Secrets of the Amateurs

An interesting hand came up in the $100 Rebuy on Pokerstars last night. I thought I'd lay out my "post hand analysis" here as an example of how to go about this. Playing 800-1600/150, the table is 7-handed and we're fairly close to the bubble. I have 75K under the gun and raise to 4200 with JJ. It's passed to the cut-off, an aggressive "ranked" player, who makes it 10600 out of his 84K, and it's folded back to me.

If I look at the stack sizes, it may be barely possible to 4-bet to something like 25K and fold to an all-in, but that's turning my hand into a bluff and I think it's a poor option (mainly because I'll end up folding when he jams AK). So the remaining options are to commit, call or even fold. Folding obviously has an EV of zero from this point.

Let's look at committing. A good starting point is to assume that your opponent will play "perfectly" and this gives you the minimum EV of the play. If I jam 70K we assume that he calls AA-JJ [1] and folds all underpairs - which sounds reasonable. If he has 2 overcards then it's not a big deal whatever he does, because he can call 64K to win 87K, so he needs to be about 42% to make the call, and AKo v JJ is 43%. I'll simply assume he calls AK and folds any other unpaired hand. So if he calls it'll be JJ v [AK, JJ+] for 153K, we'll be 36.5% to win for pot equity of 56K and overall equity at my decision point of -15K. If he folds I'll take down the 18K pot. So I can see that if he folds 50% of the time, the play will be +EV to the tune of 1.5K. [AK, JJ] is less than 3% of his total hands (when I have JJ) so if he's even 3-betting me with 6% of hands (whether the other 3% are TT, 99, AQ etc. or other semi-bluffing hands doesn't really matter) then jamming > folding. With this player and the bubble dynamic (I had been fairly active with open-raises) my judgement is that this is clearly the case and so jam > fold.

If I call it becomes more complicated, but I can still make some assumptions and estimates, and see where that goes. 12% of the time I flop a set, and then it's a question of how much I can make with the hand. Almost certainly one more bet (by check-raising), which should be at least 15K. But I won't always stack him, and don't forget I won't always win even if we get the chips in (for example v AA on the flop he'll still have 10% equity). Say on average I make another 25K off a set. That doesn't sound much but remember I'm out of position against a good player, that's not a great spot to get paid. About half the rest of the time (44%) I flop an overpair [2], and once again it's time for some guesswork. If he does have [QQ-AA] it's going in and I'll be in bad shape ; with 10% chance to suck out the EV of that is around -55K. If he doesn't, again it's a bit nebulous but I might pick up about 20K on average. Remember that a flop like T93 looks good but it's really not that great - what can he pay me off with ? TT and 99 got there and any other underpair can't stack off. Finally, if an overcard comes I'll probably have to just give up. Trying to check-call on say a Q high flop sounds dodgy, without working it out exhaustively. So that gives us the following :

12% flop set, EV +42K (the 17K in the pot when I make the pre-flop call plus 25K more)
11% [3] flop overpair but up against QQ-AA, EV -55K
33% flop overpair which is good, EV +37K
44% flop underpair, EV -6K

Total weighted EV = +8.5K.

What If ?

In the event I did call with the intention of getting it in if I flopped an overpair or a set and giving up if I didn't, and given the assumptions above that looks like the correct play (in the actual hand an Ace flopped and I check-folded the turn after the flop was checked). However, now I've done the hard work, I can learn a lot more by asking a few "what if" questions (skipping the working for these) :

What if he's 3-betting with say 75% semi-bluff hands and 25% [AA-JJ, AK], which could well be the case ? Jamming pre-flop now has an EV of .75*(+18) + .25*(-15) = +10K. Call and see the flop has an EV of +13K.

What if I start with 100K instead of 75K, is jamming still an option ? In this case, he needs to fold 55% of his hands so (perhaps surprisingly) it probably is.

What if I have a smaller pair ? According to my assumptions, if I'm jamming, then 22 is not much worse than JJ ! I can add JJ to his calling range, and 22 is 51% against AK rather than 56% (JJ). But even so, insta-4-bet-jamming 22 is profitable if he folds 55% of his hands. With TT he has to fold 53% of his hands. So with this kind of stack (40-50 BBs) I should open-raise more small pairs with the intention of 4-bet jamming, but only against the right 3-bettor !

What if I have a bigger pair ? Hard to quantify but just calling with AA/KK in particular could be very profitable indeed ; he's liable to put me on a hand more like TT/JJ and by the time he finds out the bad news a lot of chips could be in the middle.

What if I have other unpaired hands ? Well AK just jam ldo, AQs is about as good as 22-88 and all the other suited hands a little less good ; they're close and it really depends very much on his call/fold ratio of hands when I jam.

