TO Tips: Handling Imperfect numbers in Elimination formats

December 20, 2010

As a TO or Tournament Organiser, I am sure some of our readers have come across scenarios where they have to work on imperfect numbers in handling both Single and Double Elimination formats. The trick to handling these numbers is to plan ahead, not to just go ahead.

A successful TO will keep reminding himself of the number of participants for the day before using various means to pair and chart up the participants on the Tournament Tables.

Note: A perfect number is the result of 2 with positive integers as indices. The commonly used perfect numbers are 8, 16, 32, 64.

This post aims to help new or aspiring TO to understand how to handle imperfect numbers in Elimination formats. It should be read together with the previous guide on Single Elimination and Double Elimination for optimum understanding.

For the purpose of illustration, there will be 18 participants in “today’s tournament.”

Single Elimination

The crux in handling imperfect numbers is to achieve the perfect number as soon as possible. The number of participants in the tournament must be reduced to a perfect number after the end of the 1st round.

Take a look at the illustration to the left.

In this scenario, Matches 1 & 2 in the 1st round will each reduce 1 participant from the tournament. Starting from the 2nd round, there will be a perfect number of 16 remaining in the tournament. The rest of it will be simple single elimination leading to the victorious winner.


By eliminating earlier rather than later, we rule out the chance of having an odd or imperfect number in further rounds which will force a walkover to be issued. Although in Single Elimination, all matches are significant as a loss will send a participant home, the bearing of matches held in later rounds on the final outcome of the tournament have a higher weightage than matches held in earlier rounds.

Eliminate them early, save the day.

Double Elimination

Double Elimination poses more of a challenge to TO than Single Elimination due to the complexity of the Elimination Tables. This also raises the difficulty in handling the imperfect number. However, applying the same rationale and principle of eliminate earlier than later, we will work out an elimination table similiar to the above illustrations.

In Double Elimination, the earliest elimination occurs after the 2nd round of the event. That is exactly when the TO has to adjust the participants to a perfect number.

Refer to the illustration. Technically, the 1st round will only have match 1 & 2. However, to save time, the TO may conduct matches 3 to 8 at the same time. Thereafter, the defeated participant from match 1 will play in match 11, in the lower bracket, against the defeated participant from match 10. The same with the defeated participant from match 2, who will play defeated participant of match 9 in match 12. The rest of it complies directly as per normal in a double elimination.

Special Note:

Due to the complexity of the Double Elimination table, some TOs may be unable to make out that the Finalist of the Upper Bracket is ensured a top 3 finishing. This is a common mistake and should be avoided with extra precaution. In case you can’t make out which is the Upper Bracket finals, it is match 31. The overall winner will be the winner of Match 34. The defeated finalist of Match 34 is the runner up. The participant who lost in Match 33 and 32 will be 3nd and 4th respectively. Basically, the later you are eliminated from the event, the higher your ranking.

Ending Note:

Being a TO is challenging, but at the same time it can be fun. The only chance that it can happen is if you are sufficiently competent and know your stuff well. Poor management and low competency hurts your own reputation in the long run and adds to the list of dissastisfied players who will snowball your challenges as a TO. So know your stuff, and always put yourself in participants shoes when making key decisions.

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