Mathematical Expectation

[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.

[WhiteWolf]

[ QUOTE ]


Is there any theories on this or is it that it just evens out over time?


[/ QUOTE ]

To put it simply, if you do not have any variance or bankroll considerations, there are no special pot size theories here because bet size is irrelevent. You want to make the highest EV move you can in any situation.


[ QUOTE ]

Is it OK to fold a +EV when you haven't invested anything yet? No win, no loss.


[/ QUOTE ]

If your goal is to maximize profit over time, it is always wrong to fold when calling or raising has +EV

[Wacken]

Ok then, to your question:
It doesn't matter, it will even out. As long as all bets you make are +EV, it does not matter how big the pot is.

Folding when you have +EV is throwing away money. Folding is 0 EV. It does not matter if there is money from you in the pot.

Suppose there is 100 in the pot.
You have the choise to pay 100 for a 55% chance of winning it. Out of 100 times, 45 times you lose 100, 55 times you win 100. (+5500 - 4500 = 1000) So your EV is 10 dollars per bet, and you should make this bet.

Now if the pot is 340, and a 100 dollar bet would provide a 25% chance of winning, you will 75 times lose 100 and 25 times win 340. (-7500 + 8500 = +1000). Again your EV is 10 dollars. It is the same profit for you, but the variance is a little different, but when you play at the right limit for your bankroll, that shouldn't be important.

now suppose half of those 100 dollars is yours. You should not look at it like it was yours, it does not matter if it is yours, but suppose you do look as if it was yours:

If you fold, you lose 50 dollars every time. EV = -50.

If you bet 100 again with 55% chance of winning, you will 55% of the time win 50 and 45% of the time lose 150. For a total of +2750 - 6750 = -4000. Now you have an EV of -40 instead of -50. You reduced your loss from 50 to 40 dollars.

Therefore, do not care whos money is in the pot and do not care about the size of the pot after you have calculated your EV.

[J_V]

The size of the pot does not matter in relation to your expectation. If you have a 55% equity in a 1,000 dollar pot. Your expectation is 550. If you have a 55% equity in a 1 dollar pot, your expectation is 55cents. You might lose both, or win both, both your EV for the two trials was $555.55. If you are heads up and have a 45% equity in a big pot and 55% equity in a small pot - YOU ARE LOSING MONEY.


I have no idea what anyone else was saying, but it wasn't right.

[J_V]

[ QUOTE ]
Everything is the same suits and all. The only thing that changes is the pot size. If you win 7 out of 10 and each pot you win is $40, you win $280. But if the 3 that you lose were pots of $100, $150 and $90 you lose $340. Your total Value is -$60. You won more pots but lost money.



[/ QUOTE ]

This is called "bad luck." Your expectation is still positive though.


[ QUOTE ]
Is there any theories on this or is it that it just evens out over time?

[/ QUOTE ]

It will even out over time (or come fairly close). Remember just because you have a positive expectation doesn't guarantee anything. That is why their are so many good players who "run bad."

[Wacken]

[ QUOTE ]
I have no idea what anyone else was saying, but it wasn't right.

[/ QUOTE ]

Yes, you have no idea what anyone else was saying.

The theory written so far on poker isn't of the highest math. EV is basically chapter 1 stuff in a Statistics 101 textbook. I don't think most poker authors have taken more than one class in statistics, if that.

I suggest that the proper foundation before playing poker is to take a stats 101 course and then an Intro to Probability course (which usually has reqreqs of Calc I and II - so make sure you have those under your belt first). That should be the minimum.

There is math to address different pot sizes. Basically you need to look at risk adjusted returns. In fact this is the exact reason that people will pay 1 dollar for a 1:1,000,000 chance to win $1,000,000. But no one would pay $1,000 for a 1:1,000,000 chance to win a billion.

EV isnt the be all and end all of all decision making. However making repeated decisions over a similar size payoff makes ev more accurate.

IMO there is a lot of room for more indepth analogy of EV in tournaments because of the fact that in a tourney once you lose your chips you are done, and the fact that only certain number of people who get paid off.

There is also a paradox regarding EV that is similar to the situation you asked Rob. Imagine there is a game where if you flip a coin and its heads you get $2, if if its tails you flip again. If its heads taht time you get 4$, if tails flip again. Assume the payoff continues exponentially. This game would have an infinite EV. But how much would you be willing to pay?

[srm80]

[ QUOTE ]
EV isnt the be all and end all of all decision making.

[/ QUOTE ]

Theory of Poker:

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

[UATrewqaz]

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?