This is interesting but IMO it's very likely to be chosen more often than average.
If you choose a random number, then for each other player your chance of picking the same numbers as them is the same as your chance of winning: in the case of Powerball, 1 in 292,201,338 = 0.0000000034. If you instead non-randomly choose 123456, then for each player that actively avoids 123456 your chance of picking the same numbers as them only decreases by 0.0000000034 (from 0.0000000034 to 0). But for each player that actively chooses 123456, your chance of picking the same numbers as them increases by 0.9999999966 (from 0.0000000034 to 1).
We could model this more precisely by looking at the other players' choices as semi-random with some combinations weighted higher and some lower, but you see my point: even if lots of people are repelled by 'obvious' sequences like 123456, this can be outweighed by a very small number being attracted to them.
stavros|1 month ago
retsibsi|1 month ago
If you choose a random number, then for each other player your chance of picking the same numbers as them is the same as your chance of winning: in the case of Powerball, 1 in 292,201,338 = 0.0000000034. If you instead non-randomly choose 123456, then for each player that actively avoids 123456 your chance of picking the same numbers as them only decreases by 0.0000000034 (from 0.0000000034 to 0). But for each player that actively chooses 123456, your chance of picking the same numbers as them increases by 0.9999999966 (from 0.0000000034 to 1).
We could model this more precisely by looking at the other players' choices as semi-random with some combinations weighted higher and some lower, but you see my point: even if lots of people are repelled by 'obvious' sequences like 123456, this can be outweighed by a very small number being attracted to them.