Gnolaum
Sergeant
854 Posts
    
 | | 03/09/2006 1:04 PM |
| I've stated before that completely avoiding duplicate rares in a case is alot more difficult with 23 rares than it is with 24. The thought just struck me that it may in fact be impossible.
I don't feel like putting in the effort to prove it, but here is some preliminary information. Just in case someone fails their will save against their obsessive compulsive disorder... (everyone roll)
The least common multiple of 12 and 23 is 12*23=276, since 23 is prime. Thus the attempt is to distribute 12 of each of the 23 rares in 23 different cases.
Here is one case where it cannot be done (this is not a proof; to be a proof it must show that there is no case in which it can be done, to disprove it you must show 1 case in which it can be done)
1) Take 12 rares, 12 cases, and distribute one of each rare in each case.
This leaves 12 of each of the remaining 11 rares, and 11 cases.
2) Take the 11 rares and distribute 1 of each in the remaining cases.
3) You will have 11 cases with one slot left in each, and 11 rares, one of each is in each case. You matter how you distribute the remaining rares, you will end up with a duplicate in each of the 11 cases.
Thus this naive method will supply 12 cases with no duplicate and 11 cases with 1 duplicate.
Can you do better? I don't doubt that someone can, as stated with is a very naive attempt... | |
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The Defenestrator
AesophDarkfable
Warlord
5628 Posts
| | 03/09/2006 1:07 PM |
| | Why did you start a new thread for this? This could very easily have gone in the other thread that is discussing this. | |
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Gnolaum
Sergeant
854 Posts
| | 03/09/2006 1:12 PM |
| quote:
Originally posted by AesophDarkfable
Why did you start a new thread for this? This could very easily have gone in the other thread that is discussing this.
What other thread?
You mean the ones complaining about duplicate rares? Or the one about people complaining about people complaining about duplicate rares?
Entirely different discussion my friend, therefore an entirely different thread. | |
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Vash
Underboss
1995 Posts
| | 03/09/2006 1:13 PM |
| quote:
Originally posted by AesophDarkfable
Why did you start a new thread for this? This could very easily have gone in the other threads that is discussing this.
Fixed [:p] | |
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Benimoto
Underboss
1125 Posts
| | 03/09/2006 1:24 PM |
| For sure it's possible. It's not particularly easy or efficient, which is probably why Wizards didn't do it, but it's possible.
Here:
1. Take one set 23 rares and shuffle them into a random order. Do the same with another set.
2. Take the first 12 rares from the first set and put them into a case. Call this case 1.
3. Take the remaining 11 rares from the first set and put them into case 2.
4. Take one rare from the second set and put it into the last booster of case 2. If this would be a duplicate rare in the case, then take a rare from case 1, switch it with the duplicate and put the non-duplicate into case 2.
5. Repeat. When the second (filler) set runs out, make a new one.
Step 4 is the hard part, of course. Not incredibly hard, though. I'm a CS major, and I've taken industrial automation courses, and I think I could design a system that would automate this. I'm guessing that such a solution just wouldn't work with what they've got in place at the factory, which is why we have up to 3 duplicate rares in some cases. | |
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striderlotr
Commander
3370 Posts
| | 03/09/2006 1:31 PM |
| | Wow, now this is to much math... reminds me of a few games I've played... [)] | |
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Gnolaum
Sergeant
854 Posts
| | 03/09/2006 1:32 PM |
| Benimoto, I'm also a CS grad, and very nearly picked up a math degree on the way.
Your method may work, but I'm not sure. Please show how it would distribute 12 sets of rares (276 total), into 23 cases.
Thanks. | |
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Gnolaum
Sergeant
854 Posts
| | 03/09/2006 1:34 PM |
| quote:
Originally posted by Vash
quote:
Originally posted by AesophDarkfable
Why did you start a new thread for this? This could very easily have gone in the other threads that is discussing this.
Fixed [:p]
Have other threas actually discussed that it may be *impossible* to avoid duplicate rares in cases when there is 23 rares in the set? | |
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Gnolaum
Sergeant
854 Posts
| | 03/09/2006 1:38 PM |
| Nevermind, Altamont provided a trivial proof on the WoTC boards.
quote:
I don't agree.
case 1: rares 1 to 12.
case 2: rares 13 to 23, and back to 1.
case 3: rares 2 to 13.
case 4: rares 14 to 23, and 1 and 2.
case 5: rares 3 to 14.
...
case 23: rares 13-24
Confound it, trivial proof. | |
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Benimoto
Underboss
1125 Posts
| | 03/09/2006 1:38 PM |
| quote:
Originally posted by Gnolaum
Benimoto, I'm also a CS grad, and very nearly picked up a math degree on the way.
