hm.. maybe i didn't make myself clear.
lets say we both start with $520k and play $1000/wk for 10yrs then stop forever.
($520k/10 yrs = $52k/yr = $1000/wk)
at the end of those 10yrs, we both should have about the same amount of $ in front of us?
the betting system doesn't matter. at the end, we both should have about the same amount of $ in our pocket?
I'm pressing while he's flat betting.
on shorter rolls, he's ahead. on longer rolls, I'm ahead.
at the end of 10yrs, we both should have about $520k x .9963 = $518,076?
(1 - .37% = .9963)
I see what you're asking now, but you're still not giving enough information. When you say you and him play $1000 per week, that means $1000 in ACTION per week, NOT a $1000 bankroll per week. I don't think that's what you meant though. However, if you both bet $1000 action per week, then yes, you would have the same amount of money in 10 years because you both bet the same amount of money (all be it him flat betting or you pressing).
Now, here's what I think you meant to say... You both have a $1k bankroll for the week and both play "your own game" where he flat bets and you play come and press. Here's your mistake that we still touched on earlier. You're betting more money. Even if you both have a $1k "bankroll" for the week, at the end of the week the casino see's your action as let's say $10,000 in bets... but they'll only see his action in let's say $3,000 in bets. Thus you're theoretical loss will be different (monetary wise, not percentage wise). You will both lose .37% of what you BET, not your bankroll. We also don't know what happens if you bust mid-week. Are you forced to wait till the next week or do you keep playing out of your bankroll?
This idea of a $1k bankroll per week is meaningless because it has nothing to do with how much action/betting you're actually doing. As stated before you will both lose .37% of what you BET over the course of "10 years." Just because you have the same starting bankroll doesn't mean you'll start/end with the same amount of money. An easy example is you and I both have $1,000. I bet $10 on red, you bet all $1,000 on black. BOTH red and black carry a house edge of 3.5%. The math says that $10 can expect to lose $3.50, on average... but your $1,000 bet will lose $350, on average. So you both stand to lose at the same HE of -3.5%, yet it's obvious to see you're going to lose more money than I am in the long run because you're exposing more money to the HE than I am. Regardless of both of us starting with $1k, you bet a lot more, so you stand to lose a lot more in the long run.