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Expected Value, Simon Reach, 13. Mar 2003 09:21
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Can someone please help a slightly ignorant English Holdem beginner? I have come across the EV concept in Sklanskys Tournament Poker for Advanced Players and want to find out more about it. It seems like a powerful concept but much more difficult and ambiguous to use than card vs. pot odds. Am I missing the point? Does the EV of a particular hand vary depending on the number and type of players? If so how does one adjust it to give it meaning?

Many thanks in anticipation.

Simon Reach
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Re: Expected Value, stdioh, 13. Mar 2003 11:44
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on 13. Mar 2003 09:21 Simon Reach wrote:
> Can someone please help a slightly ignorant English Holdem beginner? I have
> come across the EV concept in Sklanskys Tournament Poker for Advanced Players
> and want to find out more about it. It seems like a powerful concept but much
> more difficult and ambiguous to use than card vs. pot odds. Am I missing the
> point? Does the EV of a particular hand vary depending on the number and type
> of players? If so how does one adjust it to give it meaning?
>
> Many thanks in anticipation.

Indeed, the EV of a pair of cards is a rather intangible quality. It is a most fickle quality as well. Your KK is worth an aweful lot preflop, but as soon as you 'know' an opponent is on AA it becomes worth tossing away to any bet.

In general, your expected value is the amount you expect to make from an action were that action repeated indefinitely. So if you're holding KK preflop and you were to raise it in a particular place, how much more money will you make, on average, than if you were to call. How much more for calling than for mucking? There are ways of generating +EV based on pot odds and such, but they can be tweaked quite a bit.

For instance, lets say that you're holding a flush draw and you have marginal pot odds to warrant a call. Perhaps your EV is equal to +X. Let's say your opponent now mucks his hand face up and you see a card of your suit, your EV now goes down by Y. But lets say that you were drawing to the second nuts...your EV now also gets adjusted up a little if the card he mucked was needed for the nut flush as you don't have to worry about making your draw and being beaten by a higher flush. To further that, let's say that you have a strong reason to believe that another opponent is on a made straight. He's liable to pay you off when you make your flush, so you get some "implied odds" there that add to the pot odds. Those implied odds also effect the amount you expect to make.

Essentially, the way to calculate your +EV is this:

A=how much you make if you win (best guess based on facts)
B=how much you lose if you lose (best guess based on facts)
C=chance of winning (you can be relatively sure of this for a lot of hands)
EV = (A * C) - (B * (1 - C))

If your EV is positive you expect to make money and if negative you expect to lose money. This all assumes that money in the pot is lost and gone forever. Thus, if you are bet at one the river and think your chances of winning the hand are only 1/20, but there are 19 big bets already in the pot (excluding this bet made to you) then you have a 1/20 chance of winning 21 BB by spending 1 BB meaning you have a 1/20 chance of winning 20 BB.
Folding will mean you have a 0/1 chance of winning 0 BB.

So you have a +EV for calling of (1/20)*20 - (19/20)*1 = 1 - 19/20 = 1/20...so it would be marginally worthwhile for you to call.

I hope that helps a little.
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Re: Expected Value, Simon Reach, 13. Mar 2003 13:11
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Many Thanks. It has certainly given me food for thought...
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