I had to stop thinking about poker for a bit after losing that grand, and I will be posting more about total donkey plays I made last weekend. But, I want to be clear about the hand that is the subject of this post: I am pretty sure that I love this situation. I made a brief off-handed reference to it in my earlier post. The thrust of the argument against my play below is that the preflop decision leaves me an underdog (i.e., playing AQs against a likely big pair or AK), and therefore it's not worth taking a flop. Furthermore, one could argue that the flop is at best a coin flip, so why introduce so much variance for this? Before I get deep into the analysis, let me first retell the whole situation, which should be stated and considered first before extensive analysis can be at all useful.
The hand begins on 21:09 on last Saturday when readysteady, a tight-aggressive, overpair-overplayer player on Full Tilt raised UTG to $9 in a six-handed NL HE game with $1/$2 blinds. I was right next to him and decided to call with A Q. I could have easily been dominated by AA, QQ, or AK, but felt that it would be reasonably easy to get away for a small raise on the flop if it came A or Q high. Meanwhile, having seen him play aces once before at this table, I felt he'd raised less preflop with AA from early position (probably only $6), trying to induce action. He'd won with those aces earlier, so it was unlikely he hadn't gained a temporary “must over-protect aces” philosophy. He had raise to $6 before from early position with hands like AJ, so I suspected here that he held a vulnerable big pair that didn't want to see a flop out-of-position — probably TT or JJ. But, maybe he did hold QQ or KK; I couldn't rule it out. AK was another possibility, of course.
There was still some chance he had AA, but I figured (at the time) that most of the time, he held a hand like AK or TT-KK as opposed AA. In fact, the real numbers were much better. He's a tight player who almost always holds one of those hands when he makes that raise. With an Ace in my hand, there are only three ways he can make AA, while he has 33 ways to make one of those other hands, so he's about 1-to-11 underdog, statistically, to hold AA after his $9 raise. Why am I so focused on AA in this post-hand analysis? I'll get to that shortly.
To continue with the hand itself: I decided to call his $9, and that I'd get away on the flop if I made merely one pair. I had $259 and he had me covered. He had overplayed one pair a number of times at this table; he fit the typical profile of someone who plays NL HE by being very tight preflop and getting all the money in on nearly any flop where he holds an overpair or top pair, strong kicker. I'd of course rather have a set-building hand against him, but a nut-flush-building hand wasn't too bad, and I'd have position for the rest of the hand, as I expected the rest of the four people to fold unless they had monster.
With $21 in the pot, we see the aforementioned 5 2 3. (My original quick note about the hand had the suit of the 5 wrong, but it isn't relevant since it wasn't a diamond. :) readysteady bet out $15.
I now had him read for an overpair, or maybe a feeler bet with AK (pretty unlikely). Folding on this flop seemed like a bad move; I have too many outs against so many of his possible holdings. I could call and see if the turn hit me, or raise right away. It was highly likely that he would reraise, and I decided that, before I raised, I had to know what I'd do when he reraised. If he reraised, I had to be committed to playing for all my chips. I had limited time to make this decision, but I was sure in about 20 seconds of my one minute to act that I had to be committed.
My biggest consideration was how I'd get paid off if my outs came. I thought he might put one more pot-sized bet in if I hit the flush or the straight, but he might slow down if an overcard came. If my overcards are actually live outs, then I might make another half-pot bet from him on the turn, and when I called it or raised, he'd be done with the hand because he knows that I am not going any further without a pair that beats his (i.e., his “get all money in with overpair” rule no longer applies). Meanwhile, if one of my overcards isn't good (specifically, if he holds KK), I'm a favorite (see numbers below), but it's still tough to play a Q on the turn. I was therefore ready to commit my stack.
I raised to $40, readysteady paused for about a quarter of the allotted time (15 seconds) and reraised to $100. That pause made me even a bit more sure that he didn't have AA. I felt he'd be faster to commit chips with AA, because he doesn't have to pause to consider that I might have an overpair to his. The pause, of course, could have merely been his consideration of a set, but this was a player I'd seen commit quickly to aces once at this table. I felt he would do so again. I moved in, putting my whole remaining $250, and he thought again (this time only about 2-3 seconds) and called. He showed K K and the board completed to 5 2 3 J K. His set won $521.
Now, in the moment, I didn't have time for heavy math analysis. But even after the hand, I think that the questions are really these: (a) should I fold AQs preflop to an early position raiser, and (b) should I just see if my draw hits on the turn rather than getting all my money in?
As to the first question, I don't think it is reasonable to fold the hand, even against a tight online player. The typical profile of tight players in the six-handed games on Full Tilt — a profile which this fellow fit and had confirmed by his actions — is that they overplay overpairs and/or strong top pair for all their chips. My 9-to-253 implied odds are just too huge to pass up in a six handed game. The other players behind me are highly likely to fold. I'm going to see a flop heads up with position.
Of course, I may be dominated. I need a lot of help on the flop (which I got, IMO) to put any more chips in the pot. But when I do get that help, I'm going to get his whole stack. I am focused on taking stacks in NL HE; not making sure I make the absolute direct odds pre-flop EV play. This is why I decided that for me in this hand “hitting the flop” did not include merely top pair. I definitely needed two pair or better.
