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Simply put, expected value involves the probable outcome of a given situation over time.  It is the average outcome, in terms of profit or loss, of a particular poker situation played out over many times.  We need to always assess our chances in terms of what the outcome will be over time, and stay away from particular examples of it.  This may seem easy and intuitive, but rest assured, for many players it is not.

To further illustrate this, let me give you an example from another field.  Back in my financial trading days, I used to trade my own account and those of a few clients, involving very short term trading of shares on the New York Stock Exchange.  Now, the secret to being successful at this is to discover patterns in movements of price and volume, and capitalize on this.  This is partly skill and partly hard work involving testing out particular patterns with very sophisticated software.

Now, I had this one client, a professor at a major U.S. university, who fancied himself as a trader.  He had been doing it himself for a few years in his spare time and always lost money at it.  I took on his account to do him a favor, and it didn't involve much work, and I set up a deal which was extremely favorable to me. 

However, what would happen is that he would try to interfere with it.  The bugger had some pretty decent software to monitor the markets, and would suggest these plays to me.  Almost all of them didn't make sense, and I would try my best to educate him.  More often than not, his plays didn't hit and would have resulted in his account losing money.  However, when one of them did, he'd be all over me about how I should have played it.  He'd even become a little irate at times, and didn't seem to grasp that playing this sort of pattern, while it may have made money this time, won't most of the time, and would result in a negative expectancy.

Well, as the story went, finally we had it out one morning, when he insisted I do a trade for him, which I didn't, and the thing went up real nice over the next few minutes.   It would have meant a few thousand bucks for each of us, but again, it would have been the wrong move.  Well the crap hit the fan so to speak, and we ended our business relationship.  He ended up leaving what was a very profitable partnership for him, due to his stupididy.

Now, you might ask, what does this all have to do with poker?  Well the same things happen at the poker table.  The tendency for a lot of players is to look at things the same way the professor did, putting too much weight on the short term, and not looking at the big picture.  And it's only the big picture that really matters.

Included in this group is anyone who is bothered by a "bad beat"  And I mean bothered at all.  As better than average poker players, bad beats are our best friend.  By definition, they are profitable.  Any time we have the advantage and lose, this means that this pattern, repeated, will give us a profit, as sure as the sun rises each day.  Yet many of us are put off, upset, even angered when these things happen.  This is, of course, because we are looking at things the way the professor does, only seeing the tree and not seeing the forest.

So, what we need to focus on instead is what the big picture is when we're playing.  If we have the advantage, and we bet, it's always a good thing.   Always.  This is regardless of whether we win or lose.

Not long ago, I was in a heads up tournament, and I was holding aces full.  The betting had escalated to the river, where my opponent made I large bet.  What did I do?  I raised him all in of course.  He called, and he showed me quad 4's, hitting his quads on the river.  I got hit with a one outer to beat my aces full. 

Was I upset?  Hell no.  How many times are you up against quads really?  In almost all instances, my aces full are going to hold up, especially heads up, where a just a pair of aces is a very strong hand.  If the player is drawing to a single card in the deck, this means I'm winning 44 out of 45 times.  I like those odds.

There's going to be cases where I'm going to be beat with them though, but in the big picture, this is a very, very profitable hand.  And any time I get called down with a hand like this, I'm thankful.  And this is the additude you need, and I mean need, if you're going to keep your head and do the right thing, or at least try your best to do the right thing.

Often though, people feel cheated by the poker gods when profitable situations overall yield an unprofitable instance.  This type of thinking is not only wrong, it's harmful to your game.  They are especially ticked off when players beat them with holdings they feel should have not been played.  They feel their opponent is a stupid player, and at times even will tell him how stupid he was.  It is the ticked off player who is the stupid one though.  What does he want, his opponents to play WELL against him?  And when they aren't, what does he want, to EDUCATE them to play better?

Another thing we need to be careful about is taking specific instances and applying the "shoulda" principle.  Let's say a play makes money 4 times out of 10, and loses 6.  And the money lost overall is greater than the money gained overall.  Now, 4 times out of 10, we have the opportunity to look back on the hand, after everything plays out, and say we "shoulda" played it.  Would this be wise though?  Of course not.  Yet it happens.  We want to avoid letting this happen to us though.

When we take a wider look at all this stuff though, here's what emerges.  We always want to play our good hands strongly.  We are doing so on the basis of expected value, pursuing those opportunities which yield a profit in the long run, and avoiding those which produce a loss in the long run.  And how these plays do over time needs to be our only concern.  In other words, what the expected value of the play is.  By looking at specific instances rather than the big picture, all we are doing is shooting ourselves in the foot.
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Expected Value
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