Mean Value Theorem Question

[ QUOTE ]
It's more of a statistics problem than a calc problem.

[/ QUOTE ]

Why would the mean value theorem not be applicable just because the data points come from the "real world?"

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

If I win 6BB/100, lose 3BB/100, win 6BB, lose 3BB and do this for ever.
My winrate is 3BB/100.

At what point along my graph would I ever show +3BB/100?

[Eeegah]

Without bothering to really go at it, I think it won't. It'll converge to 3.0 but not hit it.

Win rate isn't a continuous function so technically the MVT doesn't apply.

[milesdyson]

because poker winrates are stepwise functions, yes, the theorem does not technically apply. the theorem applies to continuous functions only. however if we were to apply a best-fit curve to the winrate, you would at some point show a +3 bb/100 winrate.

[Eeegah]

Hell it'd show a +3 winrate between every hand [img]/images/graemlins/smile.gif[/img]

[milesdyson]

okay let's nitpick. it would show +3 bb/100 between every other hand.

[Eeegah]

So anyway, let L be the line between (a,f(a)) and (b,f(b)). Note that L(a)=a and L(b)=b. But this means L(a)-f(a)=L(b)-f(b)=0, and so we can apply Rolle's Theorem: there exists c in [a,b] such that [L(c)-f(c)]'=0. With some manipulation then we have

L'(c)-f'(c)=0
L'(c)=f'(c) *

But L'(c)=[f(b)-f(a)]/(b-a), and so we're done. Note that * is what you actually posted, which is directly equivalent.

I only needed help for oneline of the proof this time I'm so proud ^_________^