A Less Obvious Martingale Fallacy

[GFunk911]

First off, let me state for the record that I hate this thread and everyone in it, no exceptions, and that includes myself.

The problem is looking at a situation with certain elements infinite and other elements finite. It is nonsensical.

Let's look at the avg casino win on any iteration (i.e. one roulette spin) for an infinite room of infinitely bankrolled martindalers, on a per person basis, for spin N (N is zero based)

sum{x:0->N}[ (W%*(1-W%)^x) * (2^x) ] * (1-2W%)
(W%*(1-W%)^x) = % of players who have lost x spins in a row
(2^x) = amount wagered by player who has lost x spins in a row
(1-2W%) = house edge

An infinite room of martindalers will lose money on every spin.

This won't convince anyone cause the premise is nonsensical and the actors are zealots, but there it is. I was gonna type more but I can't devote any more time to this swamp or horror.