I was playing a “cash” no-limit hold ’em game recently and got involved with a hand that switched on a few lights in my brain, thus this article. I was in early position and had Ac-Ks as my pocket cards, so I dutifully raised (3 times the Big Blind, which is what I always open-raise with). As expected, most of the other players folded, but one player, the button, called. The flop brought a K and two lower cards, all of different suits (“rainbow”). I made a pot-sized bet to see if my pair of Ks was still the best hand. If he had hit nothing, I figured he’d fold. If he flopped two-pair or a set, he’d at least call if not raise. He called. Okay, so now I figure I’m up against a “real” hand – trips or two-pair, both of which beat me handily. But the turn brought an Ace, so now I had the top two-pair: Aces and Kings. He might still have Trips, of course, but it was going to be difficult for me to get away from my hand, so this guy was about to win a big pot if he had the goods. At this point, checking would tell me nothing; if I did so and he bet, where was I? He could take my check as a sign of weakness, which is okay, if I was convinced my hand was the best and I wanted to “trap” him. However, if he really did have Trips, he’d probably bet and I wouldn’t know any more than I already did, because he might also be betting a lower two-pair. I figured what I needed to do in order to convince myself, if not him, that I had the best hand was to fire another pot-sized bet out there. I figured that he’d raise me at that point if he had Trips and then I’d have to make a decision. He called.

“What have you got, little buddy?,” I thought. The board looked like this: Kc, 7h, 3s, Ah. At this point, there were two hearts and I got the wild notion that he had the K of hearts and maybe another heart, which gave him the nut Flush draw. Fine. I was going to make him pay for that draw, so I made another pot-sized bet. Sure enough, he called and a heart came on the river. I checked and for some odd reason, he also checked. On the showdown, I had two-pair and he had the Kh, 4h for a Flush, which won him the pot. A big pot.

Normally, I just say something like “nice hand” in a situation like this, but I was feeling a bit feisty, so I made the comment: “Calls like that pay my rent,” just to be a smartass. The player who had won didn’t comment, but another player did (the table “expert”, whom we’ve all seen before). His comment was: “Why not call? He had top pair and too much money in the pot to let the hand go.” I said nothing, because I was there to make $$$, not give lessons. The winning player commented: “Yep, my thoughts exactly.” Let me show you, dear reader, the fallacy of thinking that way.

The call of the opening raise wasn’t a huge mistake because there was always the possibility that he’d flop a Flush (a 1 in 119 shot – surprising number, isn’t it?) or maybe I had raised with 10s or Jacks or A-Q, etc. and his King might be good on the flop. Well, when the flop came, he hit his King and his thoughts closed up to the point where he was thinking only about his hand. Sure, he knew I was still in the pot with him, but now his only thoughts were what it was going to take to beat me. He (apparently) never thought that I might have raised with A-A or K-K or A-K, which would make his “top pair, lousy kicker” the second-best hand. Obviously, he had not made a Flush or even two-pair, so now he was running on a wing and a prayer. Mostly prayer. After the turn card fell, there was about $45 in the pot, so when I bet that amount, he was betting $45 in an effort to win $90. That’s obviously a 2 to 1 return on his $$$, but it was a 5 to 1 shot against him making the flush. He had two hearts in his hand and there were two on the board, so of the 45 cards he hadn’t seen (remember, he didn’t know what I had at that point) only 9 worked for him.

Making bets that pay 2 to 1 when you have a 20% probability of making it is not the way to be a long-term winner at this game. Sure, you might “catch”, but you might also catch a 2 if you double on 19 at Blackjack. But does that mean you should do it? Let’s give the guy some credit and say a few other cards might work for him. If he thought I had raised with Q-Q or something like that, then naturally, he felt his hand was good and I was just trying to “buy” the pot. He may have also felt that he might pair his kicker and beat me that way, or he may have thought that another King would make him a winner. So, besides the 9 hearts, he may have felt that any 4 or any King would help him. Since he evidently didn’t think I had a King, let’s credit him with six more “outs”. That’s 15 in total, so with 45 cards left it’s a 33% probability. Beyond that, my opponent evidently thought, “I have too big an investment to quit now”, which is utter nonsense. You need to remember that any $$$ you put in the pot are gone; any attempt to get them back should be bases on probabilities, not on how much you’ve invested.

