Low Pocket Pair Vs. High Pocket Pair

I used to think that calling bets with low pocket pairs, even when I knew I was killed was an intelligent thing to do. Upon further review, I was wrong.

My thinking used to be like this, spike a set and win a huge pot. However, I've thought some more about it.

If going against a high pair, a lower pair needs to spike a set on the flop, this only happens 10.8% of the time. Let's say both stacks are at $100 and the preflop raise was $10 on top of the blinds. Let's also say there are a few other callers, which is the only time I'll go in when I know I'm beat. In theory, if I spike the set on the flop, and the guy with the high pair doesn't have the discipline to fold, I'll take ll his chips. I'll pay $10 to win a pot of about $130. That's 13 to 1 implied odds. However, about 1 time out of 6, that high pocket pair will also hit a set by the river. Let's say you're good enough to know when your set is up against a higher set on the flop. You get all your chips in on the flop with the best hand. The odds that the high pocket pair will hit a set are about 10.25 to 1 or 8.89%. So let's look at all the odds.

Pocket pair flopping a set: 10.8%, 8.26 to 1, will occur 1,080 times in 10,000 hands
High pocket pair hitting set on turn or river: 8.89%, 10.25 to 1, will occur 889 times in 10,000 hands.

If you don't flop the set, you'll lose $10 on the hand as the player with a high pocket pair will probably bet strong on the flop. So in 10,000 hands, you will fold on the flop 8,920 times and lose $8,920 over 10,000 occurrences of this situation.

Of the 1,080 times you stay in the hand, you will get outdrawn about 96 times by a higher set. On these 96 hands, the odds of you getting your quads are negligible. It will happen maybe once. The 95 successful outdraws will result in losses of your entire stack, most likely. This means a loss of $100, 95 times. $9,500 lost in total. The 985 times you win will result in a profit of $128,050. So in the long run, in 10,000 occurrences of this situation, you will win $128,050 and lose $18,420. This is a net profit of $109,630 over 10,000 occurrences. But, this is only $10.96 hand and doesn't take into the consideration the times you will both spike sets, which means you will either lose $10 if you're good enough to fold a lower set, or lose all your chips if you're not.

Here is when you should play your low pocket pairs:
If it's a limpfest and it only costs you $2 to see a flop. You can limp with deuces under the gun if you'd like, especially if the players in late position aren't typical late position raisers and you might see the flop for the cost of the blind. On the off chance you flop a set, you might be able to extract a good amount of chips from the other limpers who might catch top pair or two pair or something like that. You also might be able to see some free cards and be able to spike the set on the turn or river. Hell, your pocket pair just might stand up and win the pot. Don't count on this, though.

When playing against a raise, it becomes difficult. You don't want to go heads up when you're crushed by a higher pocket pair. Some players are so bad, that you might be able to tell you're up against Aces or Kings. However, if both of your stacks are large, say $250 or more, you might consider going heads up. About 10% of the time, you'll be able to take down $250 of profit for a $10 investment. This means losing $90 and winning $250 every 10 occurrences of the situation. That's about $16 a hand, which isn't a bad profit potential for a $10 investment.

If you have raises and re-raises, just fold the low pair. You have no idea how much it will cost you to play your pair and the likelihood of running up against a bigger set has doubled.

So play the low pairs, try to see cheap flops. If the flop is expensive, only play if you've got a large stack, your opponent(s) has/have large stacks, you have the discipline to fold a lower set, and your opponents don't have the discipline to fold an overpair.

Also, read this article:

Pesky Middling Pairs