Nonce seems to be "random" enough, but few block analysis mention otherwise. Quoting from
https://bitcoin.stackexchange.com/q/24650,
Edited: Apr 18
I wrote a small program to collect some statistical data. From recent Dogecoin block #186,299 to #145,000 (the last mandatory update)
total 41,300 blocks
number of odds = 3,891 (9.42%)
number of evens = 37,409 (90.58%)
ratio of odd to even is about 1:10
Among the evens, the number of multiples of 256 = 35,106
85% of total
93.866% of evens
Update: 4/20
I recently also checked the nonces from block 552,780 to 253,898 of Litecoin.
totally 298,883 blocks.
number of odds = 42,963 (14.374521%)
number of evens = 255,920 (85.625479%)
Among the evens, the number of multiples of 256 = 225,746
75.529890% of total
Depending on your game and whether money is involved, using nonces isn't good idea. Set a number before game started and hash it with salting to keep fairness is better idea IMO.