For the math experts (random draw of decks)

For the math experts out there, I'd like to ask some help and advice on this. I've tested a simple method of deck distribution last year during a sealed deck tournament and it went quite well (9 players), but I lack the math skills to calculate the real difference in probabilities. I thought it would be good to add some choices to players and therefore diminishing the chances of everybody not being really satisfied with the deck they get during this type of event, and thought it would be good to our pre-release events (delayed for one week due to customs problems). Basically, the organizer asks for each player to prioritize their choices given the decks available. So, let's say, I'd like to get the Baali deck, Alastor second, !Gangrel third. The organizer polls the results and see which decks had too much demand based solely on the players' first options. If he has the available number to give one type of deck or another to all that chose it as first option, he does it. Say that he has 4 copies of each deck available and only 2 players chose Alastors. They get that deck. Conversely, say that 6 players chose Baali. The organizer uses some random method to assing the 4 copies available between these players. The two unlucky ones don't get the Baali deck (say I am one of these two). Now the organizer compares which players are left with no deck and which copies are still available. He repeats the process using any player's second option. In our example there are still 2 Alastors. Say that me and two other players chose Alastor as second option. We enter a new round of random assignment. This time I'm in and get the Alastor deck. The third player is left to a new round based on third options, and so on, until everyone gets one deck to play. I assume this method greatly reduces the chance of everyone getting a third or fourth option, and at least introduces the notion that if one gets a deck they'd not normally choose, they have to be out of luck in two or three drawings instead of just one. But besides these pratical conotations, I'd like to know if I'm right regarding math. I suspect that a single, simple drawing means that *all* players could potentially get what would be otherwise third and fourth options, even if some chose decks that are not all too popular in their metagames, while the method I've used last year guarantees that at least some get their first option and maximize the chances to make (almost) everyone get their first or second options. I suspect that in my city most will choose Alastor, per example, so a single drawing could frustrate people who choose Baali or Anathema, even if not that many players want these and there are plenty of copies to satisfy them. Could someone calculate the probabilities to confirm if my suspicions are correct? best, Fabio "Sooner" Macedo V:TES National Coordinator for Brazil Giovanni Newsletter Editor ----------------------------------------------------- V:tES Brasil Site (only in Portuguese for now) http://planeta.terra.com.br/lazer/vtesbrasil/

Fabio "Sooner" Macedo wrote: > I suspect that a single, simple drawing means that *all* players could > potentially get what would be otherwise third and fourth options, even > if some chose decks that are not all too popular in their metagames, > while the method I've used last year guarantees that at least some get > their first option and maximize the chances to make (almost) everyone > get their first or second options. I suspect that in my city most will > choose Alastor, per example, so a single drawing could frustrate > people who choose Baali or Anathema, even if not that many players > want these and there are plenty of copies to satisfy them. Could > someone calculate the probabilities to confirm if my suspicions are > correct? (I assume by "simple drawing" people draw numbers, and then pick a remaining deck in order of number drawn.) Under your method, at least as many, and probably more, people will get their first pick (exact probabilities depend on how many people want each starter, of course). Conversely, less people will get their second or third pick. So you'll have more people who have their first pick, and more people who have their fourth pick. Whether this is preferable or not is up to you. It punishes people who pick the most popular starter, and rewards the people who pick the second or third most popular starter. People who pick the least popular starter are unaffected -- there will never be a situation where they won't be able to get it. --Colin McGuigan

Fabio "Sooner" Macedo wrote: > I suspect that a single, simple drawing means that *all* players could > potentially get what would be otherwise third and fourth options, even > if some chose decks that are not all too popular in their metagames, > while the method I've used last year guarantees that at least some get > their first option and maximize the chances to make (almost) everyone > get their first or second options. I suspect that in my city most will > choose Alastor, per example, so a single drawing could frustrate > people who choose Baali or Anathema, even if not that many players > want these and there are plenty of copies to satisfy them. Could > someone calculate the probabilities to confirm if my suspicions are > correct? (I assume by "simple drawing" people draw numbers, and then pick a [ quoted text not captured ]

> I've tested a simple method of deck distribution last year during a > sealed deck tournament and it went quite well (9 players), but I lack > the math skills to calculate the real difference in probabilities. There are a few too many permutations to consider to get paydata, I'd suggest giving the problem to a college student to do an Independent Study Project on. > The organizer polls the results and see which decks had too much > demand based solely on the players' first options. If he has the > available number to give one type of deck or another to all that chose > it as first option, he does it. Say that he has 4 copies of each deck > available and only 2 players chose Alastors. They get that deck. > I like your idea, good luck with it. > Conversely, say that 6 players chose Baali. The organizer uses some > random method to assing the 4 copies available between these players. > The two unlucky ones don't get the Baali deck (say I am one of these > two). > I'd actually offer to give people their second choices before using a random system. People with unpopular second choices can get their second choice and be relatively happy. Then, if the First Choice deck is still too much in demand, you roll off. > I assume this method greatly reduces the chance of everyone getting a > third or fourth option It does, but at some cost. Let's say we have 6 (AN) - 6 (B) - 2 (G) - 2 (AL). Worst case scenario is someone lists Baali and Anathema as their top 2. He has a 2/3 chance of getting his top choice - versus 1/4 - but a 0 chance of getting his second choice - versus 1/4. If the numbers are 6 (B) - 4 (AN) - 4 (G) - 2 (AL), the two players who miss out on Baali get Alastors, regardless of where it lies in their priorities. > I suspect that a single, simple drawing means that *all* players could > potentially get what would be otherwise third and fourth options That's why all of the sealed play I've seen allowed you to trade your deck. An even number of each deck is drawn for the group, and everyone gets assigned a random starter, allowed to trade before opening it. Even if you do implement your system, I'd still give people the chance to trade decks, on the off chance that Person A's Third Choice is more personally satisfying than Person B's Second Choice.

