How can you define a game?

How can you define a game?  There are many things in life we do that must adhere to set rules but we wouldn't class all of these as games.  In our professional lives we have to follow rules, policies and procedures in everything we do, yet we wouldn't consider these games.  Likewise when it comes to fun and enjoyment, it's hard to use these as determining factors for games because there are many games we must play in life that aren't enjoyable.

There is the idea of players being the defining aspect of games, where a game is defined by the number of people that play it - single player, multiplayer, etc, but even then, if you choose not to play the game, you can still be part of it.  Others can play games with you even if you don't want to, likewise you can be placed in a single player game and refuse to play, the fact you refuse to play does not nullify the game, you simply lose the game because you never tried.

The next question, assuming you managed to define what a game is, would be, when does a game stop being a game?  If you explore game theory, one theme that recurs when trying to define a game is the existence of a winning strategy.  That is to say something you can do in order to win the game, a strategy which if adhered to religiously can allow you to play a perfect game.  What I find fascinating about this is the question that arises when you accept this as the defining aspect of gaming - what happens when you memorise the winning strategy?  Is it still a game if you always win, never lose, and never fault?  Take the Rubik's Cube for example, for most people the game of the cube is trying to solve it, but when you learn the algorithms which can be used to solve the cube, the random and strategic elements are removed and it simply becomes a memory test.  If you can lift the cube every time and solve it every time remembering the algorithm, is it still a game?

By extension of this concept you can also ask, if there exists no winning strategy and the game is endless, which you can therefore never win, is it still a game?  Taking Tetris as an example, the game is one that advances in difficulty as the player progresses, in some cases depending on the version the game can be endless, where you simply continue until you fail.  Is this still a game if you can never actually win?

So we are brought back to our original question, how can you define a game?  When does it start and end being a game?