[Help] Probability of any opponent having a range of hands

[DottMySaviour]

Is there anyone out there who has a formula for calculating the probability of at least 1 opponent with a range of hands?

For example, I want to know if I have 22 against 8 opponents, what's the probability of any of them having 33+ to AA (which dominate me). I don't want an estimated probability.

I'm not sure if this is even possible with just formulae, but I would appreciate it if someone has it and is willing to share with me.

 

[XXPXXP]

36.33%

the formula is on any of the probability book of advanced maths.

 

[Excomm]

Yeah it depends how many other hands are dealt in. The probabilities are

Vs 1 player 5.88%
Vs 2 players 11.41%
Vs 3 players 16.54%
Vs 4 players 21.24%
Vs 5 players 25.46%
Vs 6 players 29.14%
Vs 7 players 32.22%
Vs 8 players 34.64%
Vs 9 players 36.33%

You probably didn't want all of those, but I figured I'd include them since you didn't want an approximation.

 

[detroitjunkie]

so what you're saying is i should shove with pocket 2's every time! SWEET!

though i think op wanted the actual formula

and i think you have posted a list that may contain odds for 22 as well as all other pp's but i may be wrong, think op wanted 33+

 

[Shaetano]

Shouldn't you also take into account possible pairs made on flop/river/turn? Those will have you dominated as well, although they're now hands that aren't made, and don't beat you as of yet...

This will also lower your expectation % .

 

[DottMySaviour]

Thanks for the replies. But I still want the formula. I also want to know for other cases like I'm holding AJ and and what's the odds any of my opponent have me dominated (AA, KK, AK, AQ).

 

[detroitjunkie]

Ok. You convinced me somehow. There are 1326 starting hands in TH. You have one of them so 1325 remain. Take how many hands you want to know about and divide by 1325.

Ex. You have 22. What are odds he has AA. AA has 6 combos. 6 /1325=.0045. Or .45%

Ex. You have AQ. Odds you are beat. AA has 3 hands. AK has 12. KK has 6. QQ has 3. Total 24. 24/1325=.018. Or 2% essentially.

Good luck and bring a calculator