Mathematical Expectation

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If someone bets such a large amount, you have to expect him to have big cards and thus your cards will need to be bigger before they provide you positive EV.

If you put all the cards in line from bad to good, it is obviously not so that the middle card is 0 EV. Against a small raise, something like AT or AJ will be +EV, against a 600 raise in this example, the first times when you do not yet have a read on your opponent, you will need a better hand to expect a +EV. After you seen him move all-in a few times, you increase his range of possible hands and with that, you also increase the range of hands with wich you expect to have +EV.
Than you can call him with any hand that is +EV for you.

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Sorry man. You're still missing the point. Even if you call with a +EV you still might lose. Say I call the $600 and I am favored, say 3to1 and have a +EV, but he draws out on me. That's the one loss in the 3to1 ratio. Now I win the other 3 times but only make$60 in the 3 hands combined. I still lost -$540, but the EV theory worked perfectly. My favored hand held up 3 times and lost once, just like it was supposed to but the one loss was for much more money.

[Wacken]

ya thats bad luck

[Dov]

The problem is that your sample is too small.

After you play 100,000 big and small pots, see where you're at.

Otherwise you are playing short term result games that don't really mean anything.

The EV equations will tell you your real edge if you know his cards.

Bayes Theorem will give you a general idea if you've seen some cards already.

Learning to read his hand will give you the best idea of all.

In short, don't worry about the bad beats. It DOES turn around.

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The problem is that your sample is too small.

After you play 100,000 big and small pots, see where you're at.

Otherwise you are playing short term result games that don't really mean anything.

The EV equations will tell you your real edge if you know his cards.

Bayes Theorem will give you a general idea if you've seen some cards already.

Learning to read his hand will give you the best idea of all.

In short, don't worry about the bad beats. It DOES turn around.

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Out of everyone that's responded to this you have made the most sense. I agree that it should even out in the long run but is that all there is to it? Is there any consideration regarding the pot size that should go into a decision when determining EV? Does anyone in a book or something address it specifically? Does NL just have a larger variance than limit because of this?

[Alex/Mugaaz]

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If someone bets such a large amount, you have to expect him to have big cards and thus your cards will need to be bigger before they provide you positive EV.

If you put all the cards in line from bad to good, it is obviously not so that the middle card is 0 EV. Against a small raise, something like AT or AJ will be +EV, against a 600 raise in this example, the first times when you do not yet have a read on your opponent, you will need a better hand to expect a +EV. After you seen him move all-in a few times, you increase his range of possible hands and with that, you also increase the range of hands with wich you expect to have +EV.
Than you can call him with any hand that is +EV for you.

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Sorry man. You're still missing the point. Even if you call with a +EV you still might lose. Say I call the $600 and I am favored, say 3to1 and have a +EV, but he draws out on me. That's the one loss in the 3to1 ratio. Now I win the other 3 times but only make$60 in the 3 hands combined. I still lost -$540, but the EV theory worked perfectly. My favored hand held up 3 times and lost once, just like it was supposed to but the one loss was for much more money.

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What are you talking about? How can you only be 3 to 1 to have +EV? You either have +EV or you don't (or it's 0). There is no inbetween, you may not be able to determine what it is but ignore that for now. If you are a 3 to 1 favorite for 600 then you will win 600 x 3 and lose 600 x 1. After the 4 runs you will be up 1200. So your call gains you $300 in expectation.


You can't lose money on a play if it's +EV. You can lose the hand, but in the long run the play makes money. Keep in mind that if you can't calculate what the EV is (or at the very least determine if it's +/-) then this idea is pretty pointless.

[subzero]

You should always choose the action that gives you the highest +EV, even if that means risking your entire stack. If your bankroll can't handle the variance, then you should be playing at a lower limit. If you can't handle the swings emotionally, then this is something you need to work on. But avoiding the highest +EV play to limit your risk is not something you want to do.

[pudley4]

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Ok, so let's say we build a random number generator that will truly generate a random number 1- 100.

You can have numbers 1-51, i'll take 52-100.

Even money bet.

You can see this is a +EV bet for you.

The catch is we only play the game ONCE and I'm a billionarie and refuse to play unless you put up every dime to your name.

Should you play?

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Of course you wouldn't take that bet. I'm not talking about some monster bet that will bankrupt me if I lose. I'm talking about the big fluctuation in pot size that occurs in NL. The average pot size at a table may be $40, but at any time someone can push all in and make it say $600. If you have the +EV(say 3to1) to call and lose you lose your $600. Now in the same situation you win the other 3 pots but they are those standard $40 pots for the level you play. You win $20 per pot because the other $20 is money you put in. So you win $60.
You won:
3 pots for $60
You lost:
1 pot for $600.

