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Poker Strategy | Advanced Poker

Calling a Raise with a Pocket Pair

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When playing limit Hold'em, one can usually see the flop cheaply with small pocket pairs. Today I want to focus on calling raises with these small pairs. People often think a call is automatic, as you can flop a set and win a big pot. Indeed if you play the lower limits, you are already quite well aware of this mantra simply from watching the other players at your tables. In no limit or even pot limit Hold'em small pairs have much greater value because the implied odds may well include entire stacks. In limit, however, the implied odds are much more limited.

As many players burn out on the high variance of no limit and switch over to limit, they bring "no limit" expectations with them, and these expectations are going to get them into trouble. To the experienced limit player, this article will likely only reinforce the norms, but should still prove constructive as to why these norms are correct play. To the novice, intermediate, and/or no limit transfer player, the article should demonstrate why the norms are correct. I hope to demonstrate that the lower pocket pairs must be played very cautiously, looking for good value spots, and certainly not blindly calling any raise. One wants neither two few nor too many callers in front or with the expectation of callers behind.

For clarification purposes, I will stipulate that the small pocket pairs range from 2-2 to 7-7. Plenty of people stop at 6-6 and think 7-7 is a medium pair. Others think 8-8 and 9-9 should be played as small pairs as well. As fun as an extended discussion of where the proper hand rankings would be, I am just going to set it aside and get to the issue at hand, calling raises. Of course, one could also play aggressively and reraise with a small pair, but I think this is a play best used at higher limits.

Let's begin with a heads up scenario to get to what I mean. If a tight solid player raises from middle position and everyone folds to you on the button and you hold 2-2 and say, "Well, I could flop a set here, so I'll call." The blinds both fold, so you are heads up with Mr. Tight. You flop a set, and play it by the book. You raise the flop, but only call Mr. Tight's 3rd bet, then raise and cap the turn. Mr. Tight checks to you on the river and calls your bet, paying off your set with his A-A.

So how much have you won? Let's leave rake out for the moment. Mr. Tight contributes two big blinds preflop, three on the flop, eight on the turn, and two more on the river for a total of 15 big blinds. Add to that, the small and big blinds, and you win 16.5 big blinds. Your initial investment was two big blinds, thus you got paid off at a rate of 8.25 to 1. Is this payoff large enough to show a profit in the long run? Just barely, you need a payoff of 7.5 to 1 just to break even because you will only flop a set one time out of every 8.5 flops. Unfortunately, Mr. Tight is not always going to have A-A and pay you off.

If Mr. Tight has A-K and misses the flop, while you hit, you may only get one continuation bet out of him. Similarly, if Mr. Tight has K-K or Q-Q and an Ace comes on the flop, you may not get more than one bet out of him. Also, horror of horrors, Mr. Tight may redraw on you and then you will lose a bigger pot. At 8.4% of the time after you flop a set, Mr. Tight will redraw a set with a bigger pair and assuming you cap the betting on the turn and the river, this will cost you 22 big blinds. All of these situations reduce the amount you can expect to win each time you flop a set. You were only making 3/4 of a big blind over break even in the dream scenario, so in the real world, expect to lose.

The best opponent to be up against isn't Mr. Tight but Mr. Fish. Mr. Fish thinks he is guaranteed to win with A-A and will cap the betting with you on every street. Let's assume Mr. Fish has a very small raising range, such as A-A and K-K. If the betting is capped on both of these streets, you can win 24 big blinds from Mr. Fish for a total pot of 25.5 big blinds, which is well over break even. You need to win only 15 big blinds to break even, so you can reasonably expect to show a profit calling a raise from Mr. Fish.

A marginal opponent to call a raise from is the loose aggressive player. Mr. Loose will try to bet you off your hand on both the flop and turn, maybe the river. The only real difference between the action of Mr. Tight and Mr. Loose is that Mr. Loose bet/folds the river. You have again won 16.5 big blinds, but with a greater expectation of Mr. Loose trying to push you off of a hand. Add rake to either of these best case scenarios, however, and even in your dreams this play is just about break even.

Against Mr. Fish, you can call away, but against a tight solid player or a loose aggressive player, things are more complicated. Against both of these players, what you really want is a multi-way pot. You are more likely to get it against Mr. Loose, of course, as others at the table will also call his loose preflop raises. I'm going to provide hand analysis for just one other caller against Mr. Tight to show that this fails to yield positive expected value (+EV). The other caller will probably not continue after the flop and will only be contributing two more big blinds to the pot (18.5 total big blinds against Mr. Tight in our dream scenario). Winnings are reduced if a drawing board hits and Mr. Tight's bet is called by the other caller. If you two bet, this may alert Mr. Tight to the strength of your hand, but being solid he will probably three bet to try and drive out the initial caller, which will probably happen if the other player doesn't have the draw. Thus the other caller has added three big blinds if he calls the first flop bet.

Now if the other player is on the draw, then you can show a profit under the following scenario. Let's say you cap the flop and both players call. Mr. Tight goes into check/call/down mode and Mr. Draw check/calls the missed turn and folds on the river. Total winnings, if the draw doesn't get there: 19.5 big blinds (5.5 preflop, 8 flop, 4 turn, 2 river). Of course the draw will get there sometimes, and other times Mr. Tight will redraw. Once of every five turn cards, the flush will hit. Let's assume Mr. Draw bets, you call hoping to fill up on the river (you have 10 outs so this is correct play in this pot), and Mr. Tight folds. When you miss the river, this costs you eight big blinds, 10 if you call the river just in case Mr. Draw is bluffing. You will redraw, however, roughly 20% of the time (I'll be more exact in a moment). Against a bad opponent you may be able to cap the river, but against a decent opponent, you may get only one bet in. Bad Mr. Draw allows you to win 23.5 big blinds, while Decent Mr. Draw only 17.5 big blinds. Let's split the difference and say 20.5 big blinds (I'm assuming lower limits so I think the chances are 50/50 of being up against a bad draw chaser). Also of note, if the flush draw hits the turn, it could be a tainted card (for Mr. Draw) that fills you up. For example, you have a set of fives on a 5s-8s-3h board and the turn card is a 3s. Against a bad player you can expect to cap both turn and river here winning 29.5 big blinds. Against a decent player on a non nut flush only, say 20.5. In this rare case (2.1%) a win of 25 big blinds.

If the draw hits the river and you pay it off, you lose 10 big blinds. Assuming you pay it off, then roughly one of every five rivers you lose, but every now and then (4.3%) that river flush will make you a full house and again I think you can expect to win roughly 25 big blinds in that scenario.

While we are thinking about these marginal cases, I'd also like to remind you of the marginal case in which Mr. Tight redraws a set of Aces on you. That will happen 4.3% of the turns and 4.3% of the rivers. In these cases, I think you'll be losing 23 big blinds on the turn redraw and 16 big blinds on the river redraw. The turn redraw loss can be slowed by a flush hitting the river, where you might actually fold after seeing Mr. Tight lead and Mr. Draw raise. Say a loss of only 15 big blinds there.

What do all these numbers mean? (Yeah, yeah, I'm getting there; just let me grab some scratch paper to add this stuff up):

*88% of the time you will miss the flop altogether, losing 2 big blinds.
*12% of the time you hit, most of the time you aren't going to be getting more than
18.5 big blinds
*A small percentage of the time you will hit with a draw on the board that the other player actually has a piece of. Let's look at the numbers for this situation.

Winnings: Losses:
59.57%=19.5bb 2.68%=16bb
3.33%=25bb 11.77%=10bb
2.1%=25bb 2.87%=23bb
3.69%=20.5bb .605%=15bb
13.31%=10bb

(If you check my math you will see that I'm only .075% off, due to rounding which is fairly insignificant). Now, if you multiply these numbers through and add them up, you get the following EV numbers:

*Win = 13.72bb Lose = 3.69bb Total = 10.03bb

Most of the time when you flop a set, there won't be any further action from the other caller; it is difficult to estimate how much extra you can get in. I've limited it to the initial preflop call, but the worse the player, the more likely he is to call one or two bets on the flop and so forth. I'll stay with my conservative analysis and assume that the other caller just folds on the non-draw flop. In this scenario you only get redrawn 8.4% of the time by Mr. Tight's A-A, so total EV is 15.1 big blinds. If we assume a drawing situation occurs 4% of the time and a non-draw board 8% then we get a total EV for when we hit our set of roughly 13.44 big blinds. That is not enough to be profitable, as we need 15 just to break even. Even if we get very hopeful and say that the non-draw board comes 10% and the draw board 2%, the EV is still only 15.1 big blinds, which is a tiny, very hopeful profit. Of course, we've been working with the luxury of Mr. Tight holding A-A, and plenty of the time he will have something less like A-Q, or 10-10 that he will not play as aggressively and so will not be capping the turn with you. Also my entire analysis has assumed that you have position on both of your other opponents and you won't always have this luxury; thus you can lower EV for other positions. All of this means that the actual EV for calling Mr. Tight's raise with a small pocket pair, when only one other player has called, is not positive but negative. You simply cannot expect to win 15 big blinds each time you hit your set; thus calling is a bad play.

What do you need aside from a fish raising his A-A to show a profit? You need more callers. This will build a bigger pot, but the more callers; the more likely it is that one of them has hit the drawing board, which reduces your expected value. It also helps if you have some bad players who overvalue top pair or some calling stations. Or perhaps some loose aggressive players who will lay into one another on the flop and turn, while you rake in the cash. Caution, however, the more players, the more vulnerable the small pairs are to oversets. Pick your spots with these small pairs based on the number and quality of your opponents, or pay the price in the long run.

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