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Raider Fan:

[nq:1]You will lose more pots when u have many callers, but you will win more money as well. Poker's about winning the most money.[/nq]
I think that's the point of this thread. The OP wants to win something less than the most amount of money and lose less pots. We've had numerous discussions out here on this subject, most notably the ones involving the winning % at showdown.

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qqqxxxyyyzzz2000:

[nq:1]now i have a new question: how much variance are you willing to accept for additional EV? is there a mathematically correct answer to this question? is there a standard unit for variance?[/nq]
I think what you're asking here is for a mathematical formula for determining risk tolerance. I don't know of any and would question the validity of any that was claimed to be one. There are too many variables that can be included to determine EV that only translate to variance in general ways. Game selection is one. Position on other players is another. Reads on players is a third.
One thing that could be considered in this discussion is the difference in risk tolerance between B&M play and online. With faster games, multiple tables, and lower pot taxes online poker gives you a much faster look at the longer term. A slightly positive expected value becomes much more attractive when you don't have to wait as long for that slight edge to be realized.

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Anonymous:

What was the title of the thread from yesterday?

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quickfold:

"how much variance are you willing to accept for additional EV? is there a
mathematically correct answer to this question? is there a standard unit
for variance?
Pulling from risk theory here..the first question does not have a unique solution. In picking stock, for instance, it is quite common to graph risk vs expected return. Risk is defined as standard deviation, the square root of variance. The curve basically says that if you are not getting a higher expected return for assuming more variance, you are making sub-optimal deciiosn, meaning that you could make more with less risk or take less risk to achieve the same return. In theory, you don't care where on the curve you are since the return is commensurate with the risk.
OK, so why doesn't everyone just adopt the highest-varaince strategy available to generate the highest return? Because people are risk averse and don't have unlimited bankrolls - the value of $1 lost in bets is greater than the value of $1 won in bets. Thus, your risk/return curve is dependent on your bankroll. The moral of the story is that you should not adopt a higher variance strategy than can be supported by your bankroll. If the variance of the different strategies can be quantified, you probably would never want to adopt a strategy with a variance of more than 57% of your bankroll in order to keep your probability of ruin less than 1%.

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garycarson:

[nq:2]You either know what you're talking about, or you don't. I thinkit's pretty clear that you don't.[/nq]
[nq:1]I think it is clear now as well. I think i'm confusing variance with standard deviation (where doubling results would double the sd)which may or may not explain most of what i wrote.[/nq]
No.
You don't know what you're talking about.
You need to get that thru your head or you'll never figure it out.

You aren't confused about some detail. You just don't know what it is. This doubling idea is just complete nonsense.
Gary

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quickfold:

Because I'm anal, I'll offer two corrections:
1. Variance and mean are not the same units. Yes, the variance of thesum is the same as sum of variances (assuming no covariance), but financial economists prefer standard deviation because it is in the same units as the mean. If the mean is calculated in dollars, variance would be in dollars-squared units and standard deviation would be dollars.
2. Doubling the mean does not double the standard deviation, either.Consider a binomial variable:
mean = np = hand played x % won

100 hands played, 50 hands won => mean = 100 x 50% = 50variance = npq = 100 x 50% x 50% = 25
standard deviation = 5
Now, if you play 200 hands,
mean = 200 x 50% = 100
variance = 200 x 50% x 50% = 50
standard deviation = 7.07
Notice that 7.07 is not twice the mean

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garycarson:

[nq:1]"how much variance are you willing to accept for additional EV? is there a mathematically correct answer to this question?[/nq]
The mathamatical approach to this question is that you need to pick a stratagy someplace along the "efficient frontier". There's been a couple of Nobel Prizes given for work in this area in finance and economics.
is there a standard
[nq:1]unit for variance?[/nq]
Well, it's the square of whatever unit you're working with. Other than that I don't understand the question.
[nq:1]Pulling from risk theory here..the first question does not have a unique solution.[/nq]
Well, not unique in the sense that's it's some scaler value, but unique in the sense that it's some well defined function or collection of values.
In picking stock, for instance, it is quite common to
[nq:1]graph risk vs expected return. Risk is defined as standard deviation, the square root of variance. The curve basically says ... bets is greater than the value of $1 won in bets. Thus, your risk/return curve is dependent on your bankroll.[/nq]
Well, no, your risk/return curve is independent of your bankroll. That's a function of the game, and the opponents you face in the game. Where you want to operate on that curve might be bankroll dependent.

