Re: 61 or more cards in toolbox decks
Mind you, I'm not arguing that I know a 61 card deck that can't be made better by removing a card. I'm just trying to say that that deck could exists. And that the burden of proof is on the person who says that something is *always* better than something else.
And if I'm allowed to construct fake cards, I could show an example. But that's just an effort in futility, as we're not playing in an imaginary world. In addition, I could most likely construct a deck with real cards that would have this property as well. However, that deck probably wouldn't be competitive, so would it really matter?
In addition, this is all just silly. If we can show that one deck is better than another, then that implies that there is exactly one best deck for each tournament. And what fun would that be?
Let's face it. No one can prove that 60 cards is always better than 61. No one can prove that there's a 61 card deck that can't be made better by cutting a single card. Everyone accepts that 60 cards is typically better than 61. And I think everyone would acknowledge that if you go with a 61 card deck instead of a 60 card deck, your chances of winning go down so little that it might affect you losing an additional game once every 100 or so tournaments. So people, just do what you want, and stop saying you can prove one thing or another!
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
tivadar
And that the burden of proof is on the person who says that something is *always* better than something else.
That's preposterous. That means if I were to come up with some crackpot rule it is your job to prove me wrong and until you do so I am infallible.
In any scientific argument, it is the burden of the person with the new theory trying to argue against the old theory to prove their point. I don't know why everyone thinks otherwise.
Similarly, I don't understand how people can say that the math behind why 60 would be better is wrong and then go ahead and talk about how the minute mathematical difference is offset by the alleged game-winning 61st card that just can't fit in the first 60.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
SpencerForHire
That's preposterous. That means if I were to come up with some crackpot rule it is your job to prove me wrong and until you do so I am infallible.
In any scientific argument, it is the burden of the person with the new theory trying to argue against the old theory to prove their point. I don't know why everyone thinks otherwise.
Ok, since "60 cards is the best" is the old theory, could you show me the evidence to back up that theory? Where's the study comparing 60 card decks to 61 card decks? Where's the proof that it's statistically significant? Point is that there's no "old" and "new" theory. No one knows these things and it's impossible to prove either. This doesn't even get into the fact that people are trying to say 60 card decks are *always* better, which is an even stronger statement. Of course the burden of proof is on the person stating that something is *always* true.
Quote:
Originally Posted by
SpencerForHire
Similarly, I don't understand how people can say that the math behind why 60 would be better is wrong and then go ahead and talk about how the minute mathematical difference is offset by the alleged game-winning 61st card that just can't fit in the first 60.
The proof that 60 is always better than 61 using the probability of drawing a good card is wrong. Its wrong because its based on the fact that if you remove the card with the lowest win percent from your deck, then clearly the average of the remaining cards is higher. What that fails to consider is that when you remove a card, those averages changes. So yes, I'm saying that that logic, as a *proof* is wrong.
I'm agreeing that 60 cards is probably best in almost all circumstances. But I'm also saying that no one can say that 61 cards is strictly wrong.
Re: 61 or more cards in toolbox decks
Well 40 red morphers and 20 islands is the same as 80 red morphers and 40 islands...but since cards are differentiated in most decks there is a hierarchy. It is definately possible to build a deck that runs better (or at least equal) at more then 60 cards...but the important part here is that you should build decks that run ideally at 60 cards.
I'll say this again...why is the argument between 60 and 61? not 60 and 80? If someone told you that you could make a 40 card minimum deck...would you still run 60/61 or 40/41?
Re: 61 or more cards in toolbox decks
Quote:
Ok, since "60 cards is the best" is the old theory, could you show me the evidence to back up that theory? Where's the study comparing 60 card decks to 61 card decks? Where's the proof that it's statistically significant? Point is that there's no "old" and "new" theory. No one knows these things and it's impossible to prove either. This doesn't even get into the fact that people are trying to say 60 card decks are *always* better, which is an even stronger statement. Of course the burden of proof is on the person stating that something is *always* true.
It's demonstrable, in a real way, that large decks, like 70+ cards, or limit N-->infinity decks are worse than 60 card decks, even if they keep the same ratio of cards.
