Why are we so afraid of variance?

[Sean Fraley]

In many posts here, I see a lot of responses that include statements such as "that is high variance play" or "high variance, low EV" or some such, and almost always expressed in a context that implies that one should avoid situations like this, as in fold your cards and get out. This doesn't make any sense to me. As far as I can tell, you are a 1.001:1 favorite to win the hand you are still a favorite, and if you can get all of your chips in the middle with a caller, over the long run doing this will win money. Your swings will be huge, but you will also maximize your potential earnings.

Now don't get me wrong, I have been through a couple downswings, both around 10 buy-ins, and I understand how painful they are. The problem here is that some people here seem to be turning this emotional reaction to variance into a factor of their playing style, and I believe that it is costing them money over the long run.

Basically, in terms of how it affects the our win/loss ration in poker, variance is the manifestation of those elements in the game that we have no means to predict or control in any quantifiable fashion. In other words, while we can calculate the odds of certain cards being dealt on subsequent rounds, we have no means whatsoever to accurately predict what the actual cards are going to hit the board. While we can take the information that we have about a player and his tendencies, correlate it with the way he has played on this and previous rounds of the hand, and then use this information to assign him a range of hands, and calculate the likelyhood of any portion of that range, we have no means of actually knowing with absolute certainty what two cards he is actually holding. The effect perceivable effect of this fundamental and inalterable lack of information is what we call variance.

Because of this, variance should be a neutral element in our decision making process. We don't have that info, there is nothing we can ever do to get that info, and therefore we simply make decisions based on what we have, not what we can never know. This is an important distinction. To illustrate this point, lets take an (admittedly hypothetical) example:

You are playing an unraked $25 NL 6-Max game against an opponent who frequently reraises all-in preflop. You have managed to amass 100,000 hand of info about him, and analysis of this info shows that of all the times he went all-in preflop and the hand went to showdown, he had two unpaired broadway 51% of the time, the other times, he had a pocket pair. It is folded to you in the SB with 2[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/club.gif[/img], and raise to $1, and Mr. All-In shoves from the BB. Both of you happen to have a full 100BB stack. What do you do?

Here is how it breaks down. Your data shows that 51% of the time, you will be against two large unpaired cards. We can never know whether or not a card will hit the board that pairs one of those cards, nor can we know if this time is one of the times that villain has a PP. All we know is that most of the time, we are ahead here. Worst case scenario with unpaired cards is that this is AKs hearts or diamonds, in which you are less than a 1% underdog, and lets face it, that isn't the case most of the time. You can generally assume that you are ahead preflop 51% of the time, and that means that folding to villain's shove essentially hands $0.50 to villain everytime that you do it. On the other hand, everytime that you call him, you are taking $0.50 from him. If we charted the the results of this decision on a graph over the course of 100,000 hands, the swings up and down would be huge, meaning that the variance would be high, but it would also be profitable. I don't know about you, but I'm in this for the profit.

Essentially, what I an saying is to actually embrace variance, or if you can't do that, at least ignore it for the most part. Instead focus on making the decisions that squeeze every last possible bit of profit out of you opponents. I don't think we should let the fish keep their money just because we don't want a downswing.

[Keys Myaths]

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As far as I can tell, you are a 1.001:1 favorite to win the hand you are still a favorite, and if you can get all of your chips in the middle with a caller, over the long run doing this will win money.

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No, you won't.

The rake would eat you alive.

[SCBielski]

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As far as I can tell, you are a 1.001:1 favorite to win the hand you are still a favorite, and if you can get all of your chips in the middle with a caller, over the long run doing this will win money.

[/ QUOTE ]

No, you won't.

The rake would eat you alive.

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lol, I think we know what he's trying to say...a better example is being a 55% favorite, although that doesn't fair much better against the rake.

[Sean Fraley]

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As far as I can tell, you are a 1.001:1 favorite to win the hand you are still a favorite, and if you can get all of your chips in the middle with a caller, over the long run doing this will win money.

[/ QUOTE ]

No, you won't.

The rake would eat you alive.

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lol, I think we know what he's trying to say...a better example is being a 55% favorite, although that doesn't fair much better against the rake.

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To get it out of the way, I intentionally ignored rake in this essay, and if you note in the hand example, I mentioned an unraked game. If necessary, just pretend that everyone plays at WPEX.

[matrix]

nice post - and I agree with the general sentiments - i.e. variance can go [censored] itself if a play is +EV I'm going for it.

but...

