The game Fair-Chess is invented by Jef Kaan in 2014; http://bookbuilder.nl
It is based on the old idea that the stronger player can play with a penalty, by missing a pawn, a certain piece, or a combination thereof.

There are various sub-variants, all compensating the different sides via less pawns, knights, or even a missing bishop i.e. giving them a handicap depending on difference in playing strength; besides giving a default penalty for white side, having the advantage of the first move as 'default' by removing one pawn, also black pawns can be removed, whereby a difference playing strength of about 60 Elo will mean one pawn difference; at beginner level; this ofcourse is a rough difference but anyway will make it possible to have more fun in chess when playing between opponents of different playing strength.

For additional information on handicap chess in general:
http://chess.stackexchange.com/questions/4/is-there-a-way-to-use-handicaps-in-chess-to-bridge-the-gap-between-players-of-di
http://chess.stackexchange.com/questions/2747/what-is-the-required-elo-to-beat-a-grandmaster-with-queen-odds
http://chess.about.com/od/tipsforbeginners/a/Choosing-The-Right-Odds.htm
(NB the indicated rating differences at the last site are clearly for more advanced players, or longer time controls).
As you can see in these linkes there is no clear-cut method (yet) to define the handicaps for rating differences, but in the above we have indicated some initial guideliness to setup such handicaps.

PLaying Strategy: same as in normal chess; however when the opponent is missing lots of pawns, or a pawn tactics can be totally different, and there will be opportunities for king attacks. Tip: if you are a lot weaker, and your opponent is missing a piece: try to exchange lots of pieces, and achieve a winning endgame; at least you will get lots of opportunities for endgame practice!