It's also demonstrable that 40 card decks are much better than 60 card decks.
The tests we have are not powerful enough to prove that 61 is inferior per-se, but it seems ludicrous to me to believe that 61 is some magical number. You have to accept the fact that 40 cards are better than 60 cards, and the fact that 60 cards are better than N-->Infinity cards. You'd then be seeking to find evidence that the otherwise decreasing function for all testable values reverses its trend and shoots upward to a maximum at n=61.
Because the trend can and has been demonstrated that smaller decks are better for every tested value, the burden of proof lies on the "61 cards are good" camp to establish why 61 cards, even for a given specific deck, is an exception to the already established rule that fewer cards are better. It doesn't have to do with who used the word "always" or something stupid like that.
One camp says, "The trend probably holds, and 60 cards is always better."
The other camp says, "Somehow you guys are stuck with burden of proof, and you can't meet the bop, therefore 61 cards in my deck is better."
The only evidence with regard to deck quality that's been thrown out is the evidence that fewer cards is better, in general. Among other things, my principle of regression, and the fact that the cards you want to be 4-ofs are seen more often.
I will say that if I somehow believed I found a deck that is better with 61 cards, I would still run 60. The probability that I misevaluated it is much larger than the probability that my deck, for whatever reason, violates the established principle, even given the fact that I evaluated it to be better than the 60 card variant. See the taxicab problem.
By the way, Maveric, why the hell are you doing a monte carlo simulation for something that needs that much precision. Monte carlo is only useful for like poker bots trying to 6 table and only needing +/- 1% accuracy. If you need more accuracy, it's actually much slower to run Monte Carlo. Right now you're trying like 1E8 trials? There are probably at most a few million permutations of just bolts and lands.
Just go through every combination. It's much faster and will actually give you a precisely accurate result instead of a (large) margin for error. Also, once you set up the table of known win turn values, you can actually set your mulligan thresholds precisely instead of guessing.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
tivadar
Ok, since "60 cards is the best" is the old theory, could you show me the evidence to back up that theory? Where's the study comparing 60 card decks to 61 card decks? Where's the proof that it's statistically significant? Point is that there's no "old" and "new" theory. No one knows these things and it's impossible to prove either. This doesn't even get into the fact that people are trying to say 60 card decks are *always* better, which is an even stronger statement. Of course the burden of proof is on the person stating that something is *always* true.
There are about 3 pages of the statistical reasoning in this thread as to why 60 is the superior number. However, as usual, we ignore what has been put on previous pages because it hurts our argument.
The "to long didn't read" version is: I want to see cards X, Y and Z asap. I run as few other cards as I possibly can that allow me to have the most streamlined game plan. One card changes this by dramatically small amounts but in the end it will affect a game somewhere some how and that is not something we want. The argument against the 61st silver bullet is because it can just as easily have been a card in your maindeck or sideboard if the deck was tuned tighter.
Re: 61 or more cards in toolbox decks
Ok, first, 60 cards is better than 61 most if not all of the time. I don't mean to be "ludicrous" and suggest otherwise. And yes, 61 *is* actually a magic number of sorts. It's the number of cards that's not what people expect you to be running that gives you the best statistical odds to draw what you want. Back in the days of Solidarity reigning, I know this can and did come into play. Many people ran 61/62 card decks to throw the math off for a good Solidarity player. I don't think these people were wrong at all and I know that there are games that they won because of it.
Quote:
Originally Posted by
Rico Suave
There is *always* a weakest card in the deck, just like there is always a strongest card in the deck. It may be difficult for us to decide which is the weakest, but it is there. Even if a number of cards end up being metagame decisions, there is still a weakest card.
Quote:
Originally Posted by
Rico Suave
No it is not always the same, but there IS a weakest card. As such, you should cut it.
This is what I'm trying to argue against. Somehow this thread devolved from "what, if anything, should I cut from this survival deck" to "a 61 card deck has to be inferior and there's proof". In general, I don't think that 61 card decks are good. But the argument above just don't hold water. A situation may exist where there is a weakest card in your deck and you *shouldn't* cut it.