But, even then, generally the reason everyone doesn't adopt high variance/high return stratagies on the efficient frontier is that most people make big mistakes. It's those big mistakes they make which give you positive returns.
The stock market is a method to fund wealth creation, poker games are a method to distribute wealth, not create it. So, there's some differences between the games other than social judgements.

The moral of the story
[nq:1]is that you should not adopt a higher variance strategy than can be supported by your bankroll.[/nq]
Not really. Game selection (size of game) is highly dependent on bankroll considerations. But, once you've chosen a game you're playing decisions are pretty much independent of bankroll, that's because you've made your game selection in such a way that you're not going to be able to generate enough risk to matter.
If the variance of the different strategies
[nq:1]can be quantified, you probably would never want to adopt a strategy with a variance of more than 57% of your bankroll in order to keepyour probability of ruin less than 1%.[/nq]
Uh. Well, you can quantifiy variance of various strategies and if you're in a game where it's even possible to generate a high enough variance to hurt you then you made a huge mistake in playing in the game in the first place.
For an example of how to quantify variance of various strategies search thru the arhives where I compared coefficeint fo variation of raising versus not raising a flush draw on the flop using a simple multinomial model.
I don't have a link for it but you can find it thru groups.google is you look for it.
That's an example of how increasing variance will actually decrease your risk of ruin becuase of the corresponding increase in EV. That's going to be generally true in poker I don't know of an example in poker where a stratagy that increases EV will also increase variance so much that it increases your risk of ruin. I think it's always true in poker that an increase in EV will decrease your risk of ruin.

Risk of ruin isn't just a function of risk, it's a function of both risk and return (and skew but that's usually ignored in the models). Gary

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Joe Long:

[nq:1]OK THATS IT NO MORE INTELLIGENT DISCUSSION Emotion: smile

heres another question; what is the EV tradeoff of having an intelligent ... been motivated to think about and therefore elevate their game? there should be some signal for RGPers at the table...[/nq]
Well, I think these discussions are win-win for those of us here, positive EV for everyone who participates and thinks about what is being posted because even if we someday lose some chips to someone we helped "educate" in one of these threads, we'll have won more overall from what we learned ourselves.
As to identifying r.g.p'ers at a table, try shouting "Presto!" when someone shows down pocket fives. I have VERY RARELY gotten the response ("Irwin!").

Joe Long
jlong (at) rnbw (dot) com

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Mtn Lover:

We've had a lot of discussion, only obliquely related to the original question.
[nq:1]how much variance are you willing to accept for additional EV?[/nq]
That depends on your own circumstances: how much money you have, what kind of game you are playing in, what kind of playing style you enjoy, and so on.
[nq:1]is there a mathematically correct answer to this question?[/nq]
Sort of. If you can specify exactly what your goal is, you can calculate how best to reach it. For instance, you might ask "given my current bankroll, will this change in my play increase or decrease my risk of ruin?"
[nq:1]is there a standard unit for variance?[/nq]
As others have said, variance carries units of dollars-squared. Standard deviation, the square root of variance, comes in the same units as whatever you are measuring the expected value of.

If you mean "standard" in the sense of "dimensionless", you may be looking for something called the Coefficient of Variation, the standard deviation divided by the expected value. The time required for you to achieve a fixed probability of showing a profit is proportional to Coefficient of variation squared (variance divided by EV^2).

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Mtn Lover:

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RE: EV vs. Variance page 3

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