Your method may work, but I'm not sure. Please show how it would distribute 12 sets of rares (276 total), into 23 cases.
Thanks.
It would distribute 24 sets of rares (552 minis) into 46 cases.
To look at my system in another way:
1. Take 46 cases and line them up.
2. Take one full set of rares and put one in every other case.
3. Take another set and look at the first two cases. You have one rare in there already, so you have 23 empty boosters and 23 rares.
4. Take a duplicate of the rare that is already placed in one case, and put it in the other as well.
5. Divide the remaining 22 minis among the 22 empty slots any way you want.
6. Repeat 3-5 for the remaining 22 sets of two cases. | |
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Zenako
Commander
3469 Posts
| | 03/09/2006 2:04 PM |
| Well the simple answer is yes you can completely avoid duplicate rares in a case. No special shuffling need apply. For example.
Case 1 - Rares 1 thru 12
Case 2 - Rares 13-23 and 1
Case 3 - Rares 2 thru 13
Case 4 - Rares 14-23 and 1-2
Case 5 - Rares 3 thru 14
and so on.
All you need is a sequentially arranged filling stack to sort the boosters as they get filled. The commons and uncommons are an independant problem and do not relate to this calculation at all.
This of course depends on the booster lines not having any defects or packaging issues that perturbs the algorithm. So all I need are 23 bins for rares booster segregation (which does differ from other recent sets) and then control the allocation of each bin to the case being filled via actuators. Case 1 comes along - Bang drop boosters from Bins 1 thru 12 into it. Step to Case 2 and the next cluster of bins drop a booster to the case.
To keep up the random appearence of the booster mix, you could refill the bins each day or shift with a different arrangement for the next collection of cases. If the same pattern was retained throughout, I am fairly certain we would have learned of it. Much like what happened with GoL where you almost always got the same three Huge Rares in a case each time (HRD, HGD and X) while the other case in the "pair" had (Titan, Glab and Y).
Now mechanical glitches in the filling system can occur and perhaps at a final stop before the carton goes to sealing, the inspector looks for a full case, if missing boosters, they can take as many as needed from the stock they have to make up shortfalls and fill the case. | |
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Zenako
Commander
3469 Posts
| | 03/09/2006 2:05 PM |
| | hmmm maybe I need to look over at those other boards sometimes... since I came to the exact same proposal... | |
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robby
Sergeant
918 Posts
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True_Blue
Underboss
2386 Posts
| | 03/09/2006 2:22 PM |
| | Dupe rares happen.. not all the time, but its possible. If it happens to you, get ready to trade. | |
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glumag
Warlord
5968 Posts
| | 03/09/2006 2:25 PM |
| quote:
Originally posted by True_Blue
If it happens to you, get ready to trade.
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jgsugden
Commander
4320 Posts
Walnut Creek, CA
| | 03/09/2006 2:30 PM |
| WotC could have avoided duplicate rares. All WotC needed to do was design a distribution order that appeared to be random, but was in fact ordered to not include duplicate rares in any case. They'd simply go through the order and make sure that no figure appeared within 11 (or to be safe, 12 or 13) places int he same series. You'd just continue to follow the order between cases.
If they used a long enough order, it would have been nearly impossible for us to catch on. It'd be relatively simple to design such an order so that the same distribution of rares would occur in every 46th case, each rare would appear in equal numbers, and there would be no repeats.
However, designing such an order and implementing it would be quite different matters. I'm sure that making the factory workers/machines follow a set distribution order would be far mroe time consuming (although I imagine that the sorting speed would still be far faster than the painting speed). | |
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Vash
Underboss
1995 Posts
| | 03/09/2006 3:01 PM |
| quote:
Originally posted by jgsugden
WotC could have avoided duplicate rares. All WotC needed to do was design a distribution order that appeared to be random, but was in fact ordered to not include duplicate rares in any case. They'd simply go through the order and make sure that no figure appeared within 11 (or to be safe, 12 or 13) places int he same series. You'd just continue to follow the order between cases.
If they used a long enough order, it would have been nearly impossible for us to catch on. It'd be relatively simple to design such an order so that the same distribution of rares would occur in every 46th case, each rare would appear in equal numbers, and there would be no repeats.
However, designing such an order and implementing it would be quite different matters. I'm sure that making the factory workers/machines follow a set distribution order would be far mroe time consuming (although I imagine that the sorting speed would still be far faster than the painting speed).
Something simple that I think illustrates your point (correct me if Im wrong of course)
Step 1: Shuffle all 23 rares.
Step 2: Seed case 1 with 12 different Rares
Step 3: Seed case 2 with the 11 remaining rares and 1 from the first 12.
Step 4: Repeat steps 1-3.
This would give us 'mated pairs' but they would be so sparsely populated throughout the world that it would be near impossible to find both parts of the pair.
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