Re: Powerball question
Any combination is equally likely to be drawn as the winner.
However, some combinations are more likely than others to be bought by other players causing you to split the prize. You can significantly improve your EV by playing "unpopular" numbers -- avoiding traditional 'lucky numbers' and birthdays.
If you do your own research and discover which six numbers are least popular, you should play those six every week to minimize your chance of a split. (If, however, you find a published list of which numbers are least popular, then you have a new meta-game, wondering how many other people found that same list and are playing bottom six off the list...)
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