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Chess Tournament Tie Breaking

by Mike Stridsberg
 

One of the hardest parts of a chess tournament to understand is the tie breaking system used for assigning trophies.  I put together this document to help explain the process, using fictitious names and results as an example.

IMPORTANT NOTE: The United States Chess Federation (USCF) rules state that whenever there is a tie, any tied player is considered to have finished in the tied position.  For example, if there is a three-way tie for second, all three players may state that they finished in second place.  Any prizes must be split equally between the tied players.  Since there is typically only one trophy for each position, however, some sort of objective system must be used to assign trophies.  Interestingly, the USCF rules also state that those who receive a trophy for a tied position may change the plate (at their own expense) to indicate the position they tied.

That being said, let’s look at the tie breaking systems used.

 

Tie Breaking Systems

The USCF specifies the following tie breaking systems be used for scholastic tournaments, in this order:

1. Modified Median

2. Solkoff

3. Cumulative

4. Kashdan

5. Games between tied players

6. Most times playing Black

7. Coin Toss

If the first tie-breaking system is unable to break the tie, the second is used for the players that are still tied, and so on, until the order is decided.  Tie breakers are only used between players that have the same score, not all players.

To make this explanation easier, I'm going to use the following results for a fictitious tournament, where 16 people finished more or less in alphabetical order... 

Example Tournament, Final Scores:

   Ann         4.0

   Bill        3.0

   Chip        3.0

   Dan         3.0

   Ed          3.0

   Faye        2.5

   Gus         2.5

   Hal         2.0

   Ivan        2.0

   Judy        2.0

   Kirk        1.5

   Lucy        1.0

   Mark        1.0

   Nan         1.0

   Ozzy        0.5

   Pete        0.0

As you can see, we have a four-way tie for 2nd place that needs to be resolved.

 

Modified Median

The Modified Median system works by comparing the scores of the opponents that the tied players faced during the tournament.  The theory is to award the person who played the stronger opponents.

The system works by adding the scores of each player’s opponents, disregarding the lowest score1

Using the example tournament results, it works out this way for the four players tied for second place with 3 points:

Bill:        Chip:        Dan:         Ed:

Ed     3     Bill   3     Ann    4     Faye   2˝

Hal    2     Faye   2˝    Hal    2     Gus    2˝

Ivan   2     Hal    2     Lucy   1     Judy   2

Mark   1     Lucy   1     Mark   1     Kirk   1˝

Total  7     Total  7˝    Total  7     Total  7

So, by the Modified Median tie breaker, Chip is awarded the 2nd place trophy, and Bill, Dan and Ed are now tied for 3rd.

The Modified Median, like most tie breakers, only works between players who have all earned the same tournament score. 

If there is still a tie after calculating the Modified Median, the Solkoff system is used for the players that are still tied

 

Solkoff

The Solkoff system is similar to the Modified Median except that no opponent scores are disregarded.  By the Solkoff system, the next step in the tournament example would look like this:

Bill:        Dan:         Ed:

Ed     3     Ann    4     Faye   2˝

Hal    2     Hal    2     Gus    2˝

Ivan   2     Lucy   1     Judy   2

Mark   1     Mark   1     Kirk   1˝

Total  8     Total  8     Total  8˝

So, using the Solkoff tie breaker, the 3rd place award goes to Ed, and Bill and Dan are tied for 4th.

If after calculating the Solkoff score there is still a tie, the Cumulative system is used.

 

Cumulative 

The Cumulative system works by adding together the players’ score after each round to get a cumulative total.  The system rewards players who win early rounds, but lose in later rounds against stronger opponents.

Let’s say that Bill won his first, third and fourth games, and Dan won his first, second, and fourth games.  The cumulative scores would be:

          Bill:        Dan:

Round 1     1           1

Round 2     1           2

Round 3     2           2

Round 4     3           3      

TOTAL       7           8

Continuing with our example, Dan would receive the 4th place trophy, and Bill would get the 5th place award.

 

Other Systems

In the rare case that there is still a tie, the Kashdan system is used.  In the Kashdan system, a player receives 4 tie breaker points for a win, 2 points for a draw, 1 point for a loss and 0 for bye.  The highest total wins the tie breaker.

If there is still a tie, the results are checked to see if the tied players played each other during the tournament.  If so, whoever won that game wins the tiebreaker.

If the game between tied players was a draw, the results are checked to see if one player played black more often than the other.  If so, that player wins the tie.

Finally, if there is still a tie, a coin toss determines the order of finish.

Most of the time, the various tie breaking systems result in the same placing.  Since that is not always the case, however, the order in which they are used is strictly specified by the USCF.

 

Conclusion

I hope you found this explanation helpful for explaining the often-confusing results of chess tournaments.  Keep in mind, of course, that the most important aspects of scholastic chess tournaments are to learn, make friends, be a good sport, and have fun.

                          --  Mike

 

1 The Modified Median rule is actually slightly more involved.  The lowest scoring opponent is disregarded only for ties between players with more wins than losses.  For players tied with more losses than wins, the highest scoring opponent is disregarded.  For players tied with an even number of wins and losses, both the highest and lowest scoring opponents are dropped.  Since the system is normally used to award trophies to top finishers, the generalization on page one is good enough for most cases.