Hero:88

Flop: 29A

Me and a friend of mine were talking about how to calculate the chance that your opponent has hit either a 9 or an A0?

My friend was thinking that if we looked at this, as if we were to deal two random cards to our opponent, then the first chance to hit one of the 6 cards, with 47 cards remaining + the second chance to hit one of the 6 cards with 46 cards remaining would equal the total chance.

6/47 + 6/46=12,7%+13%=25,8%

But wouldn't this require that my opponent is playing a random hand?

My thinking was that I'd put him on a range:
A9s+,K9s+,Q9s+,J9s+,T9s,A9o+,K9o+,Q9o+,J9o+,T9o.

And calculate how many combination of hands with either a 9 or A or both / by the total combinations.

105/201=52,2%

You have to put your opponent on a range. The one you use makes no sense though, why would he have T9o but not A8s?

Also the whole calculation is pretty useless if you exclude the hands that already beat you preflop, 99+.

And lastly, you need to weight the range based on preflop action.

You're asking a lot of questions about how to calculate a bunch of stuff, which you'd never do in real time at the table, and which are easily referenced elsewhere. I do wonder what your end goal is, and if you've thought any of what you've learned has actually made you a better player?

Well, I was just looking for the mathematical solution to calculate a percentage, after a debate with my friend on how to do it. Its just that I find the mathematical aspect of poker very interesting, not that I'm trying to crack the code of poker using math I havent considered anything about why he'd have T9 but not A8.

But in regards to excluding 99+, maybe he raises with 99+ but only calls with
A9s+,K9s+,Q9s+,J9s+,T9s,A9o+,K9o+,Q9o+,J9o+,T9o.

The first method isn’t quite right. You want to calculate the probability of hitting the first card plus the probability of hitting the second card after missing the first.

6/47+41/47*6/46 = 24.1%

You could also use combinations. There are 41 remaining cards that are neither an Ax or 9x. 41C2/47C2 = 75.9% that villain has neither card.