JH wrote:
> I have created a php-script to create random "optimal" seating orders.
> Inspiration for this were the numerous cases in local tournaments where
> a player would either join the tournament after a round or dropped
> before the preliminary rounds were over. In those cases TheArchon often
> fails to give a suitable seating order.
This is a great idea, and I'm excited that someone else has already
worked on it so much!
> Comments would be appreciated. If someone wants to test the form send me
> an e-mail or ask through the list and I'll give you a password for the
> trial.
I'd love to test it, and would happily look at source code, too. I'm
familiar with PHP, and have been working on the same problem for a
while, though I've been thinking about 2-round tournaments
specifically.
For anyone new to the discussion, here is a thread on optimal seating:
http://tinyurl.com/r63au
> Here are the optimal seating order criteria and their weighs:
All of your criteria are exactly right. Your weights may be wrong.
>From a private e-mail discussion I had with LSJ in Dec 2002, he made it
clear that a higher numbered rule is less important than a lower
numbered rule. For clarity, I'll just post that e-mail below, since I
think it's quite relevant to the discussion of using a computer program
to generate optimal seating charts.
> 3. Available VPs are equitably distributed.
> - If a player would have more vp available than average+1 or less than
> average-1 table rejected -> reroll
This may be slightly too simplistic. See LSJ's explanation in the
e-mail reposted below.
Ira
(in a private e-mail to me)
>From vte...@white-wolf.com Wed Dec 18 13:13:25 2002
Subject: Re: optimal tournament seating
At 06:00 AM 12/18/2002, you wrote:
>Hey LSJ,
>
> I have a few more questions about the seating rules; I can probably write
>a program to do "optimal" seatings, but it may be hard. Did you do all of
>the seating by hand?
Yes.
> Also, for all of these questions, assume I'm talking about 2 round
>tournaments. If the answer is different for 3 rd tournaments, feel free
>to elaborate if you have the time.
>
> > 2. No pair of players share a table through all three rounds, when
> > possible.
>
> So this rule can be completely ignored for 2 round tournaments, correct?
It would be "No players share a table in both rounds"
> > 3. Available VPs are equitably distributed.
>
> I'm not sure what this means. Does it mean that you must have only 4 and
>5 player tables? Are 3 or 6 player tables illegal?
4 and 5 are the only options.
What it means is that you can't have player A play at a 4-player table
in both rounds (8 available VPs) while player B plays at a 5-player
table in both rounds (10 avialable VPs). The maximum difference in
available VPs should be 1.
> > 4. No pair of players share a table more often than necessary.
> > 5. A player doesn't sit in the fifth seat more than once.
> > 6. No pair of players repeat the same relative position[*], when possible.
> > 7. A player doesn't play in the same seat position, if possible.
> > 8. Starting transfers are equitably distributed. [NOAL]
> > 9. No pair of players repeat the same relative position group[^], when
> > possible.
>
> What is the relative importance of these rules? For instance, what if
>one seating arrangement caused a player to sit in the same seat, and
>another causes a pair of players to repeat the same relative position, and
>everything else is equal. Which would be the more optimal seating?
The rules are listed in order.
A higher numbered rule is less important than a lower numbered rule.
> I would like to write a computer program to figure all this out, and
>ideally I'd like to give it numbers like:
>
>repeat predator prey = +1000000
>a pair of players sharing the same table = +10
>a player sitting in the 5th seat more than once = +10
>a pair of players repeating the same relative pos = +10
>a player sitting in the same seat = +10
>for each player, sum their transfers over all rounds. the target number
>is # of rounds times 2.5 transfers. For each player, for each transfer
>away from that number = +2
>a pair of players repeat the same relative position group = +5
>
> Obviously I'm choosing weights that will make a significant difference in
>the definition of "optimal." Once the weights are set, I run through
>every possible configuration, and the lowest total is the optimal one.
>
> Perhaps this whole endeavor is dumb, and if so, feel free to tell me
>that. :)
It's not dumb - it's difficult.
I've started down that path a few times myself.
Weight the highest numbered rule with a 1.
Figure out the number of "violations" of that rule that can occur.
Call that number X1.
Let the next rule be weighted at X1+1.
Figure out the maximum number of violations for that rule.
Let the next rule be weighted (X2+1)*(X1+1).
And so on.
> also, if player A and B are next to each other in round 1, and then
>sitting at different tables in round 2, then that satisfies all of the
>conditions, right?
So long as they're sitting in different numbered seats in each round
(player A isn't playing first in both rounds, for instance), and their
starting transfers are close (A sits at 1 and 2 while B sits at 3 and 4
would be improper by rule #8).
> Ideally, each round would be played against 4 new
>opponents, right?
Yes, but not possible until you get to 25 players.
(Or 16, where you see 3 new players each round).
--
LSJ (vte...@white-wolf.com) V:TES Net.Rep for White Wolf, Inc.
Links to V:TES news, rules, cards, utilities, and tournament calendar:
http://www.white-wolf.com/vtes/