Anyways Forbiddian, you're right, in terms of burden of proof, if you have a 61 card deck, cut a card. You're 99.999% doing yourself a favor. I guess I'm just cringing at the people who say "well clearly 61 cards is wrong and here's a proof!" We haven't really proved that.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
tivadar
Ok, first, 60 cards is better than 61 most if not all of the time. I don't mean to be "ludicrous" and suggest otherwise. And yes, 61 *is* actually a magic number of sorts. It's the number of cards that's not what people expect you to be running that gives you the best statistical odds to draw what you want. Back in the days of Solidarity reigning, I know this can and did come into play. Many people ran 61/62 card decks to throw the math off for a good Solidarity player. I don't think these people were wrong at all and I know that there are games that they won because of it.
I mean, that's a decent point, that good players were trying to run 61 cards at some point (for a reason other than deck quality -- to trick the opponent) but:
What good solidarity player wouldn't pile shuffle his opponent's deck before the game and count the cards out? Especially if this was a trick pulled by "many" people. Wouldn't good solidarity players know that trick?
A lot of people do that anyway to make sure the opponent has at least 60 (and if it's not exactly 60, you count the sideboard and call a judge, yippie!). If you stick your opponent with just one game loss, you're addicted!
There would have to be a preposterously slim minority of Solidarity players who 1) Care enough to count your graveyard, hand, and cards in play and then subtract (and then divide by 3), 2) Don't care enough to count your deck during shuffling, 3) Spot your library up and think it's faster to count cards in hand/graveyard/RFG/in play than it is just to count the library, 4) it actually happens in a game where they play their storm count EXACTLY to whatever would kill you and then you're able to win with the 1-2 extra cards before decking.
3 is rare, because the lethal storm count would have to be < 10 (and maybe even <7) for him to make a divergent decision to Brainfreeze rather than attempt to stack more storm count, and then it's much faster to count the library at that point than it would be to account for 30 cards in play, graveyard, RFG, etc.
Anyway, I can't imagine that was a profitable move even at the height of Solidarity. You might know a guy who knows a guy who once had it matter where he had a card left and then topdecked the lightning bolt and swung in for lethal.
But I know a guy who knows a guy who lost because he ran 61 cards and the 61st card was shit.
Re: 61 or more cards in toolbox decks
@ Forbiddian
Quote:
By the way, Maveric, why the hell are you doing a monte carlo simulation for something that needs that much precision. Monte carlo is only useful for like poker bots trying to 6 table and only needing +/- 1% accuracy. If you need more accuracy, it's actually much slower to run Monte Carlo. Right now you're trying like 1E8 trials? There are probably at most a few million permutations of just bolts and lands.
Just go through every combination. It's much faster and will actually give you a precisely accurate result instead of a (large) margin for error. Also, once you set up the table of known win turn values, you can actually set your mulligan thresholds precisely instead of guessing.
Showing the inaccuracy of our personal testing was a good reason to draw randomly instead of going through the entire search space.
It's also much easier to generate X^Y random lists than computing the non-duplicate permutations (I think they are called Necklaces). Working on the code now (I am noob though, so I'd appreciate the help of any proficient programmer). It isn't feasible to just 'eliminate' duplicate permutations, we actually need to generate the smaller set without resorting to running through all permutations.
peace,
4eak
Re: 61 or more cards in toolbox decks
@Forbiddian
Did you actually try to compute the number of deck ordering?
It's 60!/(L!*(60-L)!)
Where L is the number of lands. If L=17, then this number approximately equals: 3.87 10^14
And then, you still have to consider all the mulligans states (from 7 cards to 1 card initially drawn).
However you could consider that the game is reasonnably always over at turn T, when the number of drawn cards are 7+T. If you choose T=20. Then the number of orderings is much less, but difficult to count and each of these does not have the same weight in the mean (it's depending on how many combinations, there exists in the remaining 60-T-7 cards). I still believe that Monte Carlo is the best way to tackle the problem so far. May your creativity prove me wrong!
