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What is the best (fairest and most efficient) way to tie-break 4 player round robins?

Posted By: Neil Robins
Date: Tuesday, 4 October 2016, at 8:31 p.m.

In Response To: What is the best (fairest and most efficient) way to tie-break 4 player round robins? (sebalotek)

For my suggestion: Why not, for example, an 11pt match and a 9pt againt each opponent? Two players with four wins: then three wins in 11pter and one in 9pter beats two wins in 11pter and two in 9pters. After that, two way tie settled in favour of the winner of the 11pter between them.

So there will be no 2-way ties and actually there can be no 4-way ties either because 4 players with 3 wins each cannot all have the same number of 11pt wins.

I think the possibility of a 3-way tie should be at its highest when all matches are essentially 50/50.

So I figure to get a 3-way tie between players a, b amd c, first each must have one 11 and one 9 win among mathes between a,b and c. Whatever the results of the two matches between a and b, the other 4 matches a v c and b v c have to go a specific way. (1 in 16)

Secondly, whatever the results a has v the fourth player d have to be exactly matched in another 4 matches b v d and c v d (up to 1 in 256 for an a,b,c tie)

Finally there are 4 possible combinations of 3-way ties, bringing the maximum chance you will have any tie to break on my system to 1 in 64, if I have calculated correctly.

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