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If I was already a billionaire, I would pay up to 500 million dollars. At 500 million dollars it's a EV neutral move, but there is also entertainment value, be

If I was already a billionaire, I would pay up to 500 million dollars. At 500 million dollars it's a EV neutral move, but there is also entertainment value, because I get to see if I win or lose. If it's less than 500 million dollars, it's a EV positive move, so I'll happily take it. Since I'm not a billionaire, I would put up as much as I could comfortably lose, and still meet all of my existing financial obligations. EDIT -- Instead of paying 500 million, I would pay up to 1 billion dollars, because paying 1 billion for a 50/50 chance to win 1 billion is an EV neutral move.

toast0 4y ago
> EDIT -- Instead of paying 500 million, I would pay up to 1 billion dollars, because paying 1 billion for a 50/50 chance to win 1 billion is an EV neutral move. It's not. The EV of a 50/50 chance for $1B is $500M. The EV of paying $1B is -$1B. So paying $1B to have a 50/50 chance of $1B has an EV of -$500M. Paying $500M for a chance to win $1B is EV neutral. But marginal utility of money gets pretty weird by then. For someone with $500M, an extra $500M to get to $1B doesn't really open that many more doors, IMHO, but losing $500M would be a big deal.
- mateo411 4y ago
  Let me explain this another way, since you seem to be thinking about this the way I originally thought about it. If you wager 500 million to win 1 billion, then that be pays 2 to 1. Any 2 to 1 wager makes sense when the odds of winning is greater than 1/3. If the odds are 50/50 or 1/2, then betting the amount to win the same amount is an EV neutral move. You are correct that the marginal utility of money is pretty weird when you are billionaire.
  - toast0 4y ago
    You're saying you'll give me $1 with a 50/50 chance I give you the dollar back or keep it? I'm happy to meet and explore this in person ;) As described in the OP, you're not wagering the bid, you're paying the bid. I was not expecting a return of the bid if you win. The EV changes if you get your wager back.
    - mateo411 4y ago
      No, I'm saying I bet $1 and I have possibility to win $1, so I end up with $2. I see, if you frame it in terms of a bid that you don't get back, then your reasoning is correct.

toast0 4y ago

> EDIT -- Instead of paying 500 million, I would pay up to 1 billion dollars, because paying 1 billion for a 50/50 chance to win 1 billion is an EV neutral move. It's not. The EV of a 50/50 chance for $1B is $500M. The EV of paying $1B is -$1B. So paying $1B to have a 50/50 chance of $1B has an EV of -$500M. Paying $500M for a chance to win $1B is EV neutral. But marginal utility of money gets pretty weird by then. For someone with $500M, an extra $500M to get to $1B doesn't really open that many more doors, IMHO, but losing $500M would be a big deal.

mateo411 4y ago
Let me explain this another way, since you seem to be thinking about this the way I originally thought about it. If you wager 500 million to win 1 billion, then that be pays 2 to 1. Any 2 to 1 wager makes sense when the odds of winning is greater than 1/3. If the odds are 50/50 or 1/2, then betting the amount to win the same amount is an EV neutral move. You are correct that the marginal utility of money is pretty weird when you are billionaire.
- toast0 4y ago
  You're saying you'll give me $1 with a 50/50 chance I give you the dollar back or keep it? I'm happy to meet and explore this in person ;) As described in the OP, you're not wagering the bid, you're paying the bid. I was not expecting a return of the bid if you win. The EV changes if you get your wager back.
  - mateo411 4y ago
    No, I'm saying I bet $1 and I have possibility to win $1, so I end up with $2. I see, if you frame it in terms of a bid that you don't get back, then your reasoning is correct.