Actually, you can write a PhD thesis in decision analysis, on when bying a lottery ticket constitutes a rational decision.
Not only are the winnings burdened by up front taxes but, if the payout is over time (Which many are - 20 years or so) the time-value adjusted winnings are often less than half what is advertised. To boot, there can be multiple winners, further diluting the expected value of any payout.
(wink)