Mathematical Expectation

I've been reading about mathematical expectation. It advocates calling when you have a positive value(coin flip example). I haven't seen or heard anyone address the amount of money that is won or lost though. What I mean is if a play is a positive value and you call all in and lose $200. Then the next three times you have the same situation you call all in for $40 each you won three times but only $120, when you lost $200 on the first hand. Does anyone address the different values of specific pots in positive expected value situations?

[mudbuddha]

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

Thanks for your input but I think you did misunderstand my question. What I meant is has anyone addressed the difference in pot size when it comes positive expected value. The coin flip example is from "The theory of Poker". It is an example about flipping on an actual coin flip, not poker.

[Wacken]

You mean the difference between betting 10 on an 11% of winning 100 and betting 10 on a 55% of winning 20 ?

In cash games i'd say that doesn't make a difference at all, as long as both investments are not huge to you.

In big one time bets like the example i gave in my other post of starting a business, it does matter a lot and in you probably prefer a large chance to win not too much. 10 million dollars does not have 10 times the importance to your life as 1 million dollars.

In a tournament i am not really sure about this and it probably depends on many factors, but i am not a tournament player so i can't tell.

[Alex/Mugaaz]

[ QUOTE ]
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

[/ QUOTE ]

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

[UATrewqaz]

The law of large number on EV pretty much assumes many SIMILIAR trials.

Say you have a 51% / 49% edge on a 10 million dollar bet and lose, but every remaining 51 / 49 decicion the rest of your life is worth $1. Should you lose the big one you will never be able to make it up because of the low wager amounts.

However if you can repeat the process, you should take the 51/49 edge bet EVERY SINGLE TIME, because if you do over the long haul you will finish ahead.

I don't quite understand your point. You say if you lose the big one you can never make it up, but then you say if you take the bet every single time you will win over the long haul. Can you explain, if you lose a million then you have to win $1 one million times to break even.

[UATrewqaz]

I mean if you have hte capacity to do the million dollar 51/49 flip over and over again you should take the bet, if you have 1 million to your name it's not a good idea.

The +EV only works if you have a large neough bank roll to overcome variance. So even though a 50.1 to 49.9 even money bet has +EV value, you should not go sell everything you own to take that bet because over 1 trial the statistical different between 50.1 and 49.9 is INSIGNIFICANT. THe +EV edge will only demonstrate itself over many many many many trials.

This is why in a limit cash game players never pass on +EV situations, whereas in a NL tournament you may very well pass on a situation where say you have TT and you KNOW your opponent has AK, sure you have the edge but you cannot risk busting out of the whole tournament on a small edge, due tot he fact you cannot repeat the trial over and over should you lose.

That should be the fundamental rule, as long as you can repeat the trial/situation to as many times as your liking, take EVERY SINGLE +EV edge no matter how small.

However if you're making a "for broke" gamble, you should most likely pass on small edges and wait for a gigantic edge (say 80/20 or better) due to the fact that for a single trial variance is king over EV. Over two trials variance is still king over EV, over a billion trials variance is EV's little bitch.

[Wacken]

When the stakes are so high that losing will cause your children to die of starvation, you should look at the real value of winning vs the real cost of losing and you would probably need to be a huge favorite to make the bet. How huge is largely different for everyone of course. Starting your own bussiness often is such kind of a bet. Many people don't dare to make it, some do, some succeeed, some fail.

In poker, you are supposed to play at stakes you can afford to lose. In those stakes, the statement is simply true.

In tournaments there have been things written on this issue. In tournaments it is indeed a bit different, and it is still deferent depending if there are rebuys and probably also depending on what the buyin $ means to your own financial situation. a 25k buyin is of course something different than when you play 10+1 sng's all day long and might start to look more like the previous example of the starving children.

You are supposed to make the +EV play in each situation in which you encounter it. Sometimes the +EV play that works out will be in a small pot, sometimes it will be in a large pot. But as long as you stick to making the most +EV play, you are playing correctly.

Consider the 51-49% example. You are facing 10 bets in this scenario

$1
$10
$100
$1000
$10,000
$100,000
$1,000,000
$10,000,000
$5
$7948

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