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Optimal seatings changes
You're speaking about the current seatings. It doesn't mean there isn't a better seating for which rule 7 applies in full.Timo wrote: You are in your hunt for the best seating for 2R+F tournament.
But I was speaking of the seatings for 3R+F tournament where for 5 players tournaments, we have player 2 who play 2nd then 1st and 1st.
Without looking for extreme cases like 5 players tournaments, in 10 players tournaments, players 2 and 7 play twice in the second place and 3 and 8 twice in the 4th place.
We must first search better seatings that enforce the current rules before thinking of changing them.
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Because the more constraints we have, the less possibilities we have. And since possibilities are exponentials, having the tighest constraints is essential to achieve computation.Timo wrote: Why that ?
What I mean is that the rules which FORBID to have a player playing 5th in 2 different rounds could potentially prevent a better VP/transfer repartition while having no good effect.
The rule "COULD potentially prevent" (emphasis mine) some better results. But maybe it doesn't. On 2R it doesn't change anything, I haven't studied 3R yet.
If you have some spare time, try to find one seating where the rule prevents a better seating. If it does, okay we may think about dropping it. If it doesn't, it's a easy way to reduce the number of possible seatings.
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If you inforce strictly rule 7 (7. A player doesn't play in the same seat position, if possible.), it cuts branches in the tree of possibilities.Timo wrote: It is only a constraint of computing time ?
So you will gain some time when checking your conditions and so deleting this rule which is redundant with the rule 7 every time when you have reach a number of player big enough to avoid infringing rule 7 (always for 2R+F as you have pointed out).
And for the few cases where you have to add some odd seatings which would have been already eliminated, I guess the additional compuing time is meaningless compare to the size of the data no ?
For instance, when I must seat player 4 of a 10-players table, it removes 2 possibilities for 4. Let's say I have 5,6,7,8,9 and 10 to seat afterwards, I'm saving 2 * (5 * 4 * 3 * 2 * 1) possibilities (because there would be 5 possibilities for 5, 4 possibilities for 6, 3 for 7 etc.). A little less in truth because 5, 6, 7... also have constraints, but it's really a huge save.
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I'm starting to work on 3R+F.
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