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Now don't get me wrong, I have been through a couple downswings, both around 10 buy-ins, and I understand how painful they are.

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10 buys is *not* a "downswing" - 10 buys is normal variance.

when you've hit a 30 buyin drop and can't get a hand to hold up over a 50k stretch - then come back and tell me how painful downswings are.

and whether the rake would "eat you alive" depends on what stakes you are playing and how much the rake is (tho yes at 25NL the rake would eat you for breakfast) - thankfully in practice your edges aren't actually that small.

[Keys Myaths]

'Twas a joke, people. It was a good post.

Relax. [img]/images/graemlins/smile.gif[/img]

[Numfar]

The main problem is that people aren't robots so you also need to take into account the emotional reaction to variance as well as the odds. If someone is likely to tilt then they absolutely should not play high variance poker until they fix their problem.

I tend not to tilt too much but after a string of losing coin flips I know that I can sometimes make a bad decision or two. I recently got stacked 5 times in 5 minutes on Party when I got my chips in as a 60:40 favourite or better. They were all correct decisions but I'm sure I wasn't playing optimally after it. So whilst I was a 60:40 favourite, some of them may have been losing plays due to my reaction.

Anyway, interesting thread - thanks for bringing it up.

[LaMbaL]

[ QUOTE ]
You are playing an unraked $25 NL 6-Max game against an opponent who frequently reraises all-in preflop. You have managed to amass 100,000 hand of info about him, and analysis of this info shows that of all the times he went all-in preflop and the hand went to showdown, he had two unpaired broadway 51% of the time, the other times, he had a pocket pair. It is folded to you in the SB with 22, and raise to $1, and Mr. All-In shoves from the BB. Both of you happen to have a full 100BB stack. What do you do?

Here is how it breaks down. Your data shows that 51% of the time, you will be against two large unpaired cards. We can never know whether or not a card will hit the board that pairs one of those cards, nor can we know if this time is one of the times that villain has a PP. All we know is that most of the time, we are ahead here. Worst case scenario with unpaired cards is that this is AKs hearts or diamonds, in which you are less than a 1% underdog, and lets face it, that isn't the case most of the time. You can generally assume that you are ahead preflop 51% of the time, and that means that folding to villain's shove essentially hands $0.50 to villain everytime that you do it. On the other hand, everytime that you call him, you are taking $0.50 from him. If we charted the the results of this decision on a graph over the course of 100,000 hands, the swings up and down would be huge, meaning that the variance would be high, but it would also be profitable. I don't know about you, but I'm in this for the profit.

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If I may nitpick you here, if you interpret your data this way you are making a big mistake. Namely, when he has two overcards, you are a 55 to 45 favourite, but when he has an overpair, you are a 20 to 80 dog. For your expectation, this means that you earn (55/45)*0.51 + (20/80)*0.49 = 0.75 times your investment. In other words, you actually lose 25% each time you call him here!

I understand that this was only a theoretical example, and that the actual argument was about variance not being important, but simple logical flaws like these can cost a lot of money. That being said, I think variance plays a roll in your decision as long as your bankroll is vulnerable to variance. A lot of people cant afford to lose their bankroll, and would gladly trade a little extra profit for some more stability and security.

[Sean Fraley]

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If I may nitpick you here, if you interpret your data this way you are making a big mistake. Namely, when he has two overcards, you are a 55 to 45 favourite, but when he has an overpair, you are a 20 to 80 dog. For your expectation, this means that you earn (55/45)*0.51 + (20/80)*0.49 = 0.75 times your investment. In other words, you actually lose 25% each time you call him here!

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Good point, I'll edit the original post and make it a pair of eights. I just kind of pulled the cards and percentages out of my a** as a means to illustrate the point.

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That being said, I think variance plays a roll in your decision as long as your bankroll is vulnerable to variance. A lot of people cant afford to lose their bankroll, and would gladly trade a little extra profit for some more stability and security.

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I agree with the issue concerning bankroll and variance. I think that the more appropriate course of action would be to drop down a limit and make decisions that maximize earnings, as opposed to being more conservative in how you play. Or to put it another way, adjust your bankroll requirements, not your play. While you might lose a some in hourly rate initially, I believe that you would make up for it later by the increase in PTBB/100 when you finally moved back up. I think that one of the important things that we need to keep in mind down here in the micros is to develop good habits of play while the stakes are cheap, so that way we have as much advantage as possible when they get more expensive.

[Sean Fraley]

Dammit, I can't edit the post. Everyone, assume that you are holding eights in the example hand.