That is, until you realized not only were taxes taken out, but also you don't get the full winnings if you take the immediate cash prize. In other words, the time value of money still made not buying a lottery ticket worth the reward even that one time in my lifetime it was high enough to seem like it made sense.
Every once in awhile I buy four quick pick tickets even though it doesn’t make sense. Why? To have a couple of days of Walter Mitty dreaming of all the things I would do and working people I would quietly, very quietly help while I continued to live a not so splashy life.
As for the taxes, surely someone is over estimating them? There are sites that are official that calculate the net after taxes and based on either immediate payout or long term payments. Taxes are high but I have not seen 45%.
The long term payout seems best in most cases but depends on the interest rate you may think you could manage for the lump sum return. It is hard to have a risk free rate of even 5% these days and over a long term. It used to be 7% but I have not seen that in decades. Risk free is the operative term. There have not been 12% GICs in ages.