I did. Let's see if someone else can make a proof that you like better. (I wouldn't hold my breath if I were you).
See above post. Even when your coin toss sample size is large enough to hit 50/50, there's nothing guaranteeing you aren't winning on the small moves and losing on the big moves. I don't need to post a chart of the DOW for you, you know damn well it's biased long. How do you figure a 50/50 call method is break even in the long term when the underlying intrument is constantly trending up?
So first you want proof and now a guarantee?. Is that it?. Do you want a 19 year old big titted blonde that gives good head as well?.
And if you started trading this morning it looks short biased. What's your point? If your coin toss method only works... when it works... then what's the point?
Depends if you're able to arrange that. I said I wanted proof, show me proof. Wiki commutitive property didn't say anything.
Then it's NOT break-even? Let me ask you straight up, and, yes, "proof" means "guarantee" - is it absolutely break-even? Can you prove that it's break-even? Beating 95% of traders means nothing because you haven't PROVED that 95% are losers (since you're all about calling for proof). Again, you're implying break-even but you have not PROVED break-even. The coin toss is break-even over time, it comes out 50/50, we all get that. I want to know how you're assuming that your win and loss amounts will also remain equal in a long biased market, or even just with a variable win/loss size system (not a fixed bet amount).
EV of first toss: 0.5 X - 0.5 X -costs EV of second toss: 0.5 Y - 0.5 Y-costs ... EV of Nth toss: 0.5 N - 0.5 N-costs Sum of EV: 0 - sum of costs X, Y, ..., N are what you call the size of wins and losses. That's the best I can do. Good night. p.s.: EV is "Expected value".