In a comment, Donald the Potholer suggested that there was a way of getting the simulator to run a Swiss-style tourney. At the time I thought he was incorrect, but with further thought, I see that it is possible to do this in a limited way, specifically for 32 players in five rounds. I stand corrected (and somewhat in awe of a reader who can infer from other discussions capabilities of my simulator that I didn’t realize it had).
So how would a Swiss Miss have fared had she been allowed to join the FOTA 32 pageant?
To admit the Swiss Miss, we’ll need to alter the rules. The five-round Swiss produces a single, unique winner from 32 entrants. But instead of a unique second place, as you’d get from any of the other designs we’ve considered, she produces a five-way tie for second place.
Now, if I were setting a payout schedule for this pattern, I’d be inclined to make it 50/10/10/10/10/10. It’s no good going for winner takes all because in that case the Swiss is identical to the single elimination. If we want to keep the top prize at 65, we’ll have to make it 65/7/7/7/7/7.
It works like a charm. After fleshing our her rounds with the 55779 pattern that worked for the single elimination, Swiss Miss brings home a stunning f(C) of 40.18. That’s heaps better than the 47.77 posted by Miss DE32hCD!
But wait. Before we go snatching the crown from Miss DE32hCD, we’ll need to look at this result a bit more carefully.
One thing we learned from the abortive effort to derive optimal payouts is that fairness (C) loves payouts that spread the wealth. In fact, one way to achieve perfect fairness (C) on a 32 bracket is to simply give 3.125% of the prize fund to every player regardless of result. So some of that impressive gain in fairness comes simply from sharing the prize fund among six players rather than two.
How much? It’s hard to say. We can’t compare the Swiss Miss head-to-head against either Miss SE55779 or Miss DE32hCD because neither one of them identifies a top six players. But it is possible to compare the Swiss Miss against Miss 32TE. Miss 32TE, what with her third bracket, has four unique results and then a pair that are tied for fifth and sixth. Thus, we can get some indication of the effect of the Swiss Miss’ broad payout schedule by comparing 32TE at 65/35 with 32TE at 65/7/7/7/7/7.
Recall that Miss 32TE earned an f(C) of 49.89 with a 65/35 split. With the money split 65/7/7/7/7/7, Miss 32TE does better: 45.93. So perhaps four points or so of the Swiss Miss’ 40.18 is the result of paying more places. That still suggests that the Swiss Miss is considerably better than any of the others, or at least would be if she didn’t demand such an odd payout schedule.
As of now, my ability to simulate Swiss tournaments is rather narrowly limited to exact powers of two and the number of rounds needed to isolate a single winner. But for the special case, the fairness gain is impressive. It would not astonish me if, once they can be more rigorously tested, Swiss tournaments come to be regarded as the gold standard for fairness (C).
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