Mathematical Expectation

[J. Sawyer]

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Is it correct in ANY of those scenarios to take the 49% option?

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How could it ever be correc to take the worst of it?

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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.

[J_V]

Well one of us misunderstood his question. I'm pretty sure that wasn't me. If you didn't, then your answer doesn't answer his question at all.

[Wacken]

Well, first of all, there is the max buy-in to prevent this. You can't lose more than you are willing to put at stake.

Within that buyin, indeed you always have the idiots who go all-in when the blinds are so small that the all-in is many times the blinds.
This however is in your advantage. They put 600 at stake to win 20 dollars. Let them take those 20 dollars 20 times, and the 26th time, when you have AA or KK, you call him and you are probably an 80% favorite to win.

So you lose 20 times 20 and you win one time 600. It is exactly the other way around of what your example.

And if you lose those 600? then that is called bad luck, do this 10 times more and you will most usually win them [img]/images/graemlins/smile.gif[/img]

[Alex/Mugaaz]

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coinflips are barely +ev.. poker is all about choosing your best +ev play.. personally i hate coinflips bc. im not a casino and im not gonna plya a million hands so that law of large #'s is correct. i can put my money in better spots than a 5% edge.. but thats my personal theory..
pot odds tell u if ur decision is +ev.. maybe i misunderstood ur post

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I would cream my shorts if I had a constant 5% edge.

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Well, first of all, there is the max buy-in to prevent this. You can't lose more than you are willing to put at stake.

Within that buyin, indeed you always have the idiots who go all-in when the blinds are so small that the all-in is many times the blinds.
This however is in your advantage. They put 600 at stake to win 20 dollars. Let them take those 20 dollars 20 times, and the 26th time, when you have AA or KK, you call him and you are probably an 80% favorite to win.

So you lose 20 times 20 and you win one time 600. It is exactly the other way around of what your example.

And if you lose those 600? then that is called bad luck, do this 10 times more and you will most usually win them [img]/images/graemlins/smile.gif[/img]

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Wacken,
Again thanks for the response. I don't want to sound argumentative, just discussing this [img]/images/graemlins/grin.gif[/img]
I know and understand everything you just said but playing that way would go against a +EV if you had the best hand. Even a small favorite like a 55/45. Any bet that has a +EV is supposed to be accepted, so if you turn the all in bet down when you are the favorite the theory of Mathematical Expectation says you are wrong. It doesn't necessarily sound wrong to me but according to the theory it is wrong. That's why I was wondering if anyone has addressed it in a book or something. "It" being the difference in pot size in relation to the EV or in general.

[Alex/Mugaaz]

[ QUOTE ]
[ QUOTE ]
Well, first of all, there is the max buy-in to prevent this. You can't lose more than you are willing to put at stake.

Within that buyin, indeed you always have the idiots who go all-in when the blinds are so small that the all-in is many times the blinds.
This however is in your advantage. They put 600 at stake to win 20 dollars. Let them take those 20 dollars 20 times, and the 26th time, when you have AA or KK, you call him and you are probably an 80% favorite to win.

So you lose 20 times 20 and you win one time 600. It is exactly the other way around of what your example.

And if you lose those 600? then that is called bad luck, do this 10 times more and you will most usually win them [img]/images/graemlins/smile.gif[/img]

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Wacken,
Again thanks for the response. I don't want to sound argumentative, just discussing this [img]/images/graemlins/grin.gif[/img]
I know and understand everything you just said but playing that way would go against a +EV if you had the best hand. Even a small favorite like a 55/45. Any bet that has a +EV is supposed to be accepted, so if you turn the all in bet down when you are the favorite the theory of Mathematical Expectation says you are wrong. It doesn't necessarily sound wrong to me but according to the theory it is wrong. That's why I was wondering if anyone has addressed it in a book or something. "It" being the difference in pot size in relation to the EV or in general.

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If you saw his cards there would be nothing to discuss, you could easily calculate the EV of each specific action. The reason you may lean toward folding in a regular game is because you don't know what his hand is, and can only assign him a hand range. If you are unable to narrow it sufficiently, or if you are just incapable of hand reading then you don't know the EV of calling.

If you're only willing to give action when you have the nuts it's fine by me. I'll run over you and easily spot when I'm behind when all of a sudden you wake up. Don't get me wrong, weak-tight is a fine strategy for new players in the lower limit online games. There is nothing wrong with it there.

[mudbuddha]

i think... that....
the thing about expected value is that it is based on the law of large numbers. if hte edge is small, the more repetitions of the thing must be done to make money, and to have that many repetitions, you must have a huge bankroll (i.e. the casino) so if you have a sufficent bank roll to do a certain event and u have +ev then... give'r .. if its variance is enough to wipe you, then u should re consider.

i took university stats n barely passed so .. damn.. maybe thats why im bad at poker haha

[Wacken]

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.

[Alex/Mugaaz]

[ QUOTE ]
i think... that....
the thing about expected value is that it is based on the law of large numbers. if hte edge is small, the more repetitions of the thing must be done to make money, and to have that many repetitions, you must have a huge bankroll (i.e. the casino) so if you have a sufficent bank roll to do a certain event and u have +ev then... give'r .. if its variance is enough to wipe you, then u should re consider.

i took university stats n barely passed so .. damn.. maybe thats why im bad at poker haha

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If you can't take the gamble the game you are playing in is too rich for you. You would be better off playing in a smaller game where you can take those gambles. There is no debating thing, it's all there is to say. There are very few exceptions that aren't worth quoting because the people who know them and are capable of understanding them already do.