Is 1, 2, 3, 4, 5, 6 a bad lottery ticket?

Question

In a lottery, six numbers are drawn at random from 1 to 49. 1. Is the ticket 1, 2, 3, 4, 5, 6 less likely to win than, say, 7, 19, 23, 31, 40, 44? 2. Is it nevertheless a worse ticket to buy? Why?

Accepted Answer

Every specific combination is equally likely, so 1 to 6 wins exactly as often as any other ticket. But it is a poor ticket to buy, because thousands of people pick it and the jackpot would be split. Equally likely. The draw picks one of the 49-choose-6 = 13,983,816 combinations uniformly at random. The combination 1, 2, 3, 4, 5, 6 is one of them, with the same probability, about 1 in 14 million, as any other. "It looks non-random" is a fact about human pattern recognition, not about the draw. In the same way, a coin producing HHHHHH is exactly as likely as any particular sequence such as HTTH…

Is 1, 2, 3, 4, 5, 6 a bad lottery ticket?

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