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More swiss tournaments, best in three shorter matches and clocks

Posted By: Matt Cohn-Geier
Date: Friday, 10 October 2008, at 5:50 p.m.

In Response To: More swiss tournaments, best in three shorter matches and clocks (Bill Riles)

A recent e-mail from me to Stick, UBK, and a few others:

Suppose you feel you are the stronger player and your choices are to play one 15-point match or a series of best-of-three 5-point matches. According to the Jacobs-Trice match equity tables with 100 ELO difference, you have 56% ME from -5, -5 and 61% ME from -15, -15. There are four ways for you to win, you can win all three matches (obviously if you win the first two the final is not necessary, but bear with me), you can win the first two and lose the third, you can win the first and third and lose the second, or you can lose the first and then win the next two. That comes to:

56% * 56% * 56% = 17.5616%
56% * 56% * 44% = 13.7984%
56% * 44% * 56% = 13.7984%
44% * 56% * 56% = 13.7984%

Which adds up to about 59%. Since your ME is 61% from -15, -15, you are significantly better off going with the 15-point match rather than the series.

Your equity from -10, -10 on the 100-point ELO tables is 59%.

Similarly with a 50-point ELO table. Your ME from -5, -5 is 53.1%. Your chances of winning are:

53.1% * 53.1% = 28.1961% +
53.1% * 46.9% * 53.1% = 13.2239709% +
46.9% * 53.1% * 53.1% = 13.2239709%

which adds up to 54.6440418%. This is very slightly more than your equity from -10, -10 vs. a 50-point ELO underdog (54.5%). Since you are slightly better with the series vs. a 50-point underdog and indifferent between the series and the 10-point match with a 100-point ELO underdog, it stands to reason that as skill effects increase, you should prefer the 10-point match to the best-of-three 5-pointers. Granted, I haven't done the calculations for these.

So, unless you think there is a problem with the Jacobs-Trice tables, a 10-point match is about equivalent to a best-of-three 5-pointer series.

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