Not what the ROI be with 4 excepted winners?

I'm not sure what the question is, but the ROI is practically almost always negative with the big lotteries.

1. Earnings will be taxed at an effective rate of 30-40%

2. "Pot" isn't the present value of the winnings (i.e. lump sum). That is ~40% less

3. Probability of multiple winners can be assumed to follow a binomial distribution that increases significantly as the number of tickets increases. Assuming a winner and 100m tickets sold, the expected number of winners is 1.17. 200m tickets sold - that increases to 1.37. 400m tickets sold, that increases to 1.8. For reference, the $1.58m powerball sold 635m tickets. The $948 million previous drawing sold 440m tickets.

All that considered, the ROI of a $2 ticket with a $1b pot, 200m sold tickets, 35% taxes, and 40% lump sum reduction is around -35%. You need to ignore something significant (such as taxes or lump sum reduction) for that to be positive.