Most analysis of 5/N data looks at the numbers after they have been arranged in increasing order. I've been looking at the raw unordered drawing results of 5/N prng games to see if the up-down sequences of the numbers can elucidate something about the prng being used.
Example: The October 8 CA Fantasy Five result was 33-24-12-39-35. In my notation, the up-down sequence for this drawing is "ddud" because the 2nd number goes down with respect to the 1st, the 3rd number goes down from the 2nd, the 4th number goes up, and the 5th number goes back down. There are 16 possible up-down sequences. For any 5/N game the expected frequencies are
uuuu: 1/120 = 0.00833333333333
uuud: 4/120 = 0.0333333333333
uudu: 9/120 = 0.075
uduu: 9/120 = 0.075
duuu: 4/120 = 0.0333333333333
uudd: 6/120 = 0.05
udud: 16/120 = 0.133333333333
uddu: 11/120 = 0.0916666666667
duud: 11/120 = 0.0916666666667
dudu: 16/120 = 0.133333333333
dduu: 6/120 = 0.05
uddd: 4/120 = 0.0333333333333
dudd: 9/120 = 0.075
ddud: 9/120 = 0.075
dddu: 4/120 = 0.0333333333333
dddd: 1/120 = 0.00833333333333
The distribution of up-down sequences for CA Fantasy Five follows the theoretically expected distribution pretty closely, so I don't think there's much to milk from this. A while back I found another state's prng 5/N game that was not following the expected distribution, which suggests their prng was a little wonky, but I couldn't get much juice from it either. Maybe someone else will find this useful.
