3 land tails. Subtract that from 100%, and what's left is the chance that at least 1 lands heads.

So with a fair coin, each flip has a 50% chance of landing tails. Multiplying 50% x 50% x 50% gives you 12.5% chance all three land tails. That leaves an 87.5% chance at least one lands heads.

Extending it to "at least 2" or higher

Once you're asking for at least 2 out of a group, rather than at least 1, the maths gets more layers. You're now working out every possible way that 2 or more could come through and adding those possibilities together, rather than just looking at the one case where everything fails.

This gets complicated fast once the group gets bigger. With 3 even probability coin flips it's easy to do by hand. With 6 or 8 proper betting selections, it becomes a lot of separate combinations to work through, which is exactly why the X out of N calculator does this step for you rather than doing it manually.

The two things you always need

Whatever the size of the group or the threshold, the calculation always needs two inputs:

• The individual chance of each thing happening on its own
• How many of them need to happen for the condition to be satisfied

Once you have those two things, the calculation itself is simple to enter. Read our lesson on the X out of N calculator here.

Your job is working out those individual chances accurately in the first place, since the calculation is only as good as what you feed into it. We suggest using the betfair lay odds where available, accounting for the usual indicators such as liquidity and time to event for accuracy. Other methods for true odds calculation can be found in the lesson here for using our True Odds calculator.