Odds of flopping a set?

[B40]

What are the odds with pocket pairs of flopping a set? Is it +EV to call low pocket pairs in late position with no raisers?

[Pepsquad]

I think it's 7.5:1

[wtfomgbs]

I believe Ed Miller had a good post on this awhile back, i'll try to find it and post it here.
I think it is +EV to call with these, i find that the amount won after hitting far exceeds the required odds to make it +EV. Even after adding the losses after hitting trips i have made quite a bit of money with these hands.

I'll try and get that post from Ed miller linked for ya.

[bisser]

You have 50 cards left in the deck, of these 2 will do the job. There are a total of (50*49*48)/(2*3) = 19,600 possible flops. Of these, (48*47*46)/(2*3) = 17,296 do not contain any of the two cards that will give you a set or four-of-a-kind. The remaining 2,304 flops are good for you. The odds are 2,304 to 17,296, which is really close to 1 : 7.5 as the other poster suggested.

This was the easy part. The expected value of this call may depend on how expensive it could be to see the flop. Are you in early position? Has anyone raised before you? Being a novice at this game, I would love to read the analysis of an experienced player here.

I can add here a question about a play I made recently. I called in a pot with pocket 8's. There were 5 total players in the pot and 1 small bet was taken by the house, so there were four small bets left. The flop came 2,8,9. Somebody raised, I reraised and had one person calling my reraise with the original raiser folding. This added 5 more small bets to the pot. The turn was the Q of clubs. This was the third club on the board. I raised again and got a reraise behind me. I called, thus making it 8.5 big bets in the pot. The river did not give me a full house, so I would have lost if the other player had a flush. I checked, he bet and I folded. Was my play correct?

Two points:
1. Was I correct to raise at the turn after I saw a third club on the board? My reasoning here was that I don't want to give a free card.
2. Was I correct to fold?

[Pepsquad]

Two points:
1. Was I correct to raise at the turn after I saw a third club on the board? My reasoning here was that I don't want to give a free card.
2. Was I correct to fold?

[/ QUOTE ]

Regarding #1. Yes. You were correct to raise the turn.

Regarding #2. No! This fold almost makes me physically ill. Could villian play top 2 pair similar to the way he played this hand? Yes. Could villain have missed his flush and bet the river in the hopes that you would fold? Yes. It happened to me 3 times today alone! I call a bet on the river and villain turns over his missed flush draw. Villain's river bet put's 9.5 BB's into the pot. Is your set good once every 9 hands? In most low-limit games it most certainly is. Whenever I have doubts about my flopped set a qoute from Winning Low Limit Holdem always comes to mind. "If you NEVER folded a set you probably wouldn't be making much of a mistake." So very true.

Pep.

[DocOfDan]

The odds of making your set (or better - i.e. you might make a fh or poker) are approximately 7.5/1

There are 50*49*48 different flop permutations. There are 6 ways these can be arranged (i.e. AcKdQh is the 'same' as AcQdKh). So there are 50*49*48/6=19600 possible flops to your pocket pair.
There are two cards in the deck to make you a set. So you can have 2*49*48 useful flops if your favoured card comes first i.e. 4704. Your favoured card can come in any one of the 3 slots, and there are 6 ways in which the same flop cards can be ordered. There are therefore 2352 useful distinct flops.
19600/2352=8.33, so your odds are 7.33 to 1

[B40]

Thanks, this would be a good post to read.

Looking over my hand histories, it seems a lot of my pocket pairs, especially 8 or lower are negative BB/hand. I don't have that large of a sample yet, but some of my highest VP$IP hands are pocket pairs with negative BB/hand, but I also have a high PFR% on these hands which is an even bigger mistake.

If I'm going to tighten up my game and only call pockets lower than 8 in late position if there are no raises, doesn't this usually mean a lower pot too? I guess the ideal situation is everyone just limping which would get me maximum value. So is the correct strategy here to call these hands in late positions if there have been no raises so far and say at least half of the other players have called? What would you do with a re-raise? It'd be really tough to fold on a reraise, but if you don't hit the set, almost any face card will have you beat.

[binions]

[ QUOTE ]
Is it +EV to call low pocket pairs in late position with no raisers?

[/ QUOTE ]

It may be posEV to limp with small pairs in early position, depending on the game. Take a small stakes limit game on the net with an average pot of 20XBB. You are getting 7.5:1 to flop a set or better. If the table is relatively passive preflop (not much raising), and early limpers tend to encourage others to limp, I would open limp with 22 on that table.

This recommendation is also contained in SSHE, advocating limping with any pair in any position in loose games (6-8 people see the flop on average).

The reasons are obvious. Small pairs are easy to play, flop it or fold it.

[driller]

As the others have posted, it is 7.5:1 on flopping a set or better. One of my better memories is flopping quads on a flop of j66 when my opponent held jj. At a b&m, I would have had all his chips!

If you think you can win 7.5 times the cost of calling then it is +ev to call. Sometimes in LP you can raise, then raise again if an A hits and steal the pot, etc. Generally though, if no one has entered the pot and I'm in MP, I fold with 66 or less, reasoning that a) someone could raise behind me, and b) even if I hit, I might not win very much with few people in the pot.

[bisser]

Doc, you are double counting some of the useful flops. When you write 2*49*48, you require one of the two good cards to come in first position, but you also allow the second good card to come in second or third position. You then multiply by 3, thus double counting the flops which will give you four-of-a-kind. There are 48 such flops, so you really have 2304 useful flops.