-snip-
Regarding your second Q... No, I can not prove that I'm not playing in the game at any point of time. But, if you look at the operation of the game, you'll discover that it does not matter.
I have to disagree with you here.
Because, if I play I'll also take the risk of being the last player, just like everyone else.
Yet, if you are the last you are loosing only to yourself where regular players would lose to you. Thats an advantage for you.
If I am the #1 & #2 I'm just raising the value of initial deposit, which does not impact the way other users play the game, because they already know at any point of time anyone can be part of the game.
You raise the amount they have to risk in order to play, thats exactly the point I was so confused about. "Only one person" can lose, yes but the amount they lose is higher than everyone else previously risked.
Some rounds may have multiple investors, while some rounds may not have any... that is the luck factor everyone is playing against. Even if I assume that I'll play, then I have to play against the same luck factor.
Which is not known in advance, but thats probably just me. Id like to know my odds.