Reposted from the link below - Great stuff
Been running bad at tournaments and running/playing bad at heads up cash, it sucks, we've all been there, blah blah blah no one wants to hear me whine. Anyways, I've been doing a lot of math the last couple days to tighten up my preflop game, and I was very surprised by some of the results I got, in particular the following situation:
Middle Stages of a big field Stars MTT. Blinds are 125/250/25. 9 handed table, we're on the button with 5000 chips, both blinds cover. It folds to us on the button with A2s. Whats the play?
First let's determine if shoving is profitable, because if it is then folding can't be right. Assuming perfect calling ranges from the blinds (A2+,22+), shoving shows a small profit of 52.1 chips (plugging the ranges into SNG Power Tools), not much but worth taking and better than folding. However that's a totally unrealistic calling range; vs a more realistic but still pretty loose range of (55+,A7s+,ATo,KQs), shoving shows a very substantial profit of 298.8 chips, more than a big blind. So folding is out.
The question now is whether making a standard raise is going to be more profitable than shoving. Let's say we decide to make a raise to 600 and fold if anyone re-raises. So when both blinds fold we win 600 and when one of them re-raises we lose 600. For this option to be better than shoving, we need both blinds to fold about 3/4 of the time, so each player has to be folding about 86% of the time (or re-raising about 14% of the time. Against anyone with a clue how to play tournaments, you are going to get reshoved by any pair, any suited ace, most offsuit aces, and most broadway hands, and probably some other smaller suited hands. That range is a lot more than 14% of all hands, so raise/fold is not going to be better than shoving. Your opponents would have to be extremely tight for raise/folding to be better than shoving, and most opponents aren't nearly that tight.
What I didn't consider here is how much of a profit we'll show when someone calls our raise. It's impossible to calculate what will happen on every single flop, but A2s isn't going to flop very well and I doubt we'll show a huge profit postflop with the stacks so shallow that our opponents probably wont fold if they hit something.
Another option is raise/calling, but thats only going to work well if your opponents are each re-raising about 38% of their hands, and without reads people aren't going to be nearly that crazy. This option is also much much higher variance since you're going to be all-in without great equity vs your opponents ranges a huge % of the time. While shoving seems like it would be high variance, its actually not that high since both of your opponents will be folding over 3/4s of the time. Raise/folding is by far the lowest variance option if your opponents are never calling, but if they do call your raise there's gonna be a ton of variance postflop.
When I started cranking out these calculations, I was surprised by how much better shoving was. Even though these big overshoves are becoming more and more popular, it still feels weird to just bomb in 20 BBs in a spot where you're behind when called. But when you start running the numbers you realize why it's become so popular.
I recognize I didn't show my work here, I didn't cuz I thought it would be too boring, if people really want me to I will. |