As a 3-player fan myself, I've been working on a bracket for ranked/seeded 3p tournaments, since I can't find any good examples of such online. So far, I have two prototypes for anyone who wants to take a gander:
PROTOTYPE #1: DOUBLE UNDERDOG
In regular 2p tournaments, the highest-ranked player is paired up with the lowest ranked, and so on and so forth. The later rounds are constructed expecting the higher ranked player to advance each time. This first prototype pits the top-ranked player against the two bottom-ranked players, and so on. Here is a mock-up of what a ranked 81-entrant 3p tournament would look like under this model:
1-80-81|26-30-31|27-28-29
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8-66-67|12-58-59|13-56-57
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9-64-65|10-62-63|11-60-61
======================
2-78-79|24-34-35|25-32-33
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6-70-71|16-50-51|17-48-49
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7-68-69|14-54-55|15-52-53
======================
3-76-77|22-38-39|23-36-37
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4-74-75|20-42-43|21-40-41
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5-72-73|18-46-47|19-44-45
PROTOTYPE #2: TOP-MIDDLE-BOTTOM CYCLING
If you notice in 2p tournaments, when you sum up the first-round ranks (and expected ranks for each later round) for each match, all the sums will be the same (65 in the first round of a 64-player tournament, for example). This prototype uses a "simple" method to create 3-player match-ups that result in identical rank sums.
To do this, split up the total ranks (assuming it's in the form of 3^n) into thirds -- one top-third, one middle-third, and one bottom-third. Split each third into thirds again, and so on until you can't split them anymore. At each split, label each rank based on what third it was split into this time. For example, in the 81-rank mock-up below, rank 23 is in the first top-third, so it received a T. In the next split, it was in the bottom third, so it received a B. Next split, it's in the middle third (M). In the final split, it was the middle of three (M). Thus, #23's final designation is TBMM.
To match up the ranks, start with the expected final round of 1-2-3. Right now, that's just a simple T-M-B. For a 9-player tournament, 1, 2, and 3 are all in the top-third, so they would now be TT, TM, and TB, respectively. The rest (4, 5, 6, 7, 8, 9) would be MT, MM, MB, BT, BM, and BB, respectively. To find your match-ups, take a rank, then do one cycle up and one cycle down. For example, since rank 1 is TT, a cycle up would be BB (rank 9) and a cycle down would be MM (rank 5). If you had started with ranks 5 or 9, you'd get the same results. Do this for every round up until you are complete. Going back to 23, its first-round opponents in the 81-rank mock-up would be MTBB (rank 36) and BMTT (rank 64).
Here is the final mock-up for this 81-rank prototype. As you can see, each first-round rank sum is 123, each expected second-round rank sum is 42, and each expected third-round rank sum is 15:
1-41-81|14-54-55|27-28-68
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5-45-73|18-46-59|19-32-72
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9-37-77|10-50-63|23-36-64
======================
2-42-79|15-52-56|25-29-69
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6-43-74|16-47-60|20-33-70
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7-38-78|11-51-61|24-34-65
======================
3-40-80|13-53-57|26-30-67
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4-44-75|17-48-58|21-31-71
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8-39-76|12-49-62|22-35-66
Of course, if this 3p tournament were to be unranked, all of this is moot. Still, hopefully it's something to consider.
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Topic: 3-person isodom? (Read 4330 times)