Total value -$540

The lost $600 doesn't bankrupt me, it's just a loss.

How do you account for this variance? That's my question.

Thanks for all the input.

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Why is this thread so long? It's a one-line answer.

No one writes anything about this "phenomenon" because it's all just due to short-term variance. In the long run it all evens out.

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Theory of Poker:

Pg. 11, paragraph 2 - "Mathematical expectation is at the heart of every gambling situation."


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Not necessarily. Maybe in limit poker. But I guess the response summarizes my opinion.

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You should always choose the action that gives you the highest +EV, even if that means risking your entire stack. [bold] If your bankroll can't handle the variance, then you should be playing at a lower limit. [/bold] If you can't handle the swings emotionally, then this is something you need to work on. But avoiding the highest +EV play to limit your risk is not something you want to do


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The only time this doesn’t apply is in no-rebuy, no limit tourneys. Think about the beginning of the WSOP final event. If someone gave you a 51% bet for all your chips would you take it? Its +EV, but this is a decision that is made once. Not over a run. So +EV is meaningless. Exactly the same reason small stacks go all in on marginal hands. They don’t care about EV, but rather variance. They knowingly take a bet that only succeeds 33% of the time because they know that they need to have more chips to have any chance of long run success.

I couldn’t find the book on Amazon that I wanted to recommend so I will substitute a slightly watered down version but that is more accessible. Risk management is basically eliminated in limit poker (assuming your br is 300bb).

http://www.amazon.com/exec/obidos/AS...278368-2179035

Note, I don’t read about risk because I think it helps my poker, rather I am mildly interested in Finance.

[ellipse_87]

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I'm not talking about some monster bet that will bankrupt me if I lose. I'm talking about the big fluctuation in pot size that occurs in NL

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You're trying to isolate your question from bankroll considerations, but as far as ring games go, your question IS a bankroll question. You're supposed to anticipate variation before you choose the stakes you want to play. You should start with 10x the buy-in, 20x the buy-in, whatever benchmark it is that you're comfortable with, to sustain a reasonably probable series of losing all-in bets. Your concerns are built into, and in fact are the foundation of, beginning bankroll requirements.

If you are worried about the size of the bet you are calling, and squirming trying to get out of the conclusion EV points you toward, then you are are playing stakes that are too high for you.

Or, your question may be fundamentally about margin of error. Calculating EV involves putting your opponent on a range of hands, which is an inexact science. Of course you're going to be more cavalier about a 3x BB bet than an all-in. You accept a wider margin of error with the former bet (although ideally you shouldn't). But if you are at a state where you conclude that it is simply impossible for you to have less than 55% equity in a pot, you must call the all-in bet, if you're properly bankrolled.

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If someone bets such a large amount, you have to expect him to have big cards and thus your cards will need to be bigger before they provide you positive EV.

If you put all the cards in line from bad to good, it is obviously not so that the middle card is 0 EV. Against a small raise, something like AT or AJ will be +EV, against a 600 raise in this example, the first times when you do not yet have a read on your opponent, you will need a better hand to expect a +EV. After you seen him move all-in a few times, you increase his range of possible hands and with that, you also increase the range of hands with wich you expect to have +EV.
Than you can call him with any hand that is +EV for you.

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Sorry man. You're still missing the point. Even if you call with a +EV you still might lose. Say I call the $600 and I am favored, say 3to1 and have a +EV, but he draws out on me. That's the one loss in the 3to1 ratio. Now I win the other 3 times but only make$60 in the 3 hands combined. I still lost -$540, but the EV theory worked perfectly. My favored hand held up 3 times and lost once, just like it was supposed to but the one loss was for much more money.

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What are you talking about? How can you only be 3 to 1 to have +EV? You either have +EV or you don't (or it's 0). There is no inbetween, you may not be able to determine what it is but ignore that for now. If you are a 3 to 1 favorite for 600 then you will win 600 x 3 and lose 600 x 1. After the 4 runs you will be up 1200. So your call gains you $300 in expectation.


You can't lose money on a play if it's +EV. You can lose the hand, but in the long run the play makes money. Keep in mind that if you can't calculate what the EV is (or at the very least determine if it's +/-) then this idea is pretty pointless.

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Your totally missing the point. I'm not talking about 4 hands for a $600 pot each time. I'm talking about four hands where the pot size is different, but the hand and the EV are the same. Just forget it, I'm not interested in any more comments. Thanks for everyone's input, but you keep avoiding the issue by stating basic Mathematical Expectation.

Ps. If you are a 3to1 favorite you have a +EV. Don't know how to say it any simpler.