Difficult# Chess Ratings 3

GMAT-TXUBV1

__Harkness System__

The Harkness System was invented by Kenneth Harkness, who published it in 1956. It was used by the USCF from 1950 to 1960

and by some other organizations. When players compete in a tournament, the average rating of their competition is calculated.

If a player scores 50%, they receive the average competition rating as their performance rating. If they score more than 50%,

their new rating is the competition average plus 10 points for each percentage point above 50. If they score less than 50%, their

new rating is the competition average minus 10 points for each percentage point below 50.

"Chess Rating System." (2015): n. pag. 14 Dec. 2015. Web. 23 Dec. 2015.

__Elo Rating System__

The Elo system was invented by Arpad Elo and is the most common system. It is used by FIDE and other organizations.

FIDE classifies tournaments into categories according to the average rating of the players. Each category is 25 rating

points wide. Category 1 is for an average rating of 2251 to 2275, category 2 is 2276 to 2300, etc. For women's

tournaments, the categories are 200 rating points lower, so a Category 1 is an average rating of 2051 to 2075, etc.

"Elo Rating System." (2015): n. pag. 14 Dec. 2015. Web. 23 Dec. 2015.

__English Chess Federation System__

The English Chess Federation (formerly British Chess Federation) Grading System was devised by Richard W. B. Clarke and

first published in 1958.

Points are scored for every game played in a registered competition (generally, English congresses, local and county leagues,

and other team events). A player's grade is calculated by taking the opponent's grade and adding 50 points for a win,

subtracting 50 points for a loss, and taking the opponent's grade as it stands for a draw. For grading purposes it is assumed

that the opponent's grade is never more than 40 points above or below one's own. An ECF grade can be approximated to

an Elo rating by multiplying by 8 and adding 600. An ECF grade of 100 is approximately 1400 Elo, while 200 ECF equals

2200 Elo.

"English Chess Federation." (2015): n. pag. 3 Dec. 2015. Web. 23 Dec. 2015.

English Chess Federation grades range from about 40 for very weak club players to about 150 for very strong club players. Scores higher than this generally belong to professional players. Men and women are graded in the same way by the English Chess Federation.

Suppose that Tournament X is reserved for women with ECF grades between 50 and 150 inclusive. How many categories would be needed to score this tournament under the Elo system?