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Ask HN: How much would you pay for a 50/50 chance to win $1B?

6 points by remflight ↗ HN
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?

21 comments

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neximo64
Anything less than $500m, especially if you could redo this 50/50 chance multiple times.
al_borland
Ever 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
It depends; how much money do I have in the bank?
allears
It'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.
jepler
The 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
Does 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
Exactly 1 cent. I maximize the gain and minimize the risk.
stocknoob
So if it were offered for 2 cents you wouldn’t participate?

Now recursively apply this logic and find your actual max.

hamdouni
I wouldn't. I really value the fact that I'm not playing by other's rules...
stocknoob
You sure do, you value it more than $500M :-)
BinRoo
I'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.
muzani
There'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
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
> 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
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
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
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.

mikewarot
I'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
Very 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