Edit: The best way to tackle the problem is probably to treat each game opening, treat it until kill, and then compute how many combinations in the library are remaining. It looks possible but much more complex (both theoretically and algorithmically) than what I did in a couple of hours of my time.
Edit2: Actually, it's interesting. I'll give it a look. Damn you.
Re: 61 or more cards in toolbox decks
There are two valid reasons to run a 61-card deck;
1) You're about to enter a tournament, made some last minute changes, and really don't know what else to cut. In this case it's perfectly possible that removing the wrong card will do more damage than running 61 cards.
2) You anticipate getting your opponents to count your deck via discreet means, i.e. pile shuffling and expecting your opponent to do likewise, and you want them to discover the odd number of cards you're running and become pissed off. The optimum number in this case is actually 63, as they might consider 61 or 62 borderline reasonable if they're bad players. People actually get pissed off about this kind of thing, or if they see you running shitty cards like Scrying Sheets or Helldozer or whatever.
On a side note, the odds of drawing your 61st-best card on any given draw in a 61 card deck is 1.63%. That's really not insignificant. To put that in perspective, only 1.58% of the world's population is Mexican. That means that if you consider the distinction between 60 and 61 cards to be immaterial, it's equivalent to wiping the entire country of Mexico off the map.
Take a stand against genocide, kids. Just cut down to 60 fucking cards.
Re: 61 or more cards in toolbox decks
Algorithm.
Quote:
For all the 8+7+6+5+4+3+2=35 possible starting hands I've already explicited (knowing you'll never muligan to 0) {
...T=0
...Label 0
...T++
...Draw shock.
...Play your turn.
...If you don't kill, goto Label 0 and place label T.
...Remove Label T.
...Compute kill turn and how many card combinations are remaining in the library. Save it.
...Undo last draw.
...Draw mountain.
...Play your turn.
...If you don't kill, goto Label 0 and place label T.
...Remove Label T.
...Compute kill turn and how many card combinations are remaining in the library. Save it.
...Undo last draw.
...T--
...If T!=0, goto label T.
...Else, compute this starting hand performance expectation by average of the turns T weighted by the number of card combinations remaining in library.
}
Apply mulligan optimisation.
Compute (and enjoy) the exact performance expectation computation.
The algorithm is clunky and it would be much easier with a backtracking program language such as Prolog.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
TheInfamousBearAssassin
Take a stand against genocide, kids. Just cut down to 60 fucking cards.
I don't get your rhetoric here. Cutting to 60 is considering that Mexicans are worse than every other population and that the world would be better without them.
But I think that we have actually no way to know that the Mexicans are the right population to cut to have a perfect 6 billions world. I'd rather cut Americans actually, since it would probably lower the magic staple prices. If we don't have anymore enough population to reach the perfect 6 billions world, I'd add some scandanivian chicks. It can't be a bad move.
Re: 61 or more cards in toolbox decks
My current code is simply trying to generate and count them, no additional layers to it, just for maximum speed, and it is taking forever (I have no idea when it will be finished grinding through).
I asked for more help from some guy. He said he might be able help, but wanted more context. We might get some optimized algorithms for generating these permutations (although, it still just might be infeasible).
As a sidenote, I love tacos.
You all should read the previous thread Forbiddian had written in about this topic. His last few paragraphs were hilarious.
peace,
4eak
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
Maveric78f
@Forbiddian
I forgot that you would have to write your own hand evaluator. But yeah, you figured out a quick shortcut to running every junk permutation.
If you only look at the top 20 cards, there's around a million permutations even with 20+ lands.
The problem is, that each set is not equally likely (i.e. top 20 all bolts is more likely than top 20 all mountains in a deck with 20 mountains, 20 bolts), but there's a work around from poker that the calculators use:
There are essentially 18 different "sets" of 20 cards. Each corresponds to the different numbers of lands, from 0-17 possible.
If you can find the census data for each set, from 0-17 possible, you can simply multiply that result by the probability of having that many lands in the top 20, given the number of lands in the deck and the number of cards in the deck. Excel can do that from a binomial distribution.
This gives you your precise results.
