Assuming this is tax free, $1M would pay off all my debt, my kids’ college loans, and allow me to sock away a decent amount for grandchildren’s likely school funds and toss the rest into investments and then continue working knowing that I could comfortably retire in 5 years or so.
The gamble’s nice with a great potential, but knowing I would be completely debt-free and just working for “fun money” would be completely worth it.
and assumes neither you nor anyone in your family ever gets seriously sick, involved in some sort of traffic accident or natural disaster, or gets arrested, etc
with no meaningful safety net, random chance can easily thwart any well made plans
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“USB plug upside down?”
Oh! well, that explains a lot
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Easy. Take the mill, buy crypto, to the Moon! But seriously, if you make a habit off “all or nothing” gambles, all it takes.is one “nothing” and you’re gonna hit it 
You 100% chance of winning $1 million. In practice, you are making a bet: you give up a 50% chance of winning $1 million and that amount becomes 50x greater.
Note that there is a 50% chance for a 50x value. What is the relationship between both data?
$1 million = 100%
$50 million = 50%
It’s like every bet you make to win $1 million more, you lose a 1% chance.
$1 million = 100%
$2 million = 99%
$3 million = 98%
$50 million = x%
The problem is that if we count, like this above, from $1 million to $50 million, we will notice that we have a 51% chance of winning $50 million and not a 50% chance.
In summary: it seems to me that you will spend $1 million to increase your chance of winning $50 million by 1%.
Edited because I can’t read.
For me, as a math teacher, the odds are as such:
With that explanation, it’s obvious to me why I’d press the Red button, and it would be the mathematically prudent thing for me to do as well.
I’d also choose the $1million now, as that would enable me to retire today, rather than the current plan of retiring in 6 years.
There’s also the usual question of “How comfortable is comfortable?” The retirement industry tells me I can’t be comfortable unless I’m on some ridiculously high figure per year, when I know I can live on much less without compromising my standard of living
When the ‘expexted value’ is literally a number that the button could NEVER yield, you realize that the question is not one that can be adequately answered by math.
It means two people are talking about two different things.
@mdavis is talking about statistics - how this looks when a large-ish number of people play.
You’re talking about a single player’s experience.
Different things entirely.
I would take the million, invest half in bond-driven investments and then use the rest to live like a king in Southeast Asia, where 10k a year is plenty.
We should really assume the promise of $1 million is also at least 50% likely to be a lie or a scam
… so we might as well ask for the larger amount, if we’re going to stop and talk to these grifters at all
This is an ill-posed decision-making problem: there’s no objective function we’re asked the optimize on. Most commonly we’d be asked to optimize on (maximize) the expected reward (or minimize the risk), but we’re not even given a reward associated with each possible outcome (there are exactly three). If you assume the reward function is linear with dollars gained, then the correct answer is to take the 50 million. But the “right answer” (which I assume the OP meant by “mathematics”) depends on what we’re asked to optimize and the reward associated with each outcome. Are we to assume the reward is the dollars? Unclear.
That is what the $ symbol would appear to be indicating. Though it could be one of several different currencies that use that symbol.
Linear then. Then they mean 50 million is always 50x as good as having 1 million. Then the answer is take the 50 million.
But if 50 million isn’t 50x as good…
There is a 50/50 chance of 50 million or a guaranteed 1 million.
But it’s not like you’d be losing $1 Million of your current assets. So it’s not a question of “can you afford to lose $1 Million?” so much as “can you afford to remain in your current financial situation?”
Yes? What aren’t you following here? Is 50 million 50x as good (worth optimizing on) than 1 million.
The comments above about being able to rephrase the problem as already having 1 million and the choice being losing nothing or having a 50% chance of losing 1 million or 50% chance of gaining 49 million is exactly right: for many, losing 1 million is much more bad than the possibly gained 49 million is good.
What is the reward function?
Hahaha. Best answer.
I also always plug the usb in wrong almost every time.
You said this, but this is not an option. You cannot take the 50 million. You can only take a chance at 50 million. So, the question is not how much better 50 million is than 1 million. The question is whether the reward is sufficient for the risk. It doesn’t have to be 50x as good for the reward to be worth the risk. One could reckon that the utility of 50 million is only 5x the utility of 1 million and still believe that it is worth the risk.
