I got the following sequence from the actual game. It's very close to a pool of 5 of each, but not quite:
//5 of each
2
2
3
1
3
1
2
2
2
3
1
3
1
1
3
//5 of each
2
2
2
1
3
1
3
2
3
3
1
2
1
3
1
//5 of each
1
3
3
3
2
1
2
2
1
3
1
2
1
2
3
//Only 4 3's
2
1
3
3
1
2
1
1
2
3
1
3
2
2
//And the next is a 2, not a 3
2
3
6
3
...
https://github.com/angelali/threesjs/blob/f78756d20b5a0a19b151e87b488e936c4efd5a27/client/js/util.js#L4
I got the following sequence from the actual game. It's very close to a pool of 5 of each, but not quite: