There have been lotteries with positive payout on specific days. Specifically, both Michigan and Massachusetts have had lotteries where, when the all out in the award pool arrived at a specific sum, it was paid out to every one of the victors.
A few understudies at MIT (what other place) sorted out this and coordinated a gathering to purchase LOTS of tickets on those days. Strangely, this didn't cost the state anything - they continued to make their %, they just paid it out strangely.
For the subtleties (which are really intriguing to math nerds) see the book How not to be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg.
2) It can check out to play the lottery, regardless of whether the chances are against you, for at a few reasons:
a) The utility of cash isn't straight. For some individuals, the deficiency of (say) $10 each week is insignificant while the addition of a huge number IS noteworthy. (Obviously, on the off chance that you're Bill Gates, the addition of millions isn't noteworthy)
b) Entertainment esteem. Certain individuals get a rush out of lottery playing.
3) On the other hand, there have been a few investigations of lottery champs. It found that a large number of them, a little while later, were not excelling by any means.
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