Don't Call 3-bets to Set Mine

So yesterday, as happens many days, somebody called my 3-bet and cracked my AA with 99 when he flopped a set. This isn't a bad beat post. But I do think that calling those 3-bets to set mine is a mistake.

Let's assume that I have AA EVERY time, and I'm going to put all my money in every time. This is as favorable a situation for set-mining as one could possibly imagine. Suppose the original raiser opens for 3.5bbs, I raise to 12.5 bbs, and effective stacks are 100 bbs. Often in this spot, faced with the decision to call 9 bbs, players think, "OK, I'm 1 in 8.5 to hit my set, and then I'll stack him, so I've got implied odds to call."

Even putting aside for the moment the fact that all the money won't go in every time you flop a set (we have assumed that away for the moment), the other problem is this: sets aren't invincible! It IS possible to lose with a set. The 3-bettor might set-over-set you on the flop, or two-out you on the turn or river. The chances of that are better than you might think. Given that you have flopped a set, the chances that your opponent hits a higher set on one of the other four cards is 1 - (45/47)*(44/46)*(43/45)*(42/44) = 16.5% (If you don't see why this is the correct calculation, comment and I shall exprain). Of course this isn't totally correct because you DO see the cards on the flop when the money goes in, and you'll know that you haven't been set-over-setted yet when you flop top set, but it gives you a good idea. And I'm not even considering here the other ways that sets can lose, for instance to a straight, flush, the board showing trips and AA having a higher full house, etc.. Even if you have 88 on a 8c3s2d board, AcAd has 10% equity. Chance the 2d to a 2c and it's almost 14%. So it's very rare you will be more than a 90% favorite on the flop, even with top set.

So how much should you be willing to pay for the 1:8.5 chance to win 100 - 16.5 = 83.5% of the time? Ignoring the blinds/assuming they go to rake, the set is worth .835*100 - .165*100 = 67 bbs. Divided by 8.5 makes 7.9. The other 7.5 out of 8.5 times, you're check-folding and losing the 12.5 bbs you put in preflop. Putting that together, 67/8.5 - 12.5*(7.5/8.5) = -3.1 bbs.

That is SLIGHTLY better than folding your original pre-flop open of 3.5 bbs. But remember, we haven't included any flush/straight possibilities for your opponent, AND we have assumed that he has AA and stacks off every time. In reality, if you hit middle set on a 987 all club flop, either you're not getting all the money in, or your opponent has a club draw as well. Also, he's not going to have AA every time. He could have KK or QQ and an A flops. He could have AK and miss. He could have been 3-betting you with suited connectors that missed or now have huge equity against your hand. Even against the tightest preflop players who will stack off with overpairs almost every time, I think it's pretty clear that calling the 3-bet to set mine is a bad idea.

That doesn't mean it's never a good idea to call a 3-bet with a pocket pair. But you should do it when either you're deeper than 100 bbs, the 3-bet is small, or you're in position and you think you can win on a lot of flops where you don't hit a set.

-BRUECHIPS