some thoughts on std dev and fluctuations

So as I'm about to fall asleep, some thoughts pop into my head...


95% of the total pop. is covered in 2 std. devs.

100% of the total pop. is covered in 3 std. devs.


assume std. dev. = 10BBs/hr.


So this means that on average, for every 100 hours of poker, one will experience about 2.5 hours where one loses between 20-30BBs/hr. + Win Rate. Now, that's pretty huge! In a 10/20 game, we're talking about dropping $380-$580 per hour.


Now take the case of a "wild" game where one's std. dev. is 15BBs/hr. One can lose between $580-$880 per hour.


"Luckily" for us, there's the other 2.5 hours! =)

sam

A poker player, let's call him Sam, is playing at a game where his EV for the next 100 hours is to win $1000. (Assume that all Sam's calculations are correct.)


Sam sits down to play and after 1 hour of struggle he's down $10. Damn. Never mind, shrugs Sam, that's just fluctuation for ya. Standard Dev, what! I'm gonna nail this sucker in the end, he says to himself. So he plays on, determined to put in another 99 hours.


Is Sam's EV still +$1000 for 100 hours?

Yes, if your win rate is $10/hr at 100% precision, this means that as your poker playing hours extend toward infinity, $10/hr. is your expectation. So, in theory, after "Sam" plays 100 hours, his expected win is $1000. However, this does not mean that he will have won $1000 by the conclusion of that 100th hour. His results will most likely be above or below that number by...maybe the math experts can tackle this one. =P


sam

When you say that we have calculated our EV with "100% precision", that means that our MATHEMATICAL (ie theoretical) calculations were done correctly, as they indeed were, in our assumptions.


But when REALITY intrudes, we have to revise our calculations!


Pick that coin up, again. You are going to flip it 100 times. The expected result (calculated "100% correctly"!) is that we will have approximately 50 heads and 50 tails.


But what if we flip it 10 times and they all come out Heads? Now what?? We decide to continue and flip it 90 more times. Are we expecting to see, for the total of 100 flips, still 50/50 heads & tails??


If your answer to that question is "Yes", that would imply that the coin would somehow have a "memory" of what happened during the first 10 flips and it would try its best, like a good coin, during the next 90 flips to "correct" the situation - in order for us to have our "100% correct" answer. Only this is not so. Coins don't have a memory.


Can you see the answer to the poker question now?

Then doesn't this mean that the person does not actually have a $10/hr. win rate? The "reality" is that we can not be 100% precise in determining win rate and standard deviation, because the data is always insufficient. As I said, this data must approach infinity in order for the "100% precision". The theory behind this really has nothing to do with "memory" of cards, but more to do with the fact that it is not possible to play an infinite number of hands.


sam

Perhaps I misunderstood your meaning when you said:

"A poker player, let's call him Sam, is playing at a game where his EV for the next 100 hours is to win $1000. (Assume that all


Sam's calculations are correct.)"


I think I took that to mean that the preciseness of his calculations was exact, including the data, rather than that he calculated the formula correctly, with his available data. So I assumed his "true" win rate to be $10/hr.


sam