Throw Those Pocket Pairs Away

I was messing around with some figures on the calculator on my computer and suddenly realized I was looking at some staggering numbers. If you are dealt a pocket pair, we'll say 77 you have to figure, for the most part, that the only way you're going to win with a hand like this is if you hit trips. Ok fair enough, nothing I didn't already know.

So what are the chances that will happen? Now I was always told the odds are 7-1 You have 2 outs divide that by the number of cards not seen which is 50 and you come up with 0.04!!! What!!!! That my friends is a 4% chance. So 4 times in 100 you will hit trips. 96 times out of 100 you will hit nothing. Now if anyone sees a problem with my numbers or you see an error in the calculations please let me know but no matter how i look at it I come up 0.04 which is 4 one-hundreths which is 4%.

Now I don't know how anyone can equate that to odds of 7-1 but I have seen that number quoted on various sites on Holdem. If I'm only going to hit trips 4 times in every 100 tries you can bet your bottom dollar I fold them preflop. Even in a NL game you could not expect to make more than you will lose in the long run.

Now the only question is how high of a pocket pair do I throw away and quite honestly I have no definite answer, perhaps some of you folks do. The question to ask is what is the mininum pocket pair that has a chance to stand up on it's own and take down a pot at showdown. We all know AA KK QQ and many times JJ can and will be good enough but what about 10 10 and 99. Tough call to say the least. I think I will go in with 1010 and higher simply because of the nut straight and Royal possibilities. I know their slim but it does give me a viable reason to arrive at 10 10 as my mininum playable pocket pair. As always all opinion pro and con are welcome.

Now before someone points it out I have not included that there will be times that a hand like 55 or 66 olr 77 gives you the nut straight or even gives you the flush because the board shows 4 of one suit and you have the 5th suit and no one has the flush. These things do happen but not often enough for me to consider it in my decision making process regarding pocket pairs.

You accounted for only one card on the board! There are of course five cards (and thus five opportunites to hit your set) for the community.

Basically, the 1 in 7 is probably good true

I did a rolling calculation myself which exactly figures the odds of catching trips from a PP on the FLOP:

Hitting set from pocket pair on flop: 1 / 8.51

I find that number to be more useful with lower pocket pairs (2-6) because odds are you'll have to call another bet after the flop anyways.

Bored, so I did the calc's for catching trips BY the turn and river (which includes the 3 cards on flop)

Trips by turn: 1 / 6.44 15%
Trips by river: 1 / 5.21 19%

Basically, there's a 12% chance of catching that third card on the flop, a 16% on the turn, and a 20% by the river (roughly 1 in 5)

I'd explain in more detail how I got the exact numbers if someone finds otherwise...

Not sure where the 1 in 7 came from or what it means, but that's what I found. Of course like I stated before, it can become expensive to remain in hands until the river if you're banking only on making a set.

for the flop its about 7.164 to 1

(2 / 50) + (2 / 49) + (2 / 48) = .122482

100 / .122482 = 8.164

7.164 to 1

But that's still a 12% chance of hitting it and 88 times out of 100 you miss. I'm mucking them.

Starlight, have you studies the chances of your oponent to get a pair. You still have a huge chance to win if you have 88 and your opponent KJ. You are only checking the stats for trips but as far as i know I've won way more hands than losing with pockets even if i don't hit trips.

yeah that the way i would have worked it out as well

taking this further to the river we have

(2 / 50) + (2 / 49) + (2 / 48) + (2 / 47) + (2 / 46) = 0.208514

100/ 0.208514 = 4.796

which is 3.796 to one to make your set by the river

however i dont know if this is 100% right - ie. do you need to adjust the odds slightly in the off chance you make quads?

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Heh! 1 in 8 to flop a set. I can get 10-13 small bets into the pot when I make my set.

Ok, so is the overall consensus that I should see the flop with those small pairs? If so then in a tournament at what blind level do you stop? If it will cost you 10% of your stack do you still see the flop with a small pair?