"There must be some advantage to the lottery, otherwise they wouldn't do it that way. But what the advantage is I can't really work out mathematically."
Maybe having 43 second place winners in last Saturday's PB offers some insight. 25.5 million tickets were sold, so with the odds of winning the 2nd place prize at about 1 in 11.688 million 2.2 winners would have been statistically normal. I can't tell you the chance of having 43 winners, because with a limit of 20 decimal places my Open Office spreadsheet can't calculate it. The closest I can come is that there's a 0.00000000000000000001% chance of having 29 winners as a result of random probability. To put that in perspective, producing a PB jackpot winner by selling just 1 (one) ticket is 34 trillion times as likely.
Of course the results weren't rigged, but they weren't random, either. All of the winning numbers were calendar numbers, and we know that a lot of people use birthdays or anniversaries to pick their numbers. Even so, for 43 winners to be very likely about 28% of tickets would have use only calendar numbers. That percentage seems awfully high, so I'm wondering if perhaps a lot of people got the numbers from a fortune cookie, or there was some other reason that particular combination was played so heavily. Whatever the reason, the payout is about $40 million (not counting the power play) higher than what would have been statistically normal. More importantly, it would have been about $40 million more than what went to the prize pool from ticket sales.
The lotteries have repeatedly said that 70 to 80% of tickets are QP's, so that huge payout is the result of only 20 to 30% of players having the option of using only calendar numbers. If all 25.5 million tickets had used only calendar numbers the most likely result would have been about 150 2nd places winners, resulting in a payout of almost 3 times the total sales just for the 2nd place prizes.
A high percentage of ticket using random numbers is a necessity if the lotteries want to offer fixed prizes. If the only choice in Lotto Max is to pick one line and let the terminal generate the other 2 then the lottery knows that a minimum of 66.67% of tickets will have random numbers.