EP - I applaud your conviction and ask you to check your attitude.
Your premise - that each hand is an independent trial is of course a valid statement. I assume that you imply that you need only focus on each hand and, if each hand is played optimally, over time you will be successful. Playing this mathematical (as you put it) strategy is optimal for the ring game player where his career can be viewed and measured as one long session and variance can be overcome. This is especially true because the value of each chip does not change in this game.
But let me introduce you to tournament play especially single table SnG events as this was the context of my post. There are some very key differences between tournament play and ring games.
OK, let's do the math.
1. A tournament is a finite event. A single table SnG will last maybe 80 to 150 hands. This is a very small statistical sample. It has been 30 years since I studied statistics but if I remember correctly - a basic caveat was that sample size had to be sufficiantly large enough to overcome variance for it to be valid.
2. The way you make money in a tournament is NOT directly related to how many chips you win but rather how long you survive. In a standard 10 person SnG - only the last three survivors make any money. On UB where you and I play that pay out is 50%/30%/20% of the prize pool. Because of this pay out structure the value of an individual chip will vary considerably depending on the situation. If at the start of a $10 SnG I am given 1000 chips - each chip is worth 1 cent. If at the end of the tournament I have won all of the chips, I would hold 10,000 but they would only be worth $50 to me - or each chip would be worth only 0.5 cent. An even more interesting observation is the unlikely event that I am holding only 1 chip when the fourth place finisher is eliminated. That would mean that I am paid third place money or $20. And how much is that chip worth? By golly its worth $20. That same chip will only be worth a hapenny to the eventual winner but for me it is worth $20.
You say you don't believe in luck but I know you believe in variance because I have seen you use that term in assessing peoples stats - telling them that their sample size was too small to be reliable. Can you see that in the very short term sample of an SnG that chance, luck, variance can be a factor? Please do not discard the observations of old pros like Brunson who have logged more hours playing poker than you have breathing. They may be on to something.
Tournament poker is a different game from ring games. I would like to suggest that your premise that each individual hand is an independent trial, though valid, is insufficient as a sole basis for developing a tournament strategy.
Seriously, I am amazed to hear you view tournament poker like this. By playing as you do, you will be a marginal winner at best. To disregard the math involved because of "luck" will surely cut into your profits.