I some how just stumbled upon this when I was looking through my recent HH.

How do you calculate the preflop probability that someone has a better hand than you.

For example, if you are on the CO with 88, only 10% of hands beat you, which would make you think that 30% of the time someone behind you will have a better hand.

But this can't be right, because if you are dealt 88 at (hypothetically speaking) an 11 handed table there isn't a 100% chance that you dont have the best hand.

What is the correct way to calculate this?

The Probability Forum might already have something for this, if you try the search function.

TT

It isn't quite so straightforward as this, but it's close: if there's a 10% chance any one person to your left has a better hand than you, there's a 90% chance they don't. If there are 3 people to your left, there's a (0.9)(0.9)(0.9) = 0.729 chance none of them has a better hand than you (if you want to know the probability several things are true, you need to multiply, not add). So there is a 1 - 0.729 = 0.271 probability that at least one of the players behind you does indeed have a better hand than you.

That isn't quite right, because if everyone folds around to you, it becomes slightly more likely that the players to your left have good hands (since higher cards are more likely to be 'available' if the first few people to act all have bad enough hands that they fold). It also depends what you mean by 'better hand' - if you mean 'higher pair than 88', the probability of someone having that is much less than 10% (it's less than 3% actually).

You calculate your equity versus their range. eg they're tight and have a 10% calling range then your eights have around 40% equity. If they're looser then you have more. Versus multiple opponents it gets trickier to calculate your equity.