Knock Out System
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RAJAH 1 : Knock out system The knock out system is the fastest tournament system to find a single winner. The drawback is that it gives very little information about other players. In fact, if you have no prior information about the players, you cannot distinguish a from results of a knock out tournament whether the results of individual encounters where produced by playing or by tossing a coin. The knock out system works as below: - assign players into pairs - players in a pair play each other - leave out the losers - repeat the steps until there is only one player left Usually this is done by putting the players names in the diagram below. ----
\ a ---/ \ ---\ i ------/ \ \ / \ b ---\ / \ ---\ m ------/ \ \ / \ c ---/ \ / \ / \ ---\ / \ j ---\ ---/ \ \ / \ d ---\ / \ ---\ o ------/ \ / e ---/ / \ / ---\ / k ---/ ---/ \ / \ / \ / f ---\ / / \ / ---\ / n ------/ \ / g ---/ / \ / ---\ / l ------/ \ /
h ---/ ----
If the organisers have no prior information on players strength the players can be assigned randomly in the diagram. If prior information is available it is preferable to have the expected number 1 and 2 meet in the last round. This is achieved by placing them on the different halves of the diagram. For the semifinals the choices to try are 1-3, 2-4 or 1-4, 2-3. The latter is preferable, since it also gives a chance that the second place is fought well. Generally at the k:th last round one can use the equation below: p+o = 2**k +1, where
p is players rank in the a priori order o is opponents rank in the a priori order If the number of players is not a power of 2 then the highest players are given byes.
Double knock out Double knock out cures some problems of the randomness of the result, but more rounds are needed. After losing a game players go to losers tournament. Prior information from the winners tournament can be used. The later a player loses the better he is considered. Here is an exaple of the losers tournament. Letters come from losing the corresponding games in the wiiners tournament (see the first diagram). -m--
\
\ ----
-l--
/ \
\
/
\
----
\
/
\
-k--
\ ----
-j--
/ \
\
/
----
\
/
/ \
-i--
\
/
\
\
/
\
----
\
/
\
/
\
-n--
\ \
\ ----> to final
-a-h
/ \
/
----
/
/ \
-b-g
/
\
/ ----
-c-f
/ \
/
----
/
-d-e
/
\
/ \
/
\
/ \
/
\
/ ----
/
/
/ /
/ -o--
At the last stage the players from the winners from the winners and losers tournament meet. It is possible to decide the winner in one or more games. Deciding in one game has the advantage that it is fast, the disadvantage is that thw winner of the winners tournament (WWT) does not get a second chance. (This could be justified by saying that he had to play fewer games). It is also possible to decide that if the WWT loses another game is to be played and the winner wins the tournament.
\ a ---/ \ ---\ i ------/ \ \ / \ b ---\ / \ ---\ m ------/ \ \ / \ c ---/ \ / \ / \ ---\ / \ j ---\ ---/ \ \ / \ d ---\ / \ ---\ o ------/ \ / e ---/ / \ / ---\ / k ---/ ---/ \ / \ / \ / f ---\ / / \ / ---\ / n ------/ \ / g ---/ / \ / ---\ / l ------/ \ /
h ---/ ----
If the organisers have no prior information on players strength the players can be assigned randomly in the diagram. If prior information is available it is preferable to have the expected number 1 and 2 meet in the last round. This is achieved by placing them on the different halves of the diagram. For the semifinals the choices to try are 1-3, 2-4 or 1-4, 2-3. The latter is preferable, since it also gives a chance that the second place is fought well. Generally at the k:th last round one can use the equation below: p+o = 2**k +1, where
p is players rank in the a priori order o is opponents rank in the a priori order If the number of players is not a power of 2 then the highest players are given byes.
Double knock out Double knock out cures some problems of the randomness of the result, but more rounds are needed. After losing a game players go to losers tournament. Prior information from the winners tournament can be used. The later a player loses the better he is considered. Here is an exaple of the losers tournament. Letters come from losing the corresponding games in the wiiners tournament (see the first diagram). -m--
\
\ ----
-l--
/ \
\
/
\
----
\
/
\
-k--
\ ----
-j--
/ \
\
/
----
\
/
/ \
-i--
\
/
\
\
/
\
----
\
/
\
/
\
-n--
\ \
\ ----> to final
-a-h
/ \
/
----
/
/ \
-b-g
/
\
/ ----
-c-f
/ \
/
----
/
-d-e
/
\
/ \
/
\
/ \
/
\
/ ----
/
/
/ /
/ -o--
At the last stage the players from the winners from the winners and losers tournament meet. It is possible to decide the winner in one or more games. Deciding in one game has the advantage that it is fast, the disadvantage is that thw winner of the winners tournament (WWT) does not get a second chance. (This could be justified by saying that he had to play fewer games). It is also possible to decide that if the WWT loses another game is to be played and the winner wins the tournament.
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