Am I stupid? I can't fit these two concepts into any type of harmony.

[Alex/Mugaaz]

You misunderstood what I was trying to say. I wasn't saying you were wrong, I was asking you questions about the answer.

[Darryl_P]

If my opponents played in a way that they went all in any more often than, say, once in a million hands, then the assumption of my having a 3 BB/100 advantage would be false...it would be much greater than that.

For me to have only a 3BB/100 advantage we must rule out extremely high variance plays on the part of my opponent since those would lose too much EV.

And when you bring down the variance to "normal" levels, then the random walk model can be used with high precision even in NLH.

[Darryl_P]

OK, no problem, sorry for getting edgy on you there [img]/images/graemlins/cool.gif[/img]

[MtDon]

You didn't mention who your opponent(s) would be. If you played against a finite number of opponents, who each had a finite number of chips, then it is possible for you to win, because someone would have to win all the chips.

If you play against either a finite number of players who have an infinite number of chips, or a potentially infinite number of players with a finite (or infinite) number of chips each, then you will eventually lose all your chips. This is, of course unless all the players are so bad they always throw there hands away whatever they have and what ever the board cards are - but this doesn't fit the predicate that you have a 3bb/100 advantage in the game.

Eventually, you will run in to a run of cards where you are blinded off, if you don't lose all your money before that.

If you play for an infinite lenght of time, all possible finite runs of cards will be dealt an infinite number of times. Since you will always have an finite number of chips, you will have to run into a run of cards which will break you.

For example: You will run into these cards for as long a stretch as needed. You have AsAc, the BB has KsKc. Everyone else has nothing and folds pre flop.

Flop: AdKd2h
Turn: 2d
River: Kh

Your full house will lose to his quads every time. These same cards will be repeated, consecutively or in any order needed, as many time as are necessary for you to lose all your chips.

Having an edge, doesn't protect you from a bad run of cards.

The only type of edge that would protect you from a bad run of cards is one that was due to all your opponents playing so badly that, for example, they would fold every time you bet or raised, so that you could win every hand by betting or raising. That is, they play so badly that there would be a stategy that would allow you to win every hand you played.

[David Sklansky]

"If you play for an infinite lenght of time, all possible finite runs of cards will be dealt an infinite number of times. Since you will always have an finite number of chips, you will have to run into a run of cards which will break you."

Wrong

[Darryl_P]

[ QUOTE ]
If you play against either a finite number of players who have an infinite number of chips, or a potentially infinite number of players with a finite (or infinite) number of chips each, then you will eventually lose all your chips.

[/ QUOTE ]

This is simply not true. The only assumptions you need are the 3BB/100 advantage you have and the fact that you are at least an average player (something which IMO can be assumed from the way in which the question was posed).

That 3BB/100 advantage automatically limits the variance with which your opponents can play because there is a level above which your EV necessarily becomes higher with nothing more than average play.

This limiting variance will still be very small compared to your bankroll so you will still be able to define an amount like a million BB say which you will have a greater than 50% chance of doubling before losing. And here the random walk model applies and so the probability of EVER going broke is very small indeed.

The trouble with your reasoning is that whatever bad run you mention (say 1 trillion hands in row of quads over boat, which of course must happen eventually), the expected amount of money I will have grinded out from my 3BB/100 advantage will cover it more than enough trillion times for it to be a threat to my bankroll.

Of course such a run CAN happen before I've managed to grind out the cover for it but that has a probability of less than 0.0000000001% of happening, as shown by the random walk model.

[spaminator101]

if you had an infinite # of chips you could not go broke

[Lexander]

Question for the probabilist, since my Prob Theory course hasn't covered this yet (we are still at the beginning discussing Borel sets and sigma-fields, so allow some room for utter confusion in your answer), though I have a year of study in statistics.

Is this a matter or Convergence in Probability, or a matter of Almost Sure Convergence, or something entirely different?

Thanks.

[Darryl_P]

I'd say those are different because they examine how a series of random variables converges to another random variable. Here we are only interested in a single probability.

[pif]

if u have edge than u should use kelly criteria and u will never bust out.

the idea is to bet and precentage amount from ur bankroll (and not a fixed amount).