Esoteric Question About Limit HU Variance

[JohnnyHumongous]

I am trying to get some other opinions on HU edge and HU variance. Let's say you are playing someone you feel you have a solid edge on, but their play is such that they can "get you" if the cards fall a certain way. I.e. they are not weak in the sense that they are completely readable, miss bets, make extra calls etc. They are weaker in that they bluff too much, or are too aggro, etc. You might say they are dangerous if they catch the right cards. But remember you have a "solid edge" on the person, for sure they are playing losing poker.

You play heads-up against this person. Say it is a 25 big bet freezeout. What do you think the probability is that you will win the freezeout? How about 50 big bets?

[kapw7]

I know exactly the kind of player. It's very easy to lose 100BB with bad cards maybe 150 is still easy i.e. very probable.

A few horror example scenarios: The guy will raise every street with a gutshot and hit on the river vs your flopped set. You won't be able to bluff him ever so if you don't catch cards you'll keep losing with A-hi etc.

[noggindrill]

find new game

[Gildwulf]

There is a lot of variance in HU limit. If you have an edge on a player in the long run you will win. The end.

[JohnnyHumongous]

[ QUOTE ]
There is a lot of variance in HU limit. If you have an edge on a player in the long run you will win. The end.

[/ QUOTE ]

Of this I am sure. What I am not sure of, is how this translates into variance and EV. I am trying to get an insight into this in a roundabout way.

I know it is "easy" to be out 50 big bets or more to this type of player. (100 big bets I am not so sure though, if you play a lower-variance style and don't squeeze each small edge). But what does "easy" really mean? Against this type of player, for 25BBs, would I win 65% of the time? 60% of the time? Or 52% of the time? For 50BBs, 80%? Or 55%? That is the kind of answer I'm looking for. My personal intuition is that 25BBs can be a "toss-up", but if you play a lower variance style you can win this about 60-65% against a tricky but bad opponent. 50BBs about 75-80%. But that is just my experience/intuition and I would like to discuss and compare to others'.

[sweetjazz]

Johnny, it really depends on what your "true" winrate versus this opponent is, which will depend on how spewy he is (will he lose several big bets when it's clear he is beat or will he constantly apply pressure and call down immediately after you have shown more strength in your range than his hand) and how good you are at handling his aggression.

My SD/100 HU is 24 BB, and that includes a mixture of such aggressive opponents and some passive ones. I would imagine against such an aggressive player your SD/100 might be 30 BB. Let's say you have a big edge over him, say 5 BB/100.

Assuming a normal distribution (pretty reasonable approximation), your chance of being ahead after 100 hands is 56.6%. The chance that you are down 25 or more BBs after 100 hands is 15.9%.

After 500 hands, your chance of being up is 64.5%. The chance that you are down 25 or more BBs after 500 hands is 22.8%.

After 1000 hands, your chance of being up is 70.1%. The chance that you are down 25 or more BBs after 1000 hands is 21.5%.

After 5000 hands, your chance of being up is 88.1%. The chance that you are down 25 or more BBs after 5000 hands is 9.7%.

After 10000 hands, your chance of being up is 95.2%.

After 50000 hands, your chance of being up is 99.99%.

I know this doesn't address your exact question, but it does show you that it can a long time for skill to win out, even with a big edge.

By comparison, if your SD/100 is 24 BB, then you get the following probabilities (assuming your "true" winrate is 5 BB/100):

Chance of being up after 100 hands = 58.2%

Chance of being up after 1000 hands = 74.5%

Chance of being up after 10000 hands = 98.1%

Notice the last number: Against the very aggressive player, you were more than twice as likely to be down after 10K hands than against the average player.