You might try adapting one of the methods for assigning powers in Diplomacy, since quite a lot of noses have been poked into that bag. (In fact, it sounds like the method you adopted was a parallel to method 2A here http://www.diplom.org/Zine/F1998M/Tarzan/assign.html ) It seems that method 2C is the fairest, but then you also have to come up with an accurate "satisfaction" weighting. It's also the most complicated to compute, IMO. -- LSJ (vte...@white-wolf.com) V:TES Net.Rep for White Wolf, Inc. V:TES homepage: http://www.white-wolf.com/vtes/ Though effective, appear to be ineffective -- Sun Tzu

On Tue, 22 Feb 2005 14:17:16 -0500, Gregory Stuart Pettigrew <ethe...@sidehack.sat.gweep.net> wrote: >> Conversely, say that 6 players chose Baali. The organizer uses some >> random method to assing the 4 copies available between these players. >> The two unlucky ones don't get the Baali deck (say I am one of these >> two). >> > >I'd actually offer to give people their second choices before using a >random system. People with unpopular second choices can get their second >choice and be relatively happy. Then, if the First Choice deck is still >too much in demand, you roll off. That's a good advice. I didn't take into consideration that now we get 4 choices (I tried it with Anarchs decks, only 3 choices for 9 people. Maybe this changes probabilities, I really don't know). >It does, but at some cost. Let's say we have 6 (AN) - 6 (B) - 2 (G) - 2 >(AL). Worst case scenario is someone lists Baali and Anathema as their top >2. He has a 2/3 chance of getting his top choice - versus 1/4 - but a 0 >chance of getting his second choice - versus 1/4. >If the numbers are 6 (B) - 4 (AN) - 4 (G) - 2 (AL), the two players who >miss out on Baali get Alastors, regardless of where it lies in their >priorities. Oh yeah, I didn't think of that. But I see some point in checking in with other players to know the risks of going for the most popular option. It becomes a "no pain, no gain" situation. I like that, seems like gambling without the dreadful conotations of it. >> I suspect that a single, simple drawing means that *all* players could >> potentially get what would be otherwise third and fourth options > >That's why all of the sealed play I've seen allowed you to trade your >deck. An even number of each deck is drawn for the group, and everyone >gets assigned a random starter, allowed to trade before opening it. Even >if you do implement your system, I'd still give people the chance to trade >decks, on the off chance that Person A's Third Choice is more personally >satisfying than Person B's Second Choice. It will be allowed, of course. Just forgot to mention it, sorry. Many thanks for your insights! best, Fabio "Sooner" Macedo V:TES National Coordinator for Brazil Giovanni Clan Newsletter Editor [ quoted text not captured ]

LSJ wrote: > You might try adapting one of the methods for assigning > powers in Diplomacy, since quite a lot of noses have been > poked into that bag. > > (In fact, it sounds like the method you adopted was > a parallel to method 2A here > http://www.diplom.org/Zine/F1998M/Tarzan/assign.html > ) > > It seems that method 2C is the fairest, but then > you also have to come up with an accurate > "satisfaction" weighting. > It's also the most complicated to compute, IMO. Or, you could simply debate which satisfaction table best suits your group among the seven players. Meta meta meta. ;) Jeff

On Tue, 22 Feb 2005 14:17:16 -0500, Gregory Stuart Pettigrew <ethe...@sidehack.sat.gweep.net> wrote: >> I assume this method greatly reduces the chance of everyone getting a >> third or fourth option > > It does, but at some cost. Let's say we have 6 (AN) - 6 (B) - 2 (G) - 2 > (AL). Worst case scenario is someone lists Baali and Anathema as their > top > 2. He has a 2/3 chance of getting his top choice - versus 1/4 - but a 0 > chance of getting his second choice - versus 1/4. > > If the numbers are 6 (B) - 4 (AN) - 4 (G) - 2 (AL), the two players who > miss out on Baali get Alastors, regardless of where it lies in their > priorities. You could assign the Alastors to those aspiring Baali players who had Alastors highest up. Like, if two have it second, the problem is solved. I made a sum-utility matrix (that was loosely based on the transportation model) that aims to maximize the total combined utility of all players participating. From that apporach, giving the most possible number of players their first picks is the best solution (because in the majority of cases the majority of players will get their first pick). Shuffling with deviance-from-group-average-utility is a poor choice, given how few options there are (If your options are assigning 12 first picks, 2 second and 2 third picks, or to assign 10 first picks and 6 second picks, it is probably better to go with the former - that way, 3 out of 4 players get their first picks). -- Bye, Daneel

On Tue, 22 Feb 2005 15:56:53 -0500, "LSJ" <vtesr...@TRAPwhite-wolf.com> wrote: >You might try adapting one of the methods for assigning >powers in Diplomacy, since quite a lot of noses have been >poked into that bag. >(In fact, it sounds like the method you adopted was >a parallel to method 2A here >http://www.diplom.org/Zine/F1998M/Tarzan/assign.html >It seems that method 2C is the fairest, but then >you also have to come up with an accurate >"satisfaction" weighting. >It's also the most complicated to compute, IMO. Thanks! For the sake of brevity (and lack of an available PC/laptop at the event) I'll leave 2C aside, though I find it's a pity since it seems really the best method. I'm considering 2B. [ quoted text not captured ]