As I’ve said many times before, a hand of two-pair (two-pairs is probably correct, but it sounds weird) is often the minimum holding I want when going all-in during a No Limit Hold’em tournament. Sure, there have been plenty of times that I’ve called all-in with top pair, top kicker but I really do try to limit those situations as much as possible, like calling a desperate short stack when I’m getting really good pot odds and a loss won’t bust me.

To put my tournament “life” on the line pretty much takes a hand of two-pair or better and that little rule has definitely kept me out of a bunch of trouble over my poker playing career. The most common (and most satisfying) situation is when a player limps in with A-A or K-K and I check from the Big Blind with something like Q-7o. The flop comes Qc-Jd-7s, rainbow and I check. The limper makes a pot-sized bet, I reraise, everyone else typically folds and my opponent with the overpair pushes all-in. Of course I’m going to call, but as good as it feels, I haven’t won the hand just yet; a lot can go wrong – unfortunately – but the reality lies in the mathematics involved.

Certainly I’m a big favorite in the hand described above (roughly 70-30 if my opponent holds K-K), but s/he still has a lot of outs – two Kings and runner-runner for a straight, along with the cards that will “counterfeit” my two-pair – and that’s the big danger. The first time your two-pair is counterfeited, you may wonder just what happened; I know I did, so let me explain. The value of two-pair is measured by the top card in your hand; in this case I hold Queens. If my opponent can somehow acquire a second pair on the board, then s/he will have two-pair with Kings (or “Kings up” as it’s called), which wins the hand. Obviously, the board has to pair the Jack or 7; if another Queen comes, I’ve got trips and my opponent is dead to only a King. On the turn, my opponent has three Jacks and three 7s available. (Another player may have folded a Jack or 7, but we don’t know that.) So, there are six cards of the 45 remaining that will counterfeit our two-pair. Other combinations will beat us outright, of course, but if we’re all-in it doesn’t really matter; it’s all in the hands of the poker gods now and we’ll win 70% of the time.

But what if our opponent just calls after we raise and checks the turn when the 8h falls; should we push all-in with two-pair? By doing so, it looks like we’re trying to “buy” the pot with a pair of Queens, which might make our opponent call with the overpair. S/he will basically be drawing dead to a K, J or 7 and thus has about a 20% probability of winning the hand. A really good player who has put us on a set or two-pair may be able to fold, which is fine – I never mind winning a pot – but in my experience, nine out of ten players are going to call. So yes, if my opponent checks the turn, I’m pushing. The problem with checking the turn, beyond the fact that you’re giving the opponent another shot at making a hand, is that it’s almost mandatory to call any bet s/he makes on the river, even though you might have the losing hand. The result will be the same of course; your opponent will either make a hand or won’t, but at least by pushing, you’ve put the burden of the decision on him or her.

Let’s quickly explore the math of pushing. First of all, we’ll assume that one opponent in ten will feel they’re beat and fold, so you’ve won one of the pots outright. If the other nine of ten call (remember, I’m not talking about a single table here, but the “universe” of players you’ll be up against), you’ll lose 20% of those, which is 9 x .20 = 1.8 pots or a total of 8.2 pots won. However, if you check, presumably all ten opponents will remain in the hand and 20% of them will make a hand to beat you when the river card falls. That’s a win of 8 pots made by checking versus 8.2 if you push. The key here is how big the pots are; in a pushing situation you might win bigger pots because you’re all-in. If your opponent misses on the river, you might still push but one or two of the 9 remaining may fold so the average pot won will likely be smaller. I like pushing from a math point of view.

This is just one example of pushing with two-pair and it’s obviously very profitable. A somewhat less profitable situation comes from playing Ace-rag, with “rag” being defined as a card lower than a 10 that is not suited with the Ace. If you’re up against KK with A-7o and the flop comes Ac, Jd, 7s, your opponent is going to be quicker to fold if you bet, so this is not nearly as profitable as limping in with Q-7. Sure, you’ll probably win more pots in the long run but they’ll be much smaller on average. So, the upside is somewhat limited, but look what can happen in the case where your opponent limps with a hand like Ad-10d, which you will often see. Many players feel a hand like A-10s is too good to fold in early position but won’t raise with it, so they limp into the pot. Obviously, you’re in great shape with two-pair on the flop, (67% to 27% – there’s a 6% probability of a tie) but what if the turn call is 8d, instead of 8h? Now you’re just 55-39 in the hand; there’s still a 6% chance of a chopped pot, but your opponent can hit a 10 or any diamond to beat you. If the Jh comes on the turn, your 7s are counterfeited and you’re dead to the 7 of hearts, (although the probability of a tie has gone up to about 32%, because if the board pairs again, you both have two-pair with an Ace kicker).

I was watching at a table recently where a counterfeited hand like this played out. A player in middle position with As-Jd limped in and the Big Blind checked with Ac, 2h. The flop came Ah, 2s, 4d. At that point, the BB was 69% to win and the limper was 26%. The limper fired a pot-sized bet and the BB reraised all-in. The limper called. The turn card was 6c, which moved the BB up to almost 80%. The river was 4c, which gave the limper two-pair: Aces and fours and that beat the BB’s hand of Aces and twos. Such is the danger of playing Ace-rag.

Honestly, I doubt that I can get away from a hand like this even if my opponent will catch a card to beat me about 20% of the time. Sure, it’s painful, but what kind of hand do you need to call, if not two-pair? As the old saying goes, “I’m not smart enough to fold.”

I’ll see you here next time.