Mean Value Theorem Question

[shadow29]

This post is pretty much worhtless, but I was wondering about something today.

For those who haven't taken Calc recently, the Mean Value Theorem states (from Google):

for two points (a, f(a) ) and ( b, f(b) ), on a continuous curve, there is a point c in between where the slope f '(c) is the same as the slope, m, of the line joining the two points.

Which basically means if you average a rate, you have to be going that rate at some point.

Applying this concept to poker, we all know that we go through downswings and upswings. From the Mean Value Theorem we can deduce that if our true winrate is 3 BB/100, then for a certain period of time we have to be winning at truly 3 BB/100. That's about as far as my math skills go. So to all those math majors out there, how long does one truly win at that rate? Is it just an instant? Or does it depend?

[milesdyson]

all the mean value theorem says with respect to poker winrates is this:

look at a poker winrate graph that we've all seen before and take the first point, which is (0 hands, 0 big bets), and the last point, let's say (20000 hands, 150 big bets).

find the slope between these two points. in this case, it is (150 - 0 big bets)/(20000 - 0 hands) = 0.0075 big bets per hand.

this means that somewhere along the way, the instantaneous slope of our graph was 0.0075.

[Buckmulligan]

It's more of a statistics problem than a calc problem. Think about it like this. Plot a histogram with winrate covering the x axis. what averaging 3 BB/100 means, is that if we took an infinite amount of, say, 10000 hand sessions, the bar at x=3 BB/100 would be the highest; the bars leading up to the 3bb would form what looks like a triangle.

We are more likely to average 3bb/100 than anything else, that's how this can be interpreted.

[milesdyson]

buck: they would not form a triangle. they would form a bell curve.

[benkath1]

and the bell curve would go from 0bb/100 to 6bb/100 and back to 0bb/100?

[shadow29]

[ QUOTE ]

this means that somewhere along the way, the instantaneous slope of our graph was 0.0075.

[/ QUOTE ]

k, that's what i thought it meant. wanted some confirmation, especailly since i could write sonnets all day about calc, but not solve d(x^2). [img]/images/graemlins/wink.gif[/img]

[Eeegah]

Holy cow I have an analysis test tomorrow whose main star will be the proof of the MVT and this thread is creeping me out.

[shadow29]

[ QUOTE ]
It's more of a statistics problem than a calc problem. Think about it like this. Plot a histogram with winrate covering the x axis. what averaging 3 BB/100 means, is that if we took an infinite amount of, say, 10000 hand sessions, the bar at x=3 BB/100 would be the highest; the bars leading up to the 3bb would form what looks like a triangle.

We are more likely to average 3bb/100 than anything else, that's how this can be interpreted.

[/ QUOTE ]

ya, i think that i was talking about something other than x bar. maybe not...math is gay.

[milesdyson]

[ QUOTE ]
and the bell curve would go from 0bb/100 to 6bb/100 and back to 0bb/100?

[/ QUOTE ]
no, call x your true winrate and std your standard deviation

it would go from x - ~4std to x + ~4std

the y-axis is the # of occurrences

all it takes is 10 years of non-use and calculus is long forgotten.