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Ask HN: How much would you pay for a 50/50 chance to win $1B?
This post (https://old.reddit.com/r/wallstreetbets/comments/vkncj5/would_you_rather_get_a_guaranteed_million_dollars/) showed up on wallstreetbets and the more interesting question to me that came up was: how much is this opportunity worth? There must be a way to calculate how much someone would pay for a 50/50 chance to win $1 billion, so I’m curious how that would be calculated and what that dollar amount is?
- neximo64 4y agoAnything less than $500m, especially if you could redo this 50/50 chance multiple times.
- al_borland 4y agoEver flip a coin and get heads 2 or more times in a row? $500m is way too high of a cut off. Even if you win, you could end up $500m (or more) in the hole.
- dotcoma 4y agoIt depends; how much money do I have in the bank?
- allears 4y agoIt's important to realize that if you pay for a chance to win, if you lose you don't get your money back. That makes the risk calculation dependent on how much you can afford to lose.
- mac3n 4y agohttps://en.wikipedia.org/wiki/St._Petersburg_paradox https://en.wikipedia.org/wiki/St._Petersburg_paradox
- jepler 4y agoThe Kelly criterion (https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion) is one possible way to decide on the amount to bet, in order to "maximiz[e] the expected value of the logarithm of wealth". For a fixed probability of winning a fixed proportion of the bet, the amount turns out to depend on the size of your bankroll. However, as your example fixes the payoff but allows a variable buy-in, I don't see how to directly apply the formula from that article. But, long story short, it is almost sure to depend on the size of your current bankroll, if you accept a Kelly-like criterion.
- jstx1 4y agoDoes the Kelly criterion apply in this case? The Kelly criterion tells you what % of your bankroll to bet but the problem here is deciding how much of your net worth is in your bankroll in the first place.
- hamdouni 4y agoExactly 1 cent. I maximize the gain and minimize the risk.
- BinRoo 4y agoI'd say it depends on your "demand" to change lifestyle, from 0% to 100%, then the max bet should be: demand * min($500M, fun_money). Of course, the hard part is figuring out one's personal demand for change.
- ameixaseca 4y agoLess than $1B
- muzani 4y agoThere's a trick here. I don't really want $1B. $2M is probably the max I'd need in my life. So I'd pay about max $0.99M. If I were not as lazy (and with that much money I should be), I'd calculate the point where it's easier to earn more money. Having just 6 years runway would let me do a lot of experimental business stuff, but would those still have a 50% chance of earning a billion?
- mateo411 4y agoIf 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 agoLet 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 agoYou'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.
- mikewarot 4y agoI'd give about 1000 hours of effort to it. I'm old, so I don't have a lot of time left, but that seems reasonable to me.
- LecroJS 4y agoVery interesting to see someone with significant life experience quantifying this in terms of time instead of dollar value. I found this comment helpful as I approach my mid 20s and think about the costs of some of the bigger investments l’d like to make in life. Thanks