Two pair would be tough to play, but this fellow was likely to slow-play a set, so it'd go check-bet-call or check-bet-raise on an AQx flop should he hold a set. Either way, I would have slowed down and eventually folded two pair in that sort of situation. I might lose a bit more on the turn, but I'm only going to bet a quarter of the pot on the turn when he checks again, worrying specifically about the check-raise by that set of aces of queens. Once he check raises, I'm done — I've folded two pair many times in such a spot. So, while there are some negative implied odds for two pair against a set, I also get paid off pretty well from AK, with which he bets out rather than check-raising in that spot. (I should note that despite lots of advice out there about betting out with a set, few players do it; I didn't think readysteady was likely to.)
If I flop Broadway, I'm getting all my money in on the flop while winning. In that spot, he puts it all in with AK most of the time, and a set all the time. If I flop a flush, I almost always win but I admittedly don't make too much from him, unless he flops a set.
If I flop what I flopped, overcards, a flush draw, and a gutshot, I have to tread lightly if the flop is ten high or bigger, but in this case, with all babies, I'm in great shape.
Yes, he can wake up with AA in that spot, and I get my money in as a 36% underdog. But, going back to the hands he likely to have, given his preflop action and flop lead, he's a 1-to-11 underdog (about 8%) to have specifically AA. So, 8% of the time, I'm a 36% underdog. Another 8% of the time (when he has QQ), I'm a 44% dog. Meanwhile when he has KK (18% of the time), I'm a 51% favorite. Against the rest of the likely pairs (TT, JJ), which he holds 36% of the time, I'm about 58% favorite. I'm of course crushing AK (the extra 30%), but if his flop lead was actually a feeler bet with AK, he folds any AK when I raise.)
Anyway, I'll even set aside my read that he didn't hold AA. I'll just do the pure EV calculation that his lead bet gives us no new information (i.e., it may be an AK feeler), and that he gets all the money in with any pair (i.e., we assume no fold equity). I do the calculation by assuming I win right there when he holds AK, and that I have to face the odds with all my chips when he has any other holdings.
With these assumptions, my flop EV (when I raise on the flop, expecting him to reraise and we get it all in) is as follows:
|Hand||Probability of Holding||EV formula||EV component|
|AA||8%||36% × $271 + 64% × $-250||$-5|
|KK||18%||51% × $271 + 49% × $-250||$3|
|8%||44% × $271 + 56% × $-250||$-2|
|TT, JJ||36%||58% × 271 + 42% × $-250||$19|
Now, I agree that introducing $250 of variance for $26 of EV is nowhere near the best spot I can get find in these tight-weak games online. But, it's still a good spot that I'd take every day for $250! I believe in keeping a large bankroll (larger than most proposed recommendations), in part so you can take these tight marginal edges.
There are also meta-game considerations here to think about. I have chosen to play short handed NL HE tables precisely because the players there tend to be tight-weak preflop and play one pair too loosely after the flop. I play best in NL HE against tight-weak players who overplay one pair.
When playing against these players, I want to sometimes take these tight-edge gambles. I want them to know they are going to get action when they overplay one pair. More importantly, I want them to know that sometimes they won't be a huge underdog against me when I give them such action. (Indeed, I engaged readysteady in chat window discussion about the odds precisely to make sure he realized that I'd pushed an extremely tight edge.)
You see, I want readysteady (even his username exudes tight-weak play, did you notice that?) to overplay that KK every time. I want him to continue to believe that folding an overpair is impossible. I want everyone at the table to feel the same way. I want readysteady to call up his poker buddies, and tell him about the huge fish who pushed in with AQs with “only” 15 outs. I want them all to react this way, because, if I didn't have straight draw outs as well, I wouldn't have played the hand the way I did. I would have called with 2-to-1 direct odds on the flop, seen if I made the flush on the turn, and folded for a pot-sized bet if I didn't. It would have been a little mundane pot that wouldn't even have made it to my blog. But, I had at least three extra outs, and went for it. Sure, the math shows I'm risking $259 to chase $26 in EV. But, most of the time when I get the money in with him, I have a set of fives, not the nut flush draw with one (maybe two) overcards and a gutshot.
Some might argue this is a reckless way to play NL HE when I could sit and wait for more of lock. I'm going to ask my coach to read this one, but I'll probably need a lot convincing from him that I made the wrong move. I watch these tight-weak players bleed away money playing ultra tight and making themselves like textbooks. I want them to fear me at the table; to worry that they can't fold because maybe I have some big draw, not a set. I don't move in every time with AQs in that spot with every player. It felt right in this situation, with that board, against that player.
We can argue about “risk vs. volatility”. We can disagree that introducing $259 of variance into one's bankroll for $26 of EV is too much variance. (Although please consider that the limit HE player frequently puts 30 BBs at risk to win at most 2 BBs for a given evening — and that this situation is much better.) But, I think that's the most important point of this hand: varying a little bit from playing “by the book” (i.e., calling with AQs after a preflop raise, moving in with a big draw that may be at best a coin flip) builds a complicated table image that keeps your opponents guessing and forces them to respond to you.
We'll see what Bob says when I ask him to read this — if I'm full of crap, I'm happy to eat my words if he tells me to. :)
Update:Bob finally answered me on it.