Calling All-In Bets With J-J

Last year at around this time, I wrote a column about when to play Q-J. The general idea was that if every now and then you pick a trouble hand and try to learn as much as possible about it, eventually you'll find the decisions involving that hand to be much clearer (but perhaps no less troublesome).



I'd like to try that again, but this time with a very different hand: J-J. We sometimes joke that the right way to play J-J is to raise preflop and then fold on the flop. There's no question that it's one of the hands that most confounds players, because it mixes real strength with even more tangible playability issues. When you reach the flop with J-J, it's hard to know where you stand. In wilder limit games, it can play more like a medium pocket pair; to continue, it needs to flop a set or an unlikely board of uncoordinated undercards. In bigger limit games, it plays more like a big pocket pair, although it's more vulnerable to overcards and takes more judgment to play well than A-A, K-K, or Q-Q.



Now that no-limit hold'em has become so prevalent, a common confounding situation (and one that's relatively easy to analyze) is that of having to make an all-in call-or-fold decision. The value of J-J can change dramatically depending on your opposition: It can be a big underdog against your tightest opponents, but has a solid advantage against opponents who are playing looser. The tight and loose opponents could very well be the same people at different stages of a tournament, or even in a no-limit ring game, depending on the circumstances.



Of course, the nice part about examining all-in matchups is that it simplifies the analysis dramatically (compared to situations where chips remain). Your chances of winning vary as a function of your opponent's raising standards, which in turn vary as a function of the game situation. If you have a few good points of reference, and are comfortable pigeonholing your opponent's state of mind, you can estimate your winning percentage reasonably well.



I've made a small table that reflects a few possibilities, ranging from extremely tight (raises with the other J-J or better) to somewhat looser (raises with all pocket pairs and a few big hands, and bluffs occasionally). The table describes 12 possible opponent profiles, and lists your win percentage with J-J against each. A second win-percentage column assumes your opponent will additionally bluff 5 percent of the time with garbage hands. I'll put the complete details of how these numbers are derived (along with my spreadsheet) up on my web site. For the moment, I'll just point out that the win percentages are a weighted average of the showdown percentages against each hand (with some minor assumptions about suits), weighted according to the posterior probability of each hand. Except where indicated, I'm assuming your opponent raises 100 percent of the time with the listed hands, and 0 percent of the time with other hands (aside from bluffs). The spreadsheet can accommodate arbitrary raise percentages for the hands, and I've used that feature for the last three rows.



I'll present the table first, and then make a few observations.

The most obvious effect, which you probably knew already, is that your profitability comes from the probability that your opponent holds a weaker hand. Opponents who raise only with J-J or better have you in a very bad spot. As we add in some medium pocket pairs, your winning percentage creeps upward. As long as you feel confident that your opponent would have raised with 10-10, you're no worse than a 1.86-1 underdog, and against an opponent who would raise with 8-8 or better, it's at worst a coin flip. Of course, even being a moderate underdog is no reason to throw in the towel. There are certainly situations in which calling as a 2-1 or even a 4-1 underdog would be correct (and others in which you'd fold as a moderate favorite). These win percentages (and odds) are just the raw material with which you have to make your decisions.



A less intuitive pattern that's apparent from this table is how dramatic an effect a 5 percent bluff rate has on your win percentages. Even though 5 percent doesn't sound like a lot, it's still reasonably large compared to the baseline probability of drawing a legitimate hand. If we consider the opponent who plays only the top four pocket pairs, once you see the raise, the posterior probability of a bluff is about 67 percent, while the posterior probabilities of A-A, K-K, and Q-Q are all a bit over 10 percent. Even if your opponent raises with all aces and all pocket pairs, the posterior probability of a hand outside this set is still 13 percent.



Even much smaller bluff percentages can have a huge effect on your winning percentage. Against a player whose legitimate raises include only A-A, K-K, Q-Q, and J-J, a 1 percent bluff percentage bumps your percentage from 20 percent to 38 percent, and a 2 percent bluff percentage gets you to 48.2 percent, basically a coin flip. Of course, most opponents choose their bluff hands nonrandomly. But since J-J dominates most bluff hands, the difference is relatively minor. This dramatic effect of bluffing applies not just to J-J, but to any hand that dominates bluffing hands. Opponents who bluff too often add a tremendous amount of value to your hands. Correspondingly, if you bluff often, you're giving your opponent the opportunity to make many more profitable calls, if he's willing to do so. Adapting your bluff frequency to your opponent is, therefore, critical, especially given the number of players who call large bets too often.



I was hoping to provide an analysis of J-J to mirror what I did for Q-J last year, including a more detailed look at what happens post-flop. But playing J-J post-flop is a much subtler question about interpreting your opponent's actions, and would take a finer-grained analysis of posterior probabilities that take into account your opponent's preflop and post-flop actions. I'd like to do that analysis soon, but in the meantime, I hope this column will give you something to lean on when you're contemplating an all-in call with J-J.

Daniel Kimberg is the author of Serious Poker and maintains a web site for serious poker players at http://www.seriouspoker.com/. You can contact him at [email protected].