I mis-typed: you have two choices: take 1 million or attempt to take 50 million.
The question really is precisely how much better 50 million is than 1 million: this is packed into what you’re talking about when you talk about “reward” and “risk”. How this is formulated precisely as a decision making problem is exactly how you associate reward / risk with the various outcomes.
What you call “risk” or “reward” are things we need to associate with each possible outcome (risk is the expectation of the loss taken over outcomes conditioned on your decisions). Then, we compute the risk or expected reward / loss whatever, and pick the decision that optimizes on that (minimizes risk).
It doesn’t have to be 50x, but there are many loss functions that make taking the 1 million better: for instance,
reward(dollars) = -loss(dollars) = ln(dollars)
So, as I said: the problem is ill-posed because we don’t know the loss or reward associated with each outcome.
That’s because it is a thought experiment and the answer is based on the individual circumstances of each person who attempts to answer. As many people have explained above, it depends on age and current financial status, assuming that one wishes to optimize quality of life for the remainder of one’s lifetime with the greatest degree of surety. The math would work out the same if it was 1 dollar vs. a 50% chance of $50, but this is a thought experiment.
Indeed. We are given two numbers, but it is up to us to place valuations on those numbers. The question would look very different if it were 1 billion dollars vs. 50 billion dollars, just as it would look different if it were 10 thousand dollars vs. 50 thousand dollars because those numbers mean different things to different people. This is an example of how pure math does not work 100% of the time for making decisions.
Significantly, the question says “You” instead of “One.” It is a question of what you should do, not what one should do.
When I was in my early 20s I lived hand to mouth and had to play the “which bill do I pay this month?” game. I would have taken the guaranteed million.
I’d take the million dollars and like our U.S. ex-President Donald J Trump turn it into billions. Unlike our ex-President my casino will be like a cash cow, not go bankrupt.
My landlords have just decided to sell the house I rent, and it’s just been valued at £700k. Plus taxes, and converted to USD, that’s about $1M.
Of course, my landlords didn’t have to push a button to get that money, they had to spend £120k twenty years ago. Or more likely spend about £25k, and let me and my flatmates pay off the rest of the mortgage for them (probably several times over by now).
So yeah, $1M for me please, then I could just about afford to buy the house I live in, because fuck knows there’s no other way I can afford one.
Personally, I’d take the guaranteed million, no regrets. I’m in my 40s and financially stable, but would’ve answered the same when I was in my 20s and dumpster diving. $1M earning even a modest interest rate would be enough to turn any “regular” US salary into a “decent” salary, or allow me to work part time, or opt for more leg room on long flights if I have to fly.
Or, you know, pay health insurance premiums just until I qualify for Medicare
Another angle is the chance that you will regret your decision. If you choose the instant million, you’ll never know whether you could have had $50,000,0000. but if you chose the chance at $50 mil, there is a 50% chance that you will regret your decision.
Of course I would try to find somebody to buy a 50% chane at $50 mil from me for $20 mil.
Another angle is the chance that you will regret your decision.
I can see that. I know people who, being given a million, would go “but what if I had…”, but that’s the something you need to get over. You have what is for most people a life changing amount of money.
Even if you have 50 million over 1 million, if you don’t have a plan, it will probably go wrong.
I’d take the 1 million without hesitation even if it was taxed. I could pay off my student loans, fund my transition and still have a sizable amount left for investments.
I guarantee there are posters here with a decent salary that started saving in 401K plans in their very first jobs. Posters where their effective salary has always been 12% less because of that contribution, at every job they ever held, where the remaining take home was just how they viewed the salary. Posters who are old enough now with enough years and compounding interest that they have over a million dollars in those accounts. There’s probably a bunch over two million too.
Having a “decent salary” to do that is a huge leg up on achieving this.
but the whole thing has become an exercise in interpretation.
