under a bridge wrote:

MnM wrote:

MnM wrote:

statistics major wrote:

I would buy 1,000 in order to give myself a 100% chance of winning.

lol. Where are you a statistics major? Trump University?

In real life I would buy zero because I have no trust in the odds that I'm being told.

In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.

I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B.

I don't think that's correct. The odds of each ticket is an independent event. Chances of winning are 1-(999/1000)^x.

Right. So putting some numbers to it, if you buy 1000 tickets, and they each have a 1/1000 chance of winning, you're looking at about 73% chance of winning one or more times. The "expectation" is to win $1B. But there is still a 27% chance of wasting a million bucks for nothing.

Buying 5000 tickets on a $5 million loan if you can swing it is a pretty sure bet. The expectation is $5 billion, with a 99.3% chance that you win $1B or higher. So even if you only win once (which the odds strongly favor winning multiple times), you still are likely to get at least 20x your investment.