In my opinion, it is because the game involves mental as opposed to physical skill and ability. There are no advatages that a difference in physical size gives to one person over another. In fact, beating an opponent usin brains rather than brawn is much more satisfying than the other way around. What little player would not love beating another player that is twice his size. Also, as people play more and more they see that there are basic concepts concerning strategies and tactics that govern the game and that these can be learned and mastered. Getting better at something is always a reward in and of itself.
Makes me laugh to hear people say it would feel good to beat someone in Chess who is twice their size, for me this would never cross my mind in relation to the game. Chess, its a very in-depth game, in that the more you play the more you see, you can never really know the game. You constantly create new combination's and see new patterns. When you first start playing you may make stupid mistakes but if you play for long enough, eventually you will begin not even to have to think about these small mistakes they will be in your sub conscience mind as your brain is thinking more about the overall game plan (strategy) rather than combination's and patterns which would come more so under tactics. If you play for too much like I used to when younger, you may actually dream about chess patterns and invent them in your sleep, developing with the game is quite amazing, this power it has to grasp your 100% attention can be pretty special. And a great thing about the game in more advanced levels is that the outcome of the game is purely skill, which is great and has nothing to do with luck, except certain circumstances of course. LOL why would you bother talking about physical and mental when it comes to chess?? hhahah this is a board game, like saying this is a 'word'.
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Chess has a long history and tradition. In addition, it is an elegant game played with the mind and comes replete with the pitfalls to which humans are prone. It pits one player against another, and as often as not, it puts a player up against himself. If you do not understand this, pick a sport or game which you love and identify with, and ask yourself why thatgame should be played. The reasons will be similar.
It is a game where everything is even and the only factor that contributes to an uneven is how white starts first. The game has endless possibilities and interesting startegies used worldwide by all kinds of players.