how many moves per game

Hi Guys I'm new to the app and chess for that matter! I've played about 20 games so far and on three of my games at the point I placed my opponent in check mate the game called stalemate even though my opponent had only a king against my numerous pieces! All the games seemed to be at the 49 -50 move mark so I presumed it was 50 moves max until I lost a game at 61 moves!! I'm confused! Anybody help?

Stalemate is when your opponent cannot make a legal move, but his king is NOT in check. In that case, the result is a draw.
http://www.chess.com/echess/game?id=118962846
http://www.chess.com/echess/game?id=118916656
http://www.chess.com/echess/game?id=118868088

In all the games above, your opponent cannot make a legal move, but his king is not in check, so it's a stalemate and that's a draw.

And there is no limit on the number of moves for a chessgame.

Using the 50 move rule as a restriction, the longest game can't be greater than 49 moves per capturable piece + 49 moves per pawn move + the last move. Getting max pawn moves would be hard, but the longest game should be close to 6000 moves.

More like 1500.

From my own calculations it would be 6224 moves. (686 to capture all the knights, bishops, rooks and queens. Then 4704 moves to account for all pawn moves, including promoting at the end. Then 784 more moves to capture these promoted pieces. And at last, the 50 moves needed to be played in order to get to the 50 move rule.) Let me know if there's something I missed. I believe you can promote every single pawn if you're careful about how you capture other pieces with your pawns earlier, but this might be where I make my mistake.

I spent some time thinking about "longest possible game" given the standard drawing rules a while back as an interesting mathematical puzzle, and there are some details to note:

1. It's maximum 50 moves per capture or pawn move, not 49. Every 50th move should be a capture or pawn move.
2. The game shouldn't end "early" by insufficient material, so there needs to be a piece left on the board with the kings until the final move.
3. It's not possible for every pawn to move 6 squares without any of those moves being captures (the pawns can't pass through each other on their original files), and indeed it's a bit tricky to figure out what the minimum number of captures by pawns is

One possible capture scheme for the pawns would be for one side to use 4 captures to line up their pawns on the even files while the other side uses 4 captures to line up their pawns on the odd files. (This seems like it should be possible by cooperative piece placement for the captures, and for what it's worth I verified one legal sequence of moves to produce this result.) This is 8 captures by pawns, and while I haven't proved it I suspect this is the minimum.

That leaves 6 moves per pawn and 21 total captures: 16 promoted pawns and 14 starting pieces, minus 8 pieces captured by pawns, minus 1 piece that must remain on the board to avoid a draw by insufficient material. Plus 50 moves after all captures to produce the final result.

50 x (6x16 + 21) + 50 = 5900

If anyone sees an error or otherwise knows of a way the game could be longer (or can't be this long) I'd be interested to hear about it

edit: Ah ha, this is not quite right. There's one more complication: we can't have the same player on move for every single capture and pawn move! https://wismuth.com/chess/longest-game.html This analysis uses a forced 75-move rule to get around the fact that 50-move rule is something that normally must be claimed by one of the players, but the final move count regardless "loses" a move and a half compared to multiplying 75 by the number of pawn moves and captures. That's because about half the captures must be on white's turn instead of black's, and the solution presented switches "control" (of who's performing captures vs. who's only delaying for an extended sequence of moves) 3 times during the game, losing 3 half-moves.

... that ends in checkmate.

A pawn move, or capture on the 100th ply or earlier is required to continue the game. There are 15 pieces per side, and pawns promote to pieces before being capture. Thus 100×16×6+100×27+99×3 = 12,597 plies is the upper bound. You could get pawns all 6 moves if they capture pieces to form four files for each player, and no double push. Thus 6298 turns, with white making 6299th turn. The 99 plies are required when the player to break at the limit changes. White sac their knights to open way for black pieces, then black sacrifice 4 pieces to make way for 4 files of white pawns, white need to sacrifice 2 more pieces to make way for 4 files of black pawns, and a final exchange with white taking the last piece.