If you choose the first option, $1 million will be immediately added to your bank account, however if you choose the second option, starting from today everyday your chances of winning $1 billion increase by 0.005%. If you accept your chances will start at 0% and keep increasing.
One million is enough to live off the interests for the rest of my life if I were to invest it onto the stock market and I get to keep the million. Easy choice. Besides, I have no use for a billion.
How often are you likely to win the billion? Or is it cumulated probability of winning? Would you ever be able to win a second billion after the first one?
I’ll assume cumulative probability and never a second billion.
0.005% would take 20,000 days to certainly win, that’s less than 55 years. It would take less than a year to reach 1% probability, every year it increases by 1.825%.
Those are good long term odds, but not amazing. While I could get today a million.
With a million I can live comfortably, if I’m very careful maybe even leave my job. With a billion I can reshape politics in my country. Have a significant impact on society. Keep some 10M to myself and play minigod with the rest…
Considering I’m okay financially and quite like my job, I’ll take the chances and wait for the billion to drop, hoping to not die sooner.
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There’s a draw once a year. So yes cumulative.
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Can only win the billion once.
Starting from today, everyday your chances of winning $1 billion increase by 0.005%.
That wording 100% says to me that you get a try every day to win the billion. Looking at it like you would in a legal case, it stands as an every day chance since a year timeframe was never mentioned in the original prompt.
Sure, the million would be nice, but In today’s economy “cheap” houses that used to be 100-200k near me are going for nearly half a mil.
The billion is the clear answer to me. Short of some extremely bad luck, you’re getting that billion in a year or few. You gain 1.825% per year which doesn’t seem like much, but you’re getting that ~2% chance every single day.
A few years of living like I already am for a statistically guaranteed (but unpredictable) billion dollars is a win to me.
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I’ll take the million. Could die tomorrow, ya know? And it would be great even in the most conservative bond or index fund.
A million dollars is more than enough to do everything I want to do.
Well statistically you are likely to become a billionaire within less than a decade with the second option so yeah, that one.
How did you do this calculation?
I actually think within 2 years you’re well over 50% likely.
Within the first year you’re over 1.5% probability (0.005 * 300 = 1.5) per day.
That means in the second year youd have 365 days with a probability over 1%. According to ChatGPT, cause I didn’t feel like doing the math myself, the cumulative odds are over 50% by day 166 (which sounds about right to me), and by day 430 you’re basically guaranteed to have won.
The math for any given day is p(win) = 1-prod(1-0.00005n) from n=1->n
Bro had to use chat gpt lul
The OP specified that the probability is the cumulative probability. Otherwise I’d agree with you
I’m pretty sure what I’ve written out is regarding the cumulative probability, as in the odds over all drawings.
If the drawings are only ever year though, then that really changes things as my calcualtions were about daily drawings. If only drawing every year, then by year five you’re already at 25% chance of winning, not great and certainly could mean the million is better for those who are older.
I think you are mixing up one-time probabilities and cumulative probability.
The probability of 0.005% increasing every day is the cumulative probability. So by year 5 the odds of having won the billion are 5x365x0.005%=9.125%, no additional formula. To get to 25% cumulative probability you’d have to wait some 15 years.
I think we’re both using the wrong word, as I can’t find an actual definition for “cumulative probability”. However my formula is what you’d use to calculate the probability of having won at least once over all the drawings.
While you are right that by year five the odds of winning are 9.125%, that is the odds of winning just on the fifth draw. However, you had a chance of winning each year prior, meaning that the odds of winning by year five are higher than 9.125%.
Its like with die, the odds of rolling a 3 is always 1/6, but the odds of rolling a 3 if you roll twice is ~30%.
I would use this definition, that is in the OP, the probability given is the one of having won the draw by that time: the first year when the draw happen the probability is 0, the second year the probability of having won is 9.125%, while the probability at the third year is 18.25%. This is the sum of the probability of having won either of the two draws (you can’t win more than once).
If you want to interpret the probability as a one time probability, then I agree with you.
More of a general assumption tbh. Lets assume that each day having a chance of say 10% to becoming a billionaire is plenty likely enough. 10/0.005=2000. 2000/365= ~5.5yrs. So its fair to assume you will need much less than a decade before it’s incredibly likely.
Yeah, we took different assumptions. You assumed a daily probability, I assumed cumulative.
The OP mentioned in another comment that the draw is once a year
Also, it’s 0.005 increase in the chance per day. If you start from zero, then 0*1.005 is still zero. Even after 100 years, still zero.
But let’s assume you start from 0.005, then the next day your chance would grow to 0.005*1.005=0.005025. it’d take extremely long for the chances to be reasonable
Unless (like me) you are already over 60.
The mil. As Lionel Hutz would say. NO. Money now!
Money now is always better than money later. And a million is plenty :)
Can i get 1000 people and we all share the billion whenever one of us wins?
Haha no no. It’s an offer to one individual only
