There's a couple ways this works. Progressive jackpot games (Powerball, Mega Millions) allocate some amount of every ticket sold for winnings, but if the jackpot isn't won on a particular drawing, excess winnings are added to the prize pool for the next drawing. After a certain point, the jackpot prize for a single winner is more than the cost of buying all possible tickets. There's a chance of sharing a jackpot, which is hard to model, but makes the payout worse.
A similar game feature is "roll down", again excess prize money accumulates over several drawings, and when a certain criteria is met, the excess prize money is distributed over some set of tickets (possibly all winners). Again, this sets up the possibility of a positive expected value, and you have to consider other ticket buyers as well.
A trickier one is for scratch off games. Many lotteries share the number of tickets sold and the prizes left. If you assume all (big?) prizes are redeemed shortly after their ticket is sold, you can estimate the expected value of purchasing the remaining tickets. When the game opens, the expected value of a ticket is less than the purchase price, but depending on the observations of tickets sold and prizes redeemed, you might estimate that the expected value of the remainder of tickets has improved.
Ex: if there were 1 million scratchers printed, the cost per scratcher was $1, and there was only one prize $500,000on open the expected value of a $1 ticket would be $0.50. If the winning ticket was redeemed, the expected value of remaining tickets would be $0. If it was reported that 999,999 tickets were sold and the winner had not yet been claimed, it might be reasonable to assume a higher expected value for the last ticket --- although there's no rigorous proof there, someone may have purchased the winning ticket already and not redeemed it for whatever reason.
A similar game feature is "roll down", again excess prize money accumulates over several drawings, and when a certain criteria is met, the excess prize money is distributed over some set of tickets (possibly all winners). Again, this sets up the possibility of a positive expected value, and you have to consider other ticket buyers as well.
A trickier one is for scratch off games. Many lotteries share the number of tickets sold and the prizes left. If you assume all (big?) prizes are redeemed shortly after their ticket is sold, you can estimate the expected value of purchasing the remaining tickets. When the game opens, the expected value of a ticket is less than the purchase price, but depending on the observations of tickets sold and prizes redeemed, you might estimate that the expected value of the remainder of tickets has improved.
Ex: if there were 1 million scratchers printed, the cost per scratcher was $1, and there was only one prize $500,000on open the expected value of a $1 ticket would be $0.50. If the winning ticket was redeemed, the expected value of remaining tickets would be $0. If it was reported that 999,999 tickets were sold and the winner had not yet been claimed, it might be reasonable to assume a higher expected value for the last ticket --- although there's no rigorous proof there, someone may have purchased the winning ticket already and not redeemed it for whatever reason.