chess ranking

one good thing about chess is, the ranking system is very scientific, logical and has meaning.

the detail can be found at Wiki : http://en.wikipedia.org/wiki/Elo_rating_system

The system was invented by Professor Arpad Elo.

Instead of explaining the detail, i will say about what the ranking mean.

Say, John is 1200, and Mary is 1200. This mean, if the skill of John and Mary does not change after each game, Thus, the ranking means, the chance of John win is 50:50, thus, draw game of lose is also 50:50.

if 2 players has ranking 200 points different, thus, the higher ranking player has 0.75 chance of winning. i.e. 1200 vs 1000, the 1200 player will win in 3 games out of 4. Same for 1400 vs 1200. a600 vs 1400, 2000 vs 1800.

you may ask, well, if a player is stronger then the other, why he will lose, or not always win?? well, the answer is, in a game, too many random events, or the possible moves are almost infinite. Thus, only a single mistake at the very beginning of a game will change the course of the game, that, even the strongest player cannot predicted. in fact, the best human player can almost predict 5 or 6 moves.

So, basically, we can imagine every chess player is a biased coins. the best player, is the most biased coin. when you toss a coin, no matter how biased it is, there is still a chance that it will give the minor possible outcome.

by that setting, (200 different means 0.75 chance of winning) we can set up the winning chance for any ranking difference.

R(1600):R(1400) = 3:1
R(1400):R(1200) = 3:1
there fore, R(1600):R(1200)=9:1

0 -> 0.5
100-> 0.63
200-> 0.75
300->0.84
400->0.9
500->0.94
600->0.96
....

So, we can see, if 400 ranking difference, the winning chance is so high. if you want to get improvement, better within 200, otherwise, you only get self-questioning.

The similar method is applied to many other games, like sports, say tennis. The world champion is through winning many many games instead of just one tournament. Thus, compare to US Basketball season final, only 7 games to decide who is the winner is not precise enough. but still better then the world cup. for me, the statistic error is so big in the world cup, that, the winner has no point to feel so excited at all. the world cup is just like coin tossing. each coins pair only toss once and decide who is the winner. Oh... there is no more naive game than this.

an question: How to find the winning chance for 100 ranking different?? it is very simple problem. if you fail to do, probably you have to review primary school math, about ratio.