How many possible moves (for white for ease sake) are there after:

0 random half-moves: 20
2 random half-moves:
4 random half-moves:
6 random half-moves:
8 random half-moves:
10 random half-moves:

For example, I think there are a total of 20 opening moves for white...as for the rest, I am both too lazy and mathematically challenged to solve...

Also...just a note...I have no idea to the answers, just curious...

Also...another curiousity...is there any sort of pattern of increase in number of moves?

http://www.research.att.com/~njas/sequences/A048987
http://www.research.att.com/~njas/sequences/A006494
http://www.research.att.com/~njas/sequences/A019319
http://www.research.att.com/~njas/sequences/A089957
http://www.research.att.com/~njas/sequences/A090051
http://www.research.att.com/~njas/sequences/A057745
http://www.research.att.com/~njas/sequences/A083276

Originally posted by David113
http://www.research.att.com/~njas/sequences/A048987
http://www.research.att.com/~njas/sequences/A006494
http://www.research.att.com/~njas/sequences/A019319
http://www.research.att.com/~njas/sequences/A089957
http://www.research.att.com/~njas/sequences/A090051
http://www.research.att.com/~njas/sequences/A057745
http://www.research.att.com/~njas/sequenc ...[text shortened]... n moves, including en passant and castling information, so why are the sequences not the same?)

Originally posted by XanthosNZ
[fen]rnbqkbnr/ppp3pp/8/3pPp2/5p2/8/PPPPQ1PP/RNB1KBNR w KQkq f6[/fen]

A position is different depending on whether en passant is possible. However, the above position is the same whether or not the last move was ...f4 as even if en passant were possible it couldn't be played due to the pin according to one sequence and two different positions according to the other.

Originally posted by XanthosNZ
due to the pin

Originally posted by aging blitzer
what pin?

Originally posted by XanthosNZ
Hmmm is seems I messed up the example. Anyway, imagine the pawn that would take en passant is pinned to it's own king.