That’s some basic math of the situation and I firmly believe your play should be grounded in good, solid mathematics. That said, you certainly should not ignore the psychology of the game, which can be a very powerful weapon in your arsenal. Besides such areas like “tells” (verbal or non-verbal signals from your opponent that reliably give you information on their hand) or “looking into his soul” (which I think is BS), the psychological part of the game is worth some understanding. Thinking about what your opponent thinks you have and thinking about what he thinks you think is not just psycho-babble, although some discussions on the topic that I’ve seen certainly approach that threshold. For me, the various “levels of thinking” are best explained by an example.

Let’s say you’re on the button in a no-limit hold ’em tournament and are dealt Ac-Kc, a suited “big slick.” Everyone folds up to a middle-position player who makes an opening raise of 3 times the Big Blind. It’s folded to you and you re-raise an equivalent amount. (I’m going to ignore such things as the size of the BB, stack sizes, etc. in order to keep this simple; I do realize they may affect the play, but I think I can still make my point. Stay with me on this.) Everyone else folds and your lone opponent just calls. You immediately think he has A-K offsuit or something less, because he didn’t re-raise (three-bet) your raise, as you’d expect if he held A-A, A-Ks or K-K. Sure, he might have one of those hands and is trying to trap you, but we don’t know that yet. Now, what does he think about your hand? Well, unless he’s very new to the game, he’s likely thinking you have A-A, K-K or A-K because you re-raised. The flop comes:

and he makes a pot-size bet. You think he has A-K and is betting the two-pair, so you raise in an effort to verify that. He hesitates and (probably) thinks: “Well, he’s not afraid of A-K and all that it implies”, so he just calls. You now think he’s thinking you have A-K, because if he thought you had A-A or K-K, he’d probably fold. This has brought your thought process up one notch; you’re now thinking of what he’s thinking about your hand. Sure, he might be on a flush draw, but I doubt it, because of the rainbow flop. The turn brings a 10d (yes, I’m keeping this simple), so the board is now:

and he bets all-in. He’s obviously implying that he has Q, J and has made a Straight, but what’s he really thinking?

I propose that he thinks you have A-K and, if that’s what he has, he’s trying to steal the pot because at worst you’ll split, assuming neither of you make a Flush. You think that’s what he’s thinking, so you call and that puts you all-in. The cards will now be exposed at this point and if your opponent is a solid player, he’ll show A-K offsuit and you’ll split the pot. If, however, your opponent is not a solid player (they’re definitely in the majority), don’t be surprised if he shows A-10 or A-Q. In any event, he might show A-A or K-K, but I can’t tell you what to do about that, short of folding when he goes all-in. But with A-K in your hand and A-K on the board, the probability of that is pretty small, especially when he didn’t go all-in on your re-raise, which is what most solid players would do when facing only one opponent. By the way, your call meets one of my most important (self-imposed) rules: Call all-in only with the top two-pair or better. That obviously won’t protect you against Trips, but if he had, say, A-10, K-7 or even 7-10(!!!), you’re the winner.

But all that is not my point here. What I wanted to show you is a way of thinking – “getting inside your opponent’s head” – that will perhaps help you with making those tough decisions. You won’t always be right because poker is a game of incomplete information. But, if you’ll start thinking a little more deeply about the hands you play and how to play them, I just have to believe you’ll do better at the tables.

Next time, I’ll begin my lessons on No-Limit Hold ’em. It’s a world apart from Limit, so stay tuned.