Re: What would you do with $640 million?!?!
It's going to be a negative EV game even with a high jackpot due to multiple entrants and the inevitability of having multiple winners. Even with a very naive calculation of expected value and then looking at it via the Kelly criterion, only millionaires should even bother.
Don't let expected value fool you, either. Expected value needs to be taken in context.
To make this really obvious as to why, consider the St Petersburg Paradox: http://en.wikipedia.org/wiki/St._Petersburg_paradox
Basically, the expected value of this game is infinitely high. This means you should technically want to play this game no matter how much it costs to enter because you will gain in the long run (and infinitely so).
The problem: Obviously, you wouldn't touch this game with a ten foot pole. You don't have unlimited resources and you are likely to run out before the positive gains are realized.
Similarly, you could play the lottery until the end of time, and maybe eventually you'd win. But in most cases, you'd win back only a small percentage of everything you put into it.
Our intuition for probability is not great. There are tons of hilarious examples that can be demonstrated, but the point is that the chances of winning the lottery are retardedly low and the EV sucks anyway. So low that you can pretty much assume it's near-zero. Spend that money more wisely! Yes, you could waste a dollar and potentially make a killing.... but you could also waste a small chunk of change on stock and get a much higher return on average -- something you're more likely to ACTUALLY acquire.
"A typical graph of average winnings over one course of a St. Petersburg Paradox lottery shows how occasional large payoffs lead to an overall very slow rise in average winnings. After 20,000 gameplays in this simulation the average winning per lottery was just under 8 dollars. The graph encapsulates the paradox of the lottery: The overall upward slope in the average winnings graph shows that average winnings tend upward to infinity, but the slowness of the rise in average winnings (a rise that becomes yet slower as gameplay progresses) indicates that a tremendously huge number of lottery plays will be required to reach average winnings of even modest size."
It's going to be a negative EV game even with a high jackpot due to multiple entrants and the inevitability of having multiple winners. Even with a very naive calculation of expected value and then looking at it via the Kelly criterion, only millionaires should even bother.
Don't let expected value fool you, either. Expected value needs to be taken in context.
To make this really obvious as to why, consider the St Petersburg Paradox: http://en.wikipedia.org/wiki/St._Petersburg_paradox
Basically, the expected value of this game is infinitely high. This means you should technically want to play this game no matter how much it costs to enter because you will gain in the long run (and infinitely so).
The problem: Obviously, you wouldn't touch this game with a ten foot pole. You don't have unlimited resources and you are likely to run out before the positive gains are realized.
Similarly, you could play the lottery until the end of time, and maybe eventually you'd win. But in most cases, you'd win back only a small percentage of everything you put into it.
Our intuition for probability is not great. There are tons of hilarious examples that can be demonstrated, but the point is that the chances of winning the lottery are retardedly low and the EV sucks anyway. So low that you can pretty much assume it's near-zero. Spend that money more wisely! Yes, you could waste a dollar and potentially make a killing.... but you could also waste a small chunk of change on stock and get a much higher return on average -- something you're more likely to ACTUALLY acquire.
"A typical graph of average winnings over one course of a St. Petersburg Paradox lottery shows how occasional large payoffs lead to an overall very slow rise in average winnings. After 20,000 gameplays in this simulation the average winning per lottery was just under 8 dollars. The graph encapsulates the paradox of the lottery: The overall upward slope in the average winnings graph shows that average winnings tend upward to infinity, but the slowness of the rise in average winnings (a rise that becomes yet slower as gameplay progresses) indicates that a tremendously huge number of lottery plays will be required to reach average winnings of even modest size."
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