Checking the math:
P(7) = 31598138 / 292201338 ~= 0.108
P(~7) = 260603200 / 292201338 ~= 0.892
P(win|7) = 0
P(win|~7) = 1 / 260603200 ~= 3.84e-9
P(win) = P(win|7) * P(7) + P(win|~7) * P(~7)
= 0 + 260603200 / 292201338 * 1 / 260603200
= 1 / 292201338
You are correct, sir. I withdraw my incorrect statement.
Nevertheless, I presume that most of the surge players, who only buy tickets for very high jackpots, will not have favorite numbers, and thus you would only be avoiding splitting the pot with the regulars playing their usual numbers.
If someone plays his birthday every week, but bought an extra 10 tickets for the record jackpot, those extras are likely to be completely random draws. Judging by the increase in the pot from the last draw, there are a lot of people buying more than the usual amount of tickets.
So in the EV calculation, if the amount attributable to not splitting the pot is not greater than the actual value of your time in filling out the form to play specific numbers, you are better off taking the random draw.
