I have $\$250$ million in the bank. The odds of winning the lottery jackpot are about $1$ in $250$ million. The lottery payout gets up to $\$300$ million. A ticket costs $\$1$. The jackpot is the only payout. I am the only person playing the lottery. The lottery people can instantly tell me if I win or not, and I don't have to look through my tickets. If I buy tickets, they will be randomly selected. Duplicates are a possibility.
Should I spend $\$250$ million on lottery tickets? What is the expected value of the gamble? What is the percentage chance that I would win?
How the lottery works: you pick a set of random numbers. The lottery people pick a set of random numbers. The chances those random numbers will be identical are 1 in 250 million. If any of your tickets math the lottery numbers, you receive $\$300$ million, but not your original $\$250$ million spent. If none of your tickets match, you win nothing, and lose your $\$250$ million wager.