A Hand I Played at 1/2

Yesterday I finished the requirements for my Full Tilt bonus. From now on I'm switching my attention completely to WSEX, since I have been winning constantly there. A few Razz games have actually been running as high as 2/4 and 3/6. I've played those with success, although the last two days I've been running like shit. So I decided to put in a grinding session at NLHE. I opened two tables of 0.5/1 and two tables of 1/2 and made $150 worth of profit from this short session. I have yet to play a lot of 1/2, even though my bankroll is large enough that I feel comfortable at those stakes. I played a hand I found quite interesting. Not because I was put in an unfamiliar spot, but because I wanted to mathematically analyze a situation I've been in endless times before and figure out the soundness of the play I made. I did some EV calculations. I have hardly any experience with those, but with my experience in math, it should be easy. Unless you take interest in the mathematics of No Limit poker you can skip the rest of the post.

So the first thing I do when I analyze a hand is to analyze the situation at the table. I had sat at this particular table a handful of orbits earlier. During this time I had been pretty card dead. I had taken down the blinds a couple of times uncontested and had won a nice pot with a strong call on the river. Since I am new to these stakes, most of the players probably didn't know anything about how I played, even though it is a very small site. In my mind I had a tight image, and I thought I had a lot of respect at the table after winning every pot I entered and especially after that call on the river. There was one player - let's call him UTG, since I don't have the hand history - who was sitting with a big stack. Apparently he had stacked SB and was trying to get on SB's nerve by talking a lot of trash. SB looked like he might be tilting slightly. He lost several pots and he also 3-bet a couple of times against position raises. The other three players at the table seemed pretty innocuous about this and the general play was tight and careful.

On to the hand. I was dealt 9c8c on the button and raised to $6 when everyone folded to me. SB made it $21, BB folded and I made the call, because I have a strong hand with good semi-bluffing potential in position against what I perceived to be a wide 3-betting range. Effective stacks were $200. The flop came 6c5d3h and he bet out $31 into the pot of $44. I shoved and he folded. Now this situation is interesting because it is so simplistic in a way. There is not a whole lot of draws I can have on such a dry board. And there is also not a whole lot of hands he can call me with. So I stand to have a decent amount of fold equity. Especially against a wide preflop range.

Let's try to put him on a range of hands. Since I had such a tight image and given how the table was playing I'm giving him the benefit of the doubt and assuming that he's re-raising for value most of the time. Let's include 99+, AJ+, KQ and KJs. Let's also assume that he only 3-bets 99 and TT half of the time, KQo half of the time and that he 3-bets a good suited connector once in a while. In this approximation of his range I came to a total of 82 hand combinations, 30 of which were pairs. On this flop I am also assuming for the sake of simplicity that he bets 100% of his range and only calls the shove with his pairs. That is actually quite a realistic assumption, although he might actually fold some of his pairs due to my tight image.

On to the math. We can create a simple formula for figuring out the expected value (EV) of my play:

EV = EV(fold) * x + EV(call) * (1-x)

where 'x' equals the chance that the shove will induce a fold.

EV(fold) is the amount I win every time he folds, which is the amount that is in the pot before I make my move. So his $21 + my $21 + $2 from the BB + $31 that he bet on the flop = $75

EV(call) is the amount I win every time he calls. It can be calculated by multiplying my equity in the pot against his hand range with the total amount of money that's in the pot after we go all-in and subtract the amount of my shove. My equity with the gutshot and backdoor flush draw against 99+ is 22.5 %. The total amount in the pot will be $402 and the amount I shoved for was $179 (effective stacks minus my preflop call). Thus:

EV(call) = 402 * 0.225 - 179 = -88.6

Against the range I estimated, my fold equity is 63 %, since only 37 % of that range is pairs that he will call with. Now let's put x = 0.63 into the equation.

EV = 75 * 0,63 - 88.6 * 0.37
= 14.5

That means that on average my play stands to win $14.50 against the range I put him on in this situation. Let's also add that he needs to fold 54 % of the time for my play to be break even.

In conclusion: I made an aggressive play that stands to show a slight profit against a somewhat wide 3-betting range. If his range is tight and weighted towards high pocket pairs it might have been a losing play. On the other hand, if he is the type of player to cold-call a lot with medium pocket pairs and even slowplay high pairs, my play will show a lot of profit. In general, if his 3-betting range is wider than normal I should be able to make this play. Even if he 3-bets small suited connectors that will connect with that flop, I will have decent equity against those hands. My play will have a positive effect on metagame since I will now have more fear equity at the table. On the other hand, the variance will be rather high because of the thin edge that I'm pushing and I might go on tilt if I get called. That's the negative effect. Since I have a decent bankroll for 1/2 I like my play. If you play on a smaller roll, arguments could be made for folding in such situations. Another approach would be to float in position. The arguments against that is that he will bluff me out on a lot of overcards and he might check-raise me with overpairs. However, I'm risking a lot less to win the pot that way, and it's probably the best option against a passive opponent. Against an aggressive opponent I much prefer the shove on the flop. Since I didn't know quite what to expect from this particular player, I made the move. In fact, I'd go so far as to say that you won't make a huge mistake whatever you do in this spot.