Mathematical explanation of having advantage with big stack

[eisanm]

This is not true. Try reading anything on the topic written by Ed Miller on this forum, and I hope you will understand why. I'm not the best person to explain it to you.

But in short, it does not work that way. To stay short-stacked you would have to leave the table and re-buy as a short stack after doubling up. And this is one of the reasons that your argument does not hold up. When you lose, you don't lose everything you have won so far.