Re: 61 or more cards in toolbox decks
The truth.
Thx Forbiddian for your inspiration on how to compute an exact expectation. The fact that these numbers are close to the Monte Carlo's experiment makes me confidant about their validity.
Quote:
Originally Posted by 16/60 lands
10.587769936773933
9.68029233802506 9.333333333333334
8.91651105153967 8.196075918587304 9.177777777777777
8.285715353417906 7.091908554611495 7.909090909090909 9.022222222222222
7.8262947901831525 6.118500687868058 6.627906976744186 7.7727272727272725 8.866666666666667
7.540851354835817 5.3597544979586615 5.333333333333333 6.511627906976744 7.636363636363637 8.71111111111111
7.384065821135743 4.947604073075771 4.422713095055479 5.238095238095238 6.395348837209302 7.5 8.555555555555555
7.294986035052628 4.8464535741727754 4.070699223085461 4.372973119298341 5.142857142857143 6.27906976744186 7.363636363636363 8.4
KEEP 10.587769936773933
KEEP KEEP 9.587769936773933
KEEP KEEP KEEP 8.64767809874312
KEEP KEEP KEEP MULL 7.705489238999487
MULL KEEP KEEP MULL MULL 6.764998174268332
MULL KEEP KEEP KEEP MULL MULL 5.764953959397981
MULL KEEP KEEP KEEP MULL MULL MULL 4.966470533203395
MULL KEEP KEEP KEEP MULL MULL MULL MULL 4.512281162092423
nbLands = 16.......4.512281162092423
Quote:
Originally Posted by 17/60 lands
10.624294806368624
9.655464211846283 9.545454545454545
8.82664047921042 8.362162576881676 9.386363636363637
8.134672608671687 7.20764700009983 8.093023255813954 9.227272727272727
7.624533066514198 6.176839336607616 6.785714285714286 7.953488372093023 9.068181818181818
7.3055460263007435 5.357598627787307 5.463414634146342 6.666666666666667 7.813953488372093 8.909090909090908
7.134306011763807 4.89246281321753 4.493448637316562 5.365853658536586 6.5476190476190474 7.674418604651163 8.75
7.045739166493884 4.772808312080466 4.089643985315462 4.440122086570478 5.2682926829268295 6.428571428571429 7.534883720930233 8.590909090909092
KEEP 10.624294806368624
KEEP KEEP 9.624294806368624
KEEP KEEP KEEP 8.67782070676439
KEEP KEEP KEEP MULL 7.722486903645516
KEEP KEEP KEEP MULL MULL 6.796786579991297
MULL KEEP KEEP KEEP MULL MULL 5.8195532693910925
MULL KEEP KEEP KEEP MULL MULL MULL 4.995895710988585
MULL KEEP KEEP KEEP MULL MULL MULL MULL 4.508071722338611
nbLands = 17.......4.508071722338611
Quote:
Originally Posted by 18/60 lands
10.697995442327246
9.668232691696732 9.767441860465116
8.7734498316054 8.53966094629725 9.604651162790697
8.017857465275538 7.336096485199108 8.285714285714286 9.44186046511628
7.453175126760033 6.2483664134607535 6.951219512195122 8.142857142857142 9.279069767441861
7.096478496677107 5.367587632493293 5.6 6.829268292682927 8.0 9.116279069767442
6.9077835608123594 4.846385193753615 4.570875665215288 5.5 6.7073170731707314 7.857142857142857 8.953488372093023
6.818800266267992 4.705405965783324 4.111976346569489 4.513958849141979 5.4 6.585365853658536 7.714285714285714 8.790697674418604
KEEP 10.697995442327246
KEEP KEEP 9.697995442327247
KEEP KEEP KEEP 8.745443846508444
KEEP KEEP KEEP MULL 7.776741940611625
KEEP KEEP KEEP MULL MULL 6.831795621197604
MULL KEEP KEEP KEEP MULL MULL 5.895177859592948
MULL KEEP KEEP KEEP MULL MULL MULL 5.047458620036484
MULL KEEP KEEP KEEP MULL MULL MULL MULL 4.522402653410277
nbLands = 18.......4.522402653410277
Quote:
Originally Posted by 16/61 lands
