You say "fall back" like it is a bad thing. We aren't "falling back" on it. We have lack of information, and therefore are using our available information to make a decision.

If you want the mathematical proof of convergence http://en.wikipedia.org/wiki/Convergence

http://en.wikipedia.org/wiki/Converg...in_probability

specifically

Law of large numbers can help too

http://en.wikipedia.org/wiki/Weak_la...mbers#Weak_law

But to be honest, the mathematical proof should be trivial, as the answer is naturally intuitive.

Yeah, that does not have a proof that the sum of outcomes converge to the sums of EVs

Law of large numbers does. Expected Value is simple the Expected Result. It is generally a poker term (while sometimes used to describe other circumstances), the law of large numbers proves the convergence problem you are interested in.

Once again, it is intuitive and you shouldn't require a mathematic proof to understand the concept.

The weak law of large numbers states that the sample average converges in probability towards the expected value [4] [proof]

first line of

http://en.wikipedia.org/wiki/Weak_la...mbers#Weak_law

Page has been deleted or whatever from wiki...

Also, sometimes intuition isn't enough to convince people. Lots of facts and theorems are counter-intuitive, and so just "accepting" those that are intuitive simply because they are intuitive is a bad way to go about convincing yourself it is true.

Concrete mathematical proof can also enhance your understanding of a concept. For example, in the definition of continuity.

It hasn't been deleted...

I just didn't post it correctly, here

this is so fkn stupid. how can people write massive posts answering this idiot question

Lets say that in you're entire lifetime, u only make ONE bet. u calculate that u have 4:1 odds of wining this bet. But you are offerede 4,1:1 on your money. You know that u will never ever make any other bets. everybody can see that this is instant profit, but because u only get to bet one time, i think i would skip this bet, because the chance of losing is so much bigger than winning. But if i did this bet many times, i would make a profit and of course do it.

Seriously, why is this thread still going?? Read above for /thread

If it's a bet with any amount of variance for a sizeable part of you bankroll, there is a concept whose name I can't remember and it includes a formula to see whether or not you should go ahead and take the trial/bet/whatever it is

Originally Posted by jakey
If the situation is not repeated, it depends on how much of your roll the bet is for and what you're actual odds of winning are. EV means nothing when the situation is not repeated.

For example, say you have $100,000 in life savings. You are offered a bet where you are asked to pick a number between 1 and 1 million. If you win, you will be paid $200,000,000,000. If you lose, you owe $100,000. Expected Value says you should take the bet but actually taking it would be foolish.

Your example is not an indictment of EV as a good metric but a plug for using utility theory, which is nothing more than E[U(V)], replacing the value of a bet with a utility function.. Here the positive utility (pleasure) of winning an enormous amount of money does not overcome the negative utility (pain) of going bankrupt.

Let me restate your example. Suppose someone offered you a bet to pick a number between 1 and 100. If you win, you will be paid $200,000. If you lose you owe $1. Would you bet? Note: dollar amounts are exactly proportional to your example – both were divided by 100,000.

I know I would bet even though this situation is not to be repeated – ever. And why? Because the EV is 1/100 * 200,000 – 99/100 * 1 = $1,999.01. The pleasure in winning almost $2000 on an expected value basis, even though very unlikely, far exceeds the pain of losing $1, which is very likely.

Your own statement (bolded) that the decision depends on the amount of the bet and the odds of winning is just another way of stating you have to do an EV calculation

Well, the situation above really depends on your bankroll, and how much $1 means to you compared to you bankroll wrt the trial

The Kelly Criterion

I have not read all the posts but I do agree with Maxaon that EV is not the only thing that make you choose to fold or call. And I do thing this is an interesting question (on a theoretical and almost philosophical point of view).

If I won a satellite for WSOP and happens to be at the bubble I will certainly be able to fold an EV+ move (for instance a coin flip with a 1.2 or more to 1 odds) at the bubble because this a big amount of money for my BR.

However, in regular situation even if it is a one shot thing I will always pick the most EV+ move (as far as I can tell).
That is true that if it is a one shot thing I eventually lose or win all but my question to you Maxaon would be "why would I make another choice than the one that gave me the most EV"?
Said otherwise what else would influence your choice? instinct?