I've read that for any position, there are on average approximately 35 possible moves. But what's the maximum number of possible moves for a position?
After some searching, it seems that this composition is the current record holder. 218 moves; legal position with promotions:
R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1
Another version of the position (same number of moves):
3Q4/1Q4Q1/4Q3/2Q4R/Q4Q2/3Q4/1Q4Rp/1K1BBNNk w - - 0 1
79 moves (for black); from actual game between Davis and Panchanathan, source from Tim Krabbe's list of chess records:
4r1k1/p4pp1/2n2n1B/2b5/N6Q/P2q1N2/1r4PP/R4R1K w - - 0 1
99 moves (for white); all pieces on board:
q2Q3r/n6R/kpB1N1K1/p1p1Bppp/1PN3P1/1n1pp1b1/P1PPPP1P/r5Rb w - - 0 1
164 moves (both sides counted); all pieces on board:
R6R/pbpppK2/1B1QNNp1/1p3p1p/P1P3P1/1Pnnq1b1/2kPPPBP/r6r w - - 0 1
324 moves (both sides counted):
1QqQqQq1/r6Q/Q6q/q6Q/B2q4/q6Q/k6K/1qQ1QqRb w - - 0 1
412 moves (both sides counted); a curiosity, illegal position:
QQqQqQqq/q6Q/Q6q/q6Q/Q6q/q6Q/Q6q/QqQqQqQq w - - 0 1
Main source: Guide to Fairy Chess. The book is a bit old, so there might be new record holders, but if that's the case, I was unable to find them.
This position from actual play has 79 moves available for Black
This is a legal layout with 195 possible moves. I'm sure it isn't the absolute maximum, since I just made this one by creating a pattern with the promoted Queens and then continually optimizing the layout from there. It should give you some idea about how you might achieve the maximum number of possible moves though.
- Thanks to bof for finding a way to add 2 additional moves.