10.589052982968674
9.69801095179232 9.282608695652174
8.951833116080435 8.156667726202317 9.130434782608695
8.337771900533733 7.065244005994956 7.866666666666666 8.978260869565217
7.8924002570243585 6.106627462589219 6.590909090909091 7.733333333333333 8.826086956521738
7.616562200330913 5.363593121639736 5.3023255813953485 6.4772727272727275 7.6 8.673913043478262
7.464541082299129 4.965122489889009 4.40632742519535 5.209302325581396 6.363636363636363 7.466666666666667 8.521739130434783
7.376540153232717 4.868725666367176 4.066574628010431 4.358340820604972 5.116279069767442 6.25 7.333333333333333 8.369565217391305
KEEP 10.589052982968674
KEEP KEEP 9.589052982968674
KEEP KEEP KEEP 8.650692744097455
KEEP KEEP KEEP MULL 7.711887642684867
MULL KEEP KEEP MULL MULL 6.758307580713864
MULL KEEP KEEP KEEP MULL MULL 5.7564934442564315
MULL KEEP KEEP KEEP MULL MULL MULL 4.964815881069069
MULL KEEP KEEP KEEP MULL MULL MULL MULL 4.518264612719188
nbLands = 16.......4.518264612719188
Quote:
Originally Posted by 17/61 lands
10.614115744350432
9.662498847596936 9.488888888888889
8.852535389881561 8.317122127174729 9.333333333333334
8.178943757993856 7.175719153068565 8.045454545454545 9.177777777777777
7.684707615678623 6.160463575557915 6.744186046511628 7.909090909090909 9.022222222222222
7.376978001034605 5.358214590693408 5.428571428571429 6.627906976744186 7.7727272727272725 8.866666666666667
7.211504498296951 4.908503906994473 4.474157125790812 5.333333333333333 6.511627906976744 7.636363636363637 8.71111111111111
7.124205773262377 4.794629130478187 4.084381551362683 4.422713095055479 5.238095238095238 6.395348837209302 7.5 8.555555555555555
KEEP 10.614115744350432
KEEP KEEP 9.614115744350432
KEEP KEEP KEEP 8.669420307807643
KEEP KEEP KEEP MULL 7.717728601273368
KEEP KEEP KEEP MULL MULL 6.797262516344256
MULL KEEP KEEP KEEP MULL MULL 5.806331407398985
MULL KEEP KEEP KEEP MULL MULL MULL 4.988140058857457
MULL KEEP KEEP KEEP MULL MULL MULL MULL 4.509310121328615
nbLands = 17.......4.509310121328615
Quote:
Originally Posted by 18/61 lands
10.676247713683718
9.664402147741596 9.704545454545455
8.789677486806932 8.488517348330051 9.545454545454545
8.054110440812275 7.298447498187251 8.232558139534884 9.386363636363637
7.5072881603666115 6.2270337765045545 6.904761904761905 8.093023255813954 9.227272727272727
7.163678774056133 5.36455525606469 5.560975609756097 6.785714285714286 7.953488372093023 9.068181818181818
6.981918181123742 4.860627367042461 4.548351438917477 5.463414634146342 6.666666666666667 7.813953488372093 8.909090909090908
6.894446566343289 4.726625222950943 4.105359350642369 4.493448637316562 5.365853658536586 6.5476190476190474 7.674418604651163 8.75
KEEP 10.676247713683718
KEEP KEEP 9.676247713683718
KEEP KEEP KEEP 8.725489477403642
KEEP KEEP KEEP MULL 7.760676354519623
KEEP KEEP KEEP MULL MULL 6.821328802997435
MULL KEEP KEEP KEEP MULL MULL 5.8729483078678655
MULL KEEP KEEP KEEP MULL MULL MULL 5.032340965204721
MULL KEEP KEEP KEEP MULL MULL MULL MULL 4.51812032124002
nbLands = 18.......4.51812032124002
So, in the mountain/bolt problem, 60 cards is the best. And I can't think of a better case since 16/61 and 18/61 have almost the same performance, meaning that 17/61 is close to the best ratio but that it is not enough to justify adding 1 card into the deck.
