What choices you make depends on who you are.
Who you are is defined by the past.
You have no control over the past therefor no control over who you are and thus no control over any choices you make.
Where does "free will" come in?
This shows that with faulty premises, it's easy to reach faulty conclusions, but probably not much else besides that.
With a lottery ticket that costs 100$ with a 1 in a billion chance to win 101$ you would still be maximizing the chance to win as much money as possible by gambling.
One difference between this and what's being referred to as the "Monty Hall" problem is that in this Monty Hall problem, you're gambling with money that you didn't have to begin with, so taking a risk is more justified.
This is somewhat related, I think, to the gaming phenomenon of "playing for position", in which a player who is in 2nd place can make a move that will either result in him winning the game, or coming in last place. Faced with this choice, many players will not make the move, since they'd rather come in 2nd than risk coming in last. This is flawed playing; the point of playing a game is to try to win, and 2nd and last place are equally "negative" results, but for some reason 2nd place feels better. I can understand the mindset a bit, I guess, but it's definitely yet another problem designers have to contend with, and I'm not sure how you can take irrational play into consideration when trying to design a working game.
-Jeff
Well, go ahead and try to defend even one of your premises; perhaps start with this one: "who you are is defined by the past". If you'd like, you can do so in a PM to me so as not to take the discussion too far off topic.
I'm familiar with arguments that assert that there is not such a thing as free will, but they usually go the route of arguing for determinism (ie, that the choices we make are actually forced by the naturalistic process); your chain of logic was considerably less robust, being charitable.
-Jeff