Skip to content

Top Best Ask Show New Jobs

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

6 pointsremflight4y ago21 comments

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

18 comments · 11 top-level

hamdouni4y ago· 2 in thread

Exactly 1 cent. I maximize the gain and minimize the risk.

stocknoob4y ago

So if it were offered for 2 cents you wouldn’t participate?

Now recursively apply this logic and find your actual max.

I wouldn't. I really value the fact that I'm not playing by other's rules...

mateo4114y ago· 2 in thread

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.

toast04y 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.

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.

jepler4y ago· 1 in thread

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.

jstx14y ago

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.

neximo644y ago· 1 in thread

Anything less than $500m, especially if you could redo this 50/50 chance multiple times.

al_borland4y ago

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.

mikewarot4y ago· 1 in thread

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.

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

BinRoo4y ago

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.

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.

mac3n4y ago

https://en.wikipedia.org/wiki/St._Petersburg_paradox

muzani4y ago

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?

It depends; how much money do I have in the bank?

ameixaseca4y ago

Less than $1B

j / k navigate · click thread line to collapse