Re: 61 or more cards in toolbox decks
Very nice. Check one particular set of decks (Bolt/Mountain) off the list if you want.
For anyone who is a poor interpreter -- this isn't a proof that there is no exception to the 60-card rule. This does not prove the 60-card rule for all of magic; it is only proof (strong evidence if you are extremely picky) that the 60-card rule is true for this deck in particular.
As explained, Nihil's variance has enough influence on this deck that the benefits of moving closer to the perfect ratio do not outweigh the costs incurred through adding another card and increasing the variance factor. Other decks, which see more cards per average game, or have stronger card selection options, might not be affected as strongly by this variance.
Of course, there are a host of other large variables which we haven't even tried to take into account that could have strong impact on this problem.
peace,
4eak
Re: 61 or more cards in toolbox decks
It leads to a much wider proof: raising the number of cards of your deck to find the best land/active spell ratio (Ive heard this argument earlier) is a bad move.
I know I've not done the necessary to prove this, and I probably can't, but it looks like a direct corrolary to this result.
I'm running the shock/mountain experiment now. It's longer to compute due to the high number of turns before killing (which means that I need to cope with more library orderings). The only problem, I did not implement the end of turn discard rule which was irrelevant with bolt since we killed off 7 active spells but which is relevant with shocks.
I already have the optimal 60 cards ratio:
Quote:
Originally Posted by 11/60
14.062158485052645
13.300602226595077 12.0
12.63607186950951 10.99422614770399 11.8
12.052457684917202 10.008433835174383 10.653061224489797 11.6
11.566256301220557 9.096368205745073 9.5 10.46938775510204 11.4
11.182975954452091 8.286609181359387 8.340425531914894 9.333333333333334 10.285714285714286 11.2
10.900806751176317 7.61802305200585 7.173913043478261 8.191489361702128 9.166666666666666 10.10204081632653 11.0
10.70465705491726 7.24570821352622 6.378441536266176 7.043478260869565 8.042553191489361 9.0 9.918367346938776 10.8 100.0
KEEP 14.062158485052645
KEEP KEEP 13.062158485052645
KEEP KEEP KEEP 12.110117746980585
KEEP KEEP KEEP KEEP 11.16737523315986
MULL KEEP KEEP KEEP MULL 10.07391880151556
MULL KEEP KEEP KEEP MULL MULL 8.963263959398555
MULL KEEP KEEP KEEP MULL MULL MULL 7.936271749861053
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.1573665443332875
nbLands = 11.......7.1573665443332875
Quote:
Originally Posted by 12/60
13.935958223921041
13.108723290105383 12.244897959183673
12.375844130132288 11.190461806233982 12.040816326530612
11.726868492877783 10.15271179950355 10.875 11.83673469387755
11.181678825376304 9.18222627443102 9.702127659574469 10.6875 11.63265306122449
10.749618256943451 8.308668585057468 8.521739130434783 9.53191489361702 10.5 11.428571428571429
10.432534310605298 7.573552917813021 7.333333333333333 8.369565217391305 9.361702127659575 10.3125 11.224489795918368
10.21743210325729 7.138768092207083 6.471800452599565 7.2 8.217391304347826 9.191489361702128 10.125 11.020408163265307 100.0
KEEP 13.935958223921041
KEEP KEEP 12.935958223921041
KEEP KEEP KEEP 11.97760003205142
KEEP KEEP KEEP KEEP 11.026040502733702
MULL KEEP KEEP KEEP MULL 10.03180304691313
MULL KEEP KEEP KEEP MULL MULL 8.95677206462517
MULL KEEP KEEP KEEP MULL MULL MULL 7.927987080722664
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.1202621450107495
nbLands = 12.......7.1202621450107495
