Say I conduct a lottery where tomorrow I randomly choose a number between 1 and 100 and split the money from the one dollar tickets I sold among those who chose the winning number (refunds if no winner). Random tickets break even. But someone who pays $100 for 100 different numbers has an edge (unless everyone else does)! To see why suppose only one other player plays and buys one ticket. You win one dollar 99 times and lose $49.50 one time. The explanation is that you making sure you don’t duplicate, makes your tickets not random.
See comment for #49.
There is a web page that has discusses some similar concepts especially as it applies to actual lotteries. If the lottery prize was $10M and you had a 1 in 4M chance of winning, your EV for a $2 ticket is $0.50; how much should you bet. Search by: How to Tackle a Lottery with Mathematics – KDnuggets
You have brought up a very good points, appreciate it for the post.