Math Problem... posting here

this is as good a forum as any to post this question... and since its the most followed forum i'll ask here.

how do i calculate the possibility villain hit his hand.

for example...
villain is raising very wide and cold calling alot. he standard raises from MP and i re-raise from SB with AJo and he calls. we are deep stacked.

i put him on a huge range like... 22-99, connectors and gappers from 78 (79)-KQ (KJ), A2s-A5s.

flop is 7s 9x Ts.

how do i mathematically figure out if he hit anything given the range i am assigning him?

it would be a nice piece of information to fit into the puzzle (s) of play.

LOLOLOLOLOLOLOLOL!

it was early in the morning for me!

what i mean is...

given the range, how can i calculate the % CHANCE he connected with the flop?

there has to be some kind of probability formula for this right?

i'm i just high?

Ok, I'll bite.

Unless you can put him on some very specific hands you won't really be able to come up with a range of probabilities which you can use to make a decision. About the best you can hope for is that the more high cards on the flop, the greater chance someone hit it. Also, the more people who saw the flop, the greater chance someone hit it, regardless of the rank of the cards on the flop.

You are better off basing your decision on whether or not some one hit it based on how he bets. Check-raise? Pretty good chance he hit.

If you have a specific range in mind for him, and you have a flop in front of you, the chance (ignoring other info like betting patterns mentioned above) he hit is exactly:

# hands in range that hit
divided by
total number of hands in his range

For that to work out, you have to account for each combo, so 4x any suited hands and 12x any unsuited hands...except that you need to remove the cards that hit (like if 97s is in his range and a 9 hits, then there are only three 97s hands left).

Originally Posted by StarTracker

Ok, I'll bite.

Unless you can put him on some very specific hands you won't really be able to come up with a range of probabilities which you can use to make a decision. About the best you can hope for is that the more high cards on the flop, the greater chance someone hit it. Also, the more people who saw the flop, the greater chance someone hit it, regardless of the rank of the cards on the flop.

You are better off basing your decision on whether or not some one hit it based on how he bets. Check-raise? Pretty good chance he hit.

google search poker stove. plug in that flop and compare the equities of his range versus your hand (?? is this what you want?)

On a JJ3 flop (easier to calc), of the hands you put him on (n_hands), how many contain one or more Jacks or a pair of 3s (n_hit). The percent chance he has a Jack or a full house with his pair of 3s is n_hit/n_hands. Of course if you have one of the hands you put him on, then subtract 1 from n_hands, but that is a trivial amount.

The problem I see is that as long as n_hands is big (the range you listed has 48+32+(16*4)=144 hands), the percent you come up with hitting my example flop (KJ = 16 and 33 = 6) is so small, you can use it to call just about any bet short of putting you all in (22/144=15%).

Now, if you use his bet amount or check-raise action to reduce n_hands down to something reasonable, then you might have some percentages which will allow you to lay it down. But that is not what you asked about, you wanted to know what the chances were before his turn to bet.

Everytime I see a big bet and think 'what are the chances he has one of two cards still out there?', he has it.

Not sure I read the question right, but I'll give you a generic answer that I still think is correct. It is generally accepted that you will only "hit the flop" about 1/3 of the time. I'm sure I read this in HoH but I've seen this stated in countless other media.

Originally Posted by StarTracker

On a JJ3 flop (easier to calc), of the hands you put him on (n_hands), how many contain one or more Jacks or a pair of 3s (n_hit). The percent chance he has a Jack or a full house with his pair of 3s is n_hit/n_hands. Of course if you have one of the hands you put him on, then subtract 1 from n_hands, but that is a trivial amount.

The problem I see is that as long as n_hands is big (the range you listed has 48+32+(16*4)=144 hands), the percent you come up with hitting my example flop (KJ = 16 and 33 = 6) is so small, you can use it to call just about any bet short of putting you all in (22/144=15%).

Now, if you use his bet amount or check-raise action to reduce n_hands down to something reasonable, then you might have some percentages which will allow you to lay it down. But that is not what you asked about, you wanted to know what the chances were before his turn to bet.

Everytime I see a big bet and think 'what are the chances he has one of two cards still out there?', he has it.

tracker... i'm not a math guy. i play with basic math/odds knowledge, patterns, ranges and whatever instinct i've picked up over 250k tourney hands and some ring (which i'm still workin on).

the OP was more of a curiosity than it was to use as a basis for my play. as i said, its another tool to add to justify actions or plays at certain times.