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Originally Posted by s|k
I don't know how your lottery works, but if can you pick your own numbers, it in creases the possibility that you would end up sharing your winnings as the likely hood that someone else picked your number increases (especially if you picked numbers others are likely to pick 7,13, 42, 69, etc.
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I doubt this is true; if you used a random number generator for your own numbers while everyone else chose theirs freely (and refused to use any silly combinations the RNG produced like 1,2,3,4,5,6), I assume you'll have a slightly higher expected win amount than in a lottery where everyone was randomly allocated.
Consider the 100 person case where (if given free choice), 5 people will chose 1,2,3,4,5,6 while you use a RNG programmed to exlude that particular combination. Its obvious that your expected returns will be slightly higher than in the fully random case since youre deliberately excluded an (equally probably) combination which would result in you winning less due to splitting.
The key point is that youre picking randomly while others are clustering (to an admittedly small degree) around a particular group of numbers, which gives you a slight advantage. If everyone was randomly allocated, it would be an equal playing field.
edit: I didnt read the context of your post; Dante is right. Multiplying the number of players by the same constant factor that the prize is multiplied by doesnt affect the expected winnings, because you arent actually changing any of the distributions. Winning 80 million and sharing it with 79 other people is the same as winning 1 million outright. However in this particular case, the prize is being multipilied by a number thats almost certainly greater than that which the number of players is being multiplied by (I doubt theyll sell anywhere near 4x as many lottery tickets), so you have a higher expected value than in the normal lottery.