Probability Question

Just wondering if there was someone who could guide me in calculating or where to find the actual numbers to a probability of possible hands given an opponent's range question.

For example:

What the percentage of the time will villian have AA/KK if he is opening 7% vs 14% vs 3% etc from EP?

Given X combinations of AA/KK possible and X cards in his range that comes out with AA/KK a calculated X% of the time?

Thanks much.

Take the number of total hands in his range.

So If his range is only AA/KK there are a total of 12 hands he will play (6 of each)

Add AKs then there are now another 4 combinations. So a total of 16 meaning 1/4 of the time he is in a hand it will be with AKs (25%)

add AKo and now there are another 12 so a total of 28 combinations of hands. he is now 42% likely to have AKo and 21% to have AA.

As you can see it get bigger from there.

1. Identify the range of hands
2. determine the number of possible hands in that given range
3. divide the chosen hand by the the total possibilities of hands
4. arrive at number
5. find some way to make this process useful (I cant think of a reason to do it)

Really its better to know what the whole range is and compare his actions to the board and what he may hold and just come up with an educated guess

To answer the question. Around 13% of the time when he opens with 7% of his hands.

play around with pokerstove or propokertools so you can a feel for the equity of certain hands vs. various ranges.

Because unpaired hands are so much more common than high pairs, you're usually not in as bad a shape as you might think if you hold a pair.

i.e., if you put someone one AA-JJ, AK (which is a sick, tight range) and you have QQ, assuming you have money already invested you have 47% equity vs. that range, unless you have specific information to believe you are beat, you shouldn't fold.

Likewise, you may feel that you are only flipping at best with AK, but because of card removal (there are fewer combos of AA/KK possible when you have AK than when you have QQ), you are still in good shape against that range, about the same as QQ (40%).

It is important (I think) to note the difference between AK and AQ vs. the top of people's ranges....if you can include AQ in someone's range (AA-JJ, AQ+), AK becomes a small favorite against that range.

AQ vs. the same range is a big underdog (34%).

You can also use this:

https://www.cardschat.com/poker-odds-calculator.php

Thanks for the replys. That's good stuff. I'll definitely run some of those numbers. This kind of analysis (I think) is the key to coming up with more accurate equity decisions post flop. I did a little more research and ran across the "flopzilla" program which estimates the percentage of time an opponent's range hits certain flops - as well as combinations of possible hands that he is continuing with on further streets based on his opening/calling range. I haven't played around with it very much yet, but so far it looks very promising. If you haven't checked it out, it would definitely be worth a look.

Somewhat related: one of my favorite "plays" is to flat an EP raiser with a small/medium PP and then float or raise his cbet even if I don't hit a set when the flop comes out Jacks or lower. According to the flopzilla program, a raiser with an EP opening range of around 8% will have an overpair a little less than 30% of the time. At which point, your poket pair now has about 75% equity in the hand vs what is essentially an overcard draw. You can raise the cbet if the raiser is looser and the flop obviously didn't hit his range or flat and evaluate on the turn. Obviously, do the same with a set or 10+ out draw and it will make it hard for your opponent to get a good read on you. And as an added benefit, it puts a lot of pressure on overpairs while you're playing in position.

Anyway, thanks for the input. I really appreciate it. It's always good to sanity check the math the old fasioned way.