Low buy-in folding equity

[AJay]

In PrayingMantis's thread on Folding Equity, there is a discussion on the importance of fold equity, and how it may or may not apply as much at lower levels. As with most threads, there are arguments back and forth and not always a concensus, but there's definitely a strong argument made that even at very low buy-ins, it is important, under the right conditions to push pre-flop.

An example given is AK on the bubble. Rather than limping in and then pushing once an A or K comes on the flop, it is argued that it would simply be better to have pushed pre-flop.

I think this underestimates how likely people are NOT to fold at lower levels. I sat down with a spreadsheet to look at possible outcomes.

1) I push pre-flop with AK which is a 6:4 favorite against any pocket pair, any two broadway, and any Ax.

2) I limp and wait to push when an A or K hits on the turn. In such a case, the AK is a 3:1 favorite.

Next I estimated how likely I was to be called. Of course, this is the tricky part. But at low levels people call with a lot, so I would estimate that with 4 or 5 people left, if I push pre-flop with AK, there's about a 1 in 3 chance I'll be called (ignoring stacks sizes, etc). If I wait until the flop, I think the chances are probably about the same or less. For one, someone either has to hit the flop (a 1 in 3 chance) *and* not hit the bottom pair on the flop (though yes, for some people, that's enough) or else have "good" over cards (say KQ on a flop of 9 7 4...and yes, I know that's not really a great hand, but at the low levels, on the bubble, some would consider it a monster :-). Given that, I'd say the chance of someone calling my all-in on the flop is no better than 1 in 3.

So, what do I wind up with? Well, if you want, you can do the math, but the key, is that my all-in on the flop is no more likely to be called than my pre-flop push. Yet, my all-in on the flop is much more likely to win since I only pushed if an A or K flopped.

Given that, I don't see anyway to argue you should push pre-flop. Mathematically, I will lose more often.

Comments?

[splashpot]

You didn't provide any math in your arguement. All you did was speculate that you'll get called 1 in 3 if you push either preflop or on the flop. Neither of which is universally true. And you didn't mention the size of the blinds at all. Which is the most important part.

[AJay]

Well, for one, I assumed that blind sizes were not tiny. People don't push when they're 10. So let's say 100. I figured a number in that vicinity was a given since we're talking about pushing.

Then, with 4 or 5 folks left, the average stack size will be around 3000, with one guy probably having 5000, a couple around 3000, and another one or two around 1500.

(I think all that could be surmised.)

As for the math, I don't think you need to do it.

If I'm 3:2 favorite and will be called x% of the time vs. 3:1 favorite and I will still be called x% of the time...well, I can do the math and give specific numbers, but using algebra, it should be clear that I will win more often when a 3:1 favorite vs. 3:2 favorite if I am called the same percentage of time.

[splashpot]

How often you will get called is directly related to how high the blinds are compared to the stacks. You can't just throw that around lightly.

[splashpot]

Also, for the times that you are not called, the size of the blinds tell you how much you gain from stealing. So what I'm saying is that EVERYTHING has to do with how high the blinds are.

[wiggs73]

One thing that you don't account for is the times on the bubble that you limp in and push the flop and the players that would have called a pre-flop push with a worse hand than AK fold. You're giving up EV in such a situation. You also don't account for the times that someone would have folded to a push pre-flop but hits a better hand than you on the flop and calls your push. There again, this is not a good situation to find yourself in. I also didn't see any mention of the times that you're going to give away chips when you limp in for a sizeable amount and then fold the flop.

In short, aside from the times that you should open-fold AK on the bubble or you reach the bubble early and stacks are not short enough so that pushing is optimal, you'd be foolish to pass on a 60% edge. This is the nature of SNGs... you have to be ready to jump on small edges, especially in late game situations.

I'm open to the fact that there may be a better, more +EV way of playing AK in late game situations than pushing. However, I'd like to see something more than "I put some numbers in a spreadsheet". As splashpot said, seeing some actual math would be nice and make sure when you post the math that you don't over simplify the situation. Be sure to account for probabilities of hands being dealt, calling ranges, blinds, etc. I'd suggest downloading SNGPT and Pokerstove before getting too involved and also becoming familiar with the theory behind ICM if you aren't already.

[wiggs73]

[ QUOTE ]
If I'm 3:2 favorite and will be called x% of the time vs. 3:1 favorite and I will still be called x% of the time...well, I can do the math and give specific numbers, but using algebra, it should be clear that I will win more often when a 3:1 favorite vs. 3:2 favorite if I am called the same percentage of time.

[/ QUOTE ]

But you won't be. I mean, come on. If it were this simple, do you not think that everyone would limp AK on or near the bubble?

[AJay]

I understand that the blind size is relevant. Hugely.

I simply figured (incorrectly apparently) that it was obvious that I was not talking about blinds of 10 (since pushing isn't utilized by 2+2ers at this level). So, use my numbers from above: blinds of 100, with 4-5 people left.

I think at LOW buy-ins, people are fairly likely to call an all-in push with something like A6 when the blinds are 100. I think fold equity is overvalued by some at those levels.

In the above example (AK), I have to be called almost twice as often after the flop (when I'm 3:1) as I do pre-flop. When the table is down to 4 or 5, I simply don't think that's very likely at the low levels, where KQ and A6 are consider hands that are worthy of calling a push.

[Wolfram]

Wiggs, where's your avatar?

[splashpot]

[ QUOTE ]
I simply figured (incorrectly apparently) that it was obvious that I was not talking about blinds of 10 (since pushing isn't utilized by 2+2ers at this level). So, use my numbers from above: blinds of 100, with 4-5 people left.

[/ QUOTE ]
A BB of 100 is massively different than a BB of 150. (What starting stacks are you talking about anyways? At Party, 100 isn't a high blind anymore) It matters a lot. Calling ranges will be entirely differnt.