*Originally posted by tommygecko*

So let's say you have never played a poker hand before. For the next infinite hands you play EV= actual profit because variance evens out in the long run.

How about this scenario. You played 10000 hands and ran 10bi under ev. By the concept of varianve in the long run, the next infinite hands you play EV= actual profit. But that effectively means you will still be 10bi under EV. Shouldn't you be running at EV if variance evens out?

Perhaps you are correct in absolute terms, but after playing several hundred thousand hands, that 10 bi is totally insignificant.

The term "expected value" is used many different ways.

I prefer to state the case this way:

"Over a large sample size, everyone will get the same number of each of the 1326 possible starting hands. For each starting hand, each of your opponents can have only 1 of the remaining 1325, 1324 ... hands".

Thus on a 6-handed table, that means that there are 1325x1325x1324x1323x1322x1321.

So at any 6-handed table there are 5 x 10^18 possible combinations of hole cards.

Now we come to the flop.

Let's not. I think that you get the picture.

If you play 12 tables of zoom at 150 hands per hour 10 hours per day 7 days per week all year, you only play 6.5 million hands per year.

At that rate, it would take 100 billion years to play each and every combination of HOLE CARDS ONLY.

There will be long strings of crappy cards, and long strings of good ones, and short strings of each as well.

It is not that it "evens out", but it "is the same for everyone".

So if it is the same for everyone, then the determining factor is your skill level. You must build that up, because it is the only thing at the table you yourself control.

Another example, in roulette (ignore the green 0) there's equal chance of hitting black and red. So in the long run EVBlack=50% and EVRed=50%. If the concept of variance is true, wouldn't it be profitable to bet red if 75% of the last 100 results are black? But no. EVBlack for next 100 results=50, not 25.

Hence it seems like the this statement about variance is the likely cause of the gamblers fallacy. Because you expect to run better after you ran bad. There should be a better way to explain variance.

The idea that "a run of good luck inevitably follows a run of bad luck" is indeed the gambler's fallacy. Especially in poker.

It may be true, but how good and how long matter too.

I am convinced that some "pros" are actually not that good -- just on incredibly long heaters.

The true pros can make money even from garbage hands, by reading the board and knowing their opponents.

Read the quote at the bottom of my sig.

Great post!

Oh -- and if I totally screwed up the math, please somebody post the real numbers.

all the best,

--VS