What if I have some crap ? Can I 4-bet bluff to 25K ? Possibly. The mantra on 2+2 is "never put 1/3 of your chips in pre and then fold", and it's certainly not something you want to do habitually so that it's exploitable, but as a one-off against this kind of player it's an option. It does look pretty strong. I would prefer to have about 15K more chips back just so I can raise a bit bigger ; even making it 25K here leaves almost exactly one pot sized bet for the flop, and the raise is small enough so he can just call it, which would be awkward. I was watching a replay of the 10K SCOOP final that Jude Ainsworth won and there was a certain amount of this kind of thing going on, which was interesting.

What if he outplays me on the flop ? Primarily by not putting any more money in when JJ is good. Now the EV of calling pre goes way down. If he plays perfectly [4] the EV of calling drops to about +2K, if he's 50% semi-bluffing pre (cf +8.5K), and about +6K if it's 25/75 (cf +13K). The better he plays post-flop, the more I should lean towards jamming rather than calling pre (fairly obvious really).

What if he's not a good player but an egg ? Two things. Firstly his pre-flop range is going to be much tighter. If he's an egg with weak-tight stats, he's pretty much never re-raising with TT or worse [5]. Now jamming is just a spew, but calling for set value alone becomes the best option, because he's a) more likely to have an overpair on the flop and b) he's an egg so will pay off more. And of course we can call with any lower pair for set value just as profitably. I need to have the discipline to let it go when I flop an overpair though, which is easier said than done !

What if I'm in position ? If the reraise comes out of the blinds, it's hard to quantify but it's clear enough that this makes calling pre-flop better. I can make more money when I flop a set, or an overpair that's good, and I have a better (albeit still quite small) chance of getting to showdown with JJ if an overcard flops.

What if he does call with TT/99 ? Sounds unlikely but if he views me as a LAG it could be possible. If he also calls with just TT, the EV of jamming increases by up to 5K (in the case where he calls/folds 50/50 pre). Of course this makes jamming a small pair much less attractive. This might come into play if there's some history between me and the particular villain.

If two options are close, which one is lower variance ? If he's 75% semi-bluffing/25% [AK, JJ] then if I jam, I'll be knocked out of the tournament 16% of the time. If I just call, I'm only knocked out if I flop an overpair/set and lose which I reckon is about 10-12% of the time. So calling pre-flop looks like the lower variance play (not really a surprise). Note however that in some circumstances, for example if this is the last tournament of the night that I'm still in, I might actually choose the higher variance play if EV is close !

How Do I Like His Play ?

In a vacuum, he's putting in 10.5K to win 7K, so if I fold at least 40% of the time, it's immediately profitable. That's going to depend how wide my opening range is. Under the gun, even though it's bubble time and I'm playing fairly aggressively, it's not that wide. I think he probably has to find some more equity post flop. What I don't like is that he's pretty much giving me set odds by only making it 6500 more, with 80K "to be won". I like this play a lot more if the reraise is closer to 10% of (remaining stack + pot), so he'd have to make it about 12K with these stacks ; or the raise to 10500 would be good if starting stacks were about 60 rather than 75. The other good thing about the bigger raise is that it pretty much removes 4-bet/fold as a bluff from my options. Of course the downside is that the bigger raise makes 4-bet jamming more attractive.

We can also see that a mix of 25% value/75% semi-bluff (folding the 75% to a jam) makes jamming any pair clearly good for me (the initial raiser). To make this 50-50 I think a semi-bluffing range of [AQ(s), KQ(s), AJs-QJs] is not bad ; remember that these hands only come into play when I call, and I'm mostly going to call with middle pairs like JJ/TT. Of course the play has metagame advantages because now he can get more action when I 3-bet AA/KK. Again note that I can screw this play up most effectively if I just call AA/KK as the initial raiser.

Conclusion

So all in all, we can learn quite a lot from this, hopefully. The "vacuum" play looks something like jam [AK, QQ], call [AA, KK, JJ], jam [AQs, TT-22, maybe some suited broadway] against a LAG opponent most of the time, and call [TT-22] for set value against an egg.

I should do this kind of analysis more often, and I'll put it up on this blog where appropriate. One final point, take a look at how small the equity differences are compared to stacks and pot. We're playing 75K for potentially a 150K pot, and we're talking about differences in equity of around 5K from play to play, and that's going to vary quite a bit according to how accurate (or not) my assumptions are. So don't sweat the close ones, especially if you jam and he turns over AA !

[1] It makes little difference whether we add JJ to that range or not because there's only one combination of it, and the equity is split in that case anyway. We'll put it in there just for completeness.

[2] At one point I worked out how likely various pairs were to be an overpair on the flop, and that's the number for JJ IIRC.

[3] Assuming here that his hand range is 25% AA-QQ, 25% AK, 50% something else.

[4] But still assuming he pays off with an overpair if I flop a set. He isn't a superuser !

[5] And even AK is weighted lower because weaker players usually make a bigger 3-bet with AK