HI all

Does anyone have any limks to a good site or posts that explain the maths well? I know all the odds of a flush coming in or a straight etc but i really dont understand all this +ev -Ev etc etc

Any help would be awesome

Thanks

this sites pretty good.

EV = Expected Value

Its a weighted average of all possible outcomes that may occur
The weights are the liklehood of that particular outcome.

Like EV of Raising with AK from MP2 after 2 limpers..
You would consider all possible actions by players left, and flops to come, and assuming we make best play going forward....
Then asign liklehoods (percentages) to these future flops/turns/rivers/ and possible player actions.

So you would have say 24,553,224,2543,236,789,654,882,943 possible combinations of the way the hand plays out. Each combination would have some likelihood associated with it, between 0 and 1. The sum of all these likelihoods must add up to 1.

Multiply the likehood of an event by the profit/loss you make if it occurs
Then sum up all these products to get the Expected Value

We say +EV for a play that is likely to be profitable.


hope that helps

To expand on what Actuary said, here are some simple examples of EV in action, for you.

Say you have a coin. Your friend says he will pay you $2 if you flip tails, but you have to pay him $1 if you flip heads. Of course, flipping heads or tails is equally likely.

The EV of the event is:

EV = Prob of Outcome 1 x Value of Outcome 1 + Prob of Outcome 2 x Value of Outcome 2

EV = (0.5)($2) + (0.5)(-$1)
EV = $1 - $0.5
EV = $0.50

This means that in the long run, you will make 50 cents each time you make this bet, so over 10000 coinflips, you would make 10000 x .50 = $5000.

----------------------------------

Applied to LHE:

1 card left to come, you hold A :icon_suit_spade: K :icon_suit_spade:

The board reads 2 :icon_suit_spade: 4 :icon_suit_spade: 7 :icon_suit_diamond: J :icon_suit_heart:

Say your opponent flipped up his cards accidentally, and he holds AA (no spades, obviously).

This means that the only way you can win the hand, is by hitting one of your 9 spade outs in the deck. In this case, since we've seen the opponents cards, there are 52 - 8 = 44 unexposed cards left.

The probability of hitting your spade on the river then is 9/44 = 0.2045.

Let's say that we are playing 5/10. The pot is $90. You opponent bets $10.

Your decision is now whether or not to call $10. If you hit your spade, you win $100, if you don't, you lose $10.

EV = (9/44)(100) + (35/44)(-10)
EV = $12.5

This implies that by making the call wins you $12.5 each time, over the long run. If you were faced with this exact situation 10000 times, you would win, on average $12.50, each time.

--------------------

Those are just simple examples of EV. The idea is to make decisions that have a positive EV. That way, we win in the long run.

- Zach

I thought my more abstract complex explanation was far superior to one a person could actually understand and apply.

nh, Zach.

When people write, "+EV," they don't actually calculate. They just mean that play is profitable. For example, raising with AA is +EV. Raising 72o is -EV. I don't need to run a simulation or solve equations to see that.

Of course, but that is all based on previously calculations. We just familiarize ourselves with what is profitable. We also use concepts such as pot odds to estimate EV and quickly calculate it at the table.

- Zach

someone else already did.

But yeah, actually I go thru all the calcultions every time.
I"m really good at math.

Is there an echo in here?