pocket pair odds

Just wondered if any of the members knew what the odds were of someone having a pp higher than another pp, e.g. at a full table say I got pp7's what would be the odds of someone at the same table having a higher pair. I think I'm asking this because if you get dealt a pp usually you will have the best hand at the table as even pp2's beats AK, so if for example I get dealt pp4's or 5's and I'm on the button or near it with 15bb and someone raises from ep would it be a good move to shove thinking that the odds are with me in that he has not got a pp and is raising with AK or the like. Hope I've put this well? Thanks all again

Well, first you need to know 2 things:

1. How many people at the table.
2. How high of a pocket pair do you have. (If you have AA, you probably have the best PP. LOL)

If you have pocket 7's on a full table I think its roughly 1 in 4.

The problem with small pocket pairs is that you are either way behind or about even.

Re-raising all-in with a small pocket pair can be right, but is often not very good. It all depends on what range we put our opponent on, and how likely it is that he will fold.
We also have to think about the risk of one of the blinds waking up with a big pair.

does anyone know the percentages? E.g. if I have sevens what is the percentage per higher pair I'm sure I read once it was about 3% chance per higher pair so if there was pp8s through to ppAA's that would equate to a 21% chance that someone held a higher pair, can anyone confirm this? I'm sort of asking about this because of the option of shoving when short

The percent chance that a specific opponent has a better pair is as follows:

Take the chance that his first card is better. (Eg: If you have pocket 2's, there are 48/50 cards that are better.) Multiply by the chance that the second card pairs the first, (Always 3/49) and you get the odds of them having a better pair. Multiply by the number of opponents to get the chance that anyone at the table has a better pair. I'll leave the chance that more than one person has a better pair as an exercise for the reader.



But I'm not sure how useful this is at the table. If they are already raising, then the likelyhood that they have pockets goes up. Since the cards have already been dealt, the chance that they have a better pair is either 100% or 0%. At this point, I think your read on the opponent is more important in deciding whether to shove.

(Disclaimer: I think the math is correct, but I don't guarantee it.)

Here is a way to approximate the percentage. It's an approximation because the math below is based on a full 52 card deck and not a 50 card deck missing a pair of 7's.

The chances of drawing any two cards out of deck making a pair is 1/17 (3/51).

The chances of that pair being bigger than 77 is 7/13 (7 pairs consisting of 88, 99, TT, JJ, QQ, KK, or AA)

Since each of the 8 other players has the same chance the result is (1/17)*(7/13)*8 = appx 25%

Again, the more correct calculation needs to take into effect that you are currently holding pocket 77 and there are only 50 cards left, not 52. The difference between the correct answer and the estimate of 25% is minimal.

I don't think I've overlooked anything but feel free to correct me if I have.

great answers guys thanks for the explanation it seems to me to be around 4% per higher pair at a full table, like I said it's valuable to know I think if you are short stacked, that the odds are with you and that even AK has to draw out on you. I'll down load this chart it's great you have took the time to post this on x2486 thanks mate.