Michael Tang today announced his intention to bring back the Grand Causeway Challenge during the 1st week of December 2016. This will be an individual tournament, as opposed to the traditional Causeway Scrabble Challenge which is a team tournament, revived last year with host Singapore beating Malaysia 102.5-97.5, and set to continue this year with Malaysia hosting Singapore in the first half of August.

The Grand Causeway Challenge will be held over 5 days with a total of 45 games. The format will be King of the Hill (KOTH) with repeats for the entire 45 games, with players grouped into divisions of 50 by their WESPA ratings. Incidentally, 45 rounds of KOTH with repeats was also the format for the premier division of the last edition of Causeway in 2011.

Supporters of the KOTH with no repeats find the format appealing for its transparency and simplicity (as opposed to some more sophisticated pairing systems which may invite scrutiny and even suspicion of unfairness by those who don’t fully appreciate the logic), and its supposed ability to prevent the leader from running away (and hence keep the tournament exciting for a longer time). Its detractors though feel that the pairing unfairly punishes the early leaders who will keep getting tougher opponents. Also, people who want diverse opponents may dislike the prospect of meeting the same player again and again in the same tournament. An exceptional example of this occurred no other than in Causeway 2011, where Phillip “the Phenomenon” Edwin-Mugisha played Rodney Judd a whopping 17 times out of the 45 games.

So naturally the question popped up in discussions here: what is the maximum number of repeats that can occur in a 45-round no-repeat KOTH? Mathematically, it would be 45 (i.e. if player 25 and 26 tied all 45 of their games), but of course this is too remote a possibility. Without ties, some theorize that at most there will be half of the rounds plus 1, i.e. 23 repeats. One argument also surfaced that Causeway 2011 premier division had a big gap of rating among the players which caused the excessive repeats, which may not occur in a tighter division. I decided to find out empirically instead.

I simulated 1000 tournaments with 45 rounds KOTH-round of no-repeat consisting of 50 players selected from among the current top 100 rated players in WESPA ratings, ranging from Nigel Richards (rating 2298) to Quickpen Ben (rating 1918). The 50 are randomly selected with the exception of Nigel, who is included in every tournament.

The maximum derived from the simuation, which happened twice in the 1000 tournaments, is 26 games. In both cases it’s where somebody managed to push Nigel to the limit at the top: Nigel beat Adam Logan 14-12 in one virtual tournament, and Conrad Bassett-Bouchard 15-11 in another. For repeats at the bottom half of the field, 24 games were played between Trevor Hovelmeier and Andrew Goodwin in one instance. The Mugisha-Judd episode doesn’t seem that ridiculous now.

However, looking at the whole data shows even more how common such repeats are.

Here clearly it can be seen that although 26 head-to-head games is an outlier, repeats in the double digits are actually the norm. The average highest number of repeats across 1000 tourneys is * 14.29*, (standard deviation of 3.20). A 16-peat happens 7.5% percent of the time. Note that this simulation does allow ties between players, but the prevalence is low (.4% of the games) and it doesn’t seem to affect the amount of repetition.

So if Grand Causeway Challenge does proceed with its KOTH full repeat format, you better make sure you’re in the middle of your division, or be prepared to make a very good acquaintance with another fellow player of comparable rating.

My take would be that once a player is out of contention for place, you earmark them to have no repeats, purely so those players at the bottom of the pool get variety.

Interesting graph-work. If it is normal for one pairing to occur say 12-14 times, what is the average subset of the field played by a given player, and how does that change as your win expectation increases? What I mean is, could it be the case at extremes that one very good player might just face four or five different opponents, most of the time?

Andrew, interesting area to observe, I’ll investigate and update in the next post.

To note though that Barry ran a separate simulation and his result shows that the max most-repeats was 20 times, with an average at 8.5 . Sounds plausible, but we haven’t worked out where the simulations may differ, with the likeliest possibility at the moment being how we modeled the simulated spreads.

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