X or Y to occur
Understanding X Or Y To Occur
Before applying this to betting, it helps to understand that "or" doesn't always work the same way. Sometimes only one of the two things can possibly happen, and sometimes both could happen, and that difference changes how you calculate the combined chance.
When only one can happen
Imagine rolling a single die. You want to know the chance of rolling either a 6 or a 1. These two outcomes can't both happen on the same roll, only one number comes up. When outcomes can't overlap like this, you simply add their individual chances together. A 6 has a 1 in 6 chance, a 1 has a 1 in 6 chance, so rolling either one is a combined 2 in 6 chance. For a sports example, Player A or B to score the first try is mutually exclusive. Only one first try can be scored, so only one of the two outcomes can ever come true. You can use our Combined Odds calculator for this, and read its associated lesson here.
When both could happen
Now imagine flipping 2 separate coins and asking for the chance that at least one of them lands heads. Unlike the die, both coins could land heads at the same time. Simply adding the two individual chances together would overcount that overlap, since the case where both land heads would get counted twice.
The reliable way to handle this is to work out the chance that neither one happens, then subtract that from 100%. Each coin has a 50% chance of landing tails, so both landing tails together is 50% x 50% = 25%. That leaves a 75% chance at least one of them lands heads. This is the same approach used for X out of N to occur.
For another sports example, Player A or B to score a try is not mutually exclusive. Both players could score, so more than one outcome could happen. Pull the true odds from Betfair if the market's liquid enough, or apply vig to the best available odds, and use the X out of N calculator and read its associated lesson here.
The two things you always need
Whatever the situation, working out the combined chance of "X or Y" needs:
- The individual chance of each thing happening on its own
- Whether the two things can overlap, or whether only one of them can ever happen
Getting that distinction right at the start decides whether you simply add the chances together, or need the neither happens approach instead. Get it backwards and the answer will be wrong even if every other number going in is accurate.