What exactly do you find arbitrary about this? When gambling or investing, more wealth is better than less wealth.
'Almost surely' is a technical term which means 'with probability 1'.
'Almost surely' is a technical term which means 'with probability 1'.
Either you're claiming that the theorem I attempted to describe is false, or you're misunderstanding the theorem I am trying to describe.
I never wrote anything about 'high probability' either so I don't know why you introduced that notion.