Quote:
Originally Posted by 13/60
13.892966348705121
13.00165916855973 12.5
12.200555446075915 11.401330822061517 12.291666666666666
11.484576925109666 10.315905459804922 11.106382978723405 12.083333333333334
10.876913459494718 9.290710271529996 9.91304347826087 10.914893617021276 11.875
10.391126331846978 8.355945174464077 8.71111111111111 9.73913043478261 10.72340425531915 11.666666666666666
10.033506630717767 7.555135926371092 7.5 8.555555555555555 9.565217391304348 10.53191489361702 11.458333333333334
9.794322010381139 7.055206746793807 6.575502302720123 7.363636363636363 8.4 9.391304347826088 10.340425531914894 11.25 100.0
KEEP 13.892966348705121
KEEP KEEP 12.892966348705123
KEEP KEEP KEEP 11.928679982761388
KEEP KEEP KEEP MULL 10.967838595627164
KEEP KEEP KEEP KEEP MULL 10.025744553786776
MULL KEEP KEEP KEEP MULL MULL 8.996147028080241
MULL KEEP KEEP KEEP MULL MULL MULL 7.965586462831094
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.126385700481913
nbLands = 13.......7.126385700481913
Quote:
Originally Posted by 14/60
13.919494173707967
12.966222742764323 12.76595744680851
12.097743248242693 11.626694865663728 12.553191489361701
11.313908078192206 10.497169098247266 11.347826086956522 12.340425531914894
10.641018597447887 9.420510475774071 10.133333333333333 11.152173913043478 12.127659574468085
10.097091425859462 8.426940677189448 8.909090909090908 9.955555555555556 10.956521739130435 11.914893617021276
9.693543007169566 7.561350837982569 7.674418604651163 8.75 9.777777777777779 10.76086956521739 11.702127659574469
9.42507499046256 6.993984685593185 6.689714376316564 7.534883720930233 8.590909090909092 9.6 10.565217391304348 11.48936170212766 100.0
KEEP 13.919494173707967
KEEP KEEP 12.919494173707967
KEEP KEEP KEEP 11.949771853644375
KEEP KEEP KEEP MULL 10.978983688348542
KEEP KEEP KEEP MULL MULL 10.023340350232825
MULL KEEP KEEP KEEP MULL MULL 9.069051892093484
MULL KEEP KEEP KEEP MULL MULL MULL 8.042230881388335
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.1714298763074655
nbLands = 14.......7.1714298763074655
Re: 61 or more cards in toolbox decks
Shock/mountain deck.
Quote:
Originally Posted by 11/61
14.103197545955226
13.354528457045767 11.96078431372549
12.703504233117267 10.963497483845245 11.764705882352942
12.132959553965328 9.987008832333979 10.62 11.568627450980392
11.658723588772881 9.08555376190147 9.46938775510204 10.44 11.372549019607844
11.285593564112084 8.287488243915668 8.3125 9.306122448979592 10.26 11.176470588235293
11.011101082910184 7.631146218740125 7.148936170212766 8.166666666666666 9.142857142857142 10.08 10.980392156862745
10.819818390665203 7.270070860324469 6.364586604503605 7.0212765957446805 8.020833333333334 8.979591836734693 9.9 10.784313725490197 100.0
KEEP 14.103197545955226
KEEP KEEP 13.103197545955226
KEEP KEEP KEEP 12.152336133996146
KEEP KEEP KEEP KEEP 11.21130243964525
MULL KEEP KEEP KEEP MULL 10.09598082364132
MULL KEEP KEEP KEEP MULL MULL 8.975871217325851
MULL KEEP KEEP KEEP MULL MULL MULL 7.947539786982111
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.172603789648985
nbLands = 11.......7.172603789648985
Quote:
Originally Posted by 12/61
13.96078450479939
13.147099077403322 12.2
12.428771805937826 11.153875497016527 12.0
11.794231773989386 10.12534873730319 10.83673469387755 11.8
11.262642504501411 9.165657173456538 9.666666666666666 10.653061224489797 11.6
10.842480620695303 8.304335487902486 8.48936170212766 9.5 10.46938775510204 11.4
10.53470284309352 7.582446944651587 7.304347826086956 8.340425531914894 9.333333333333334 10.285714285714286 11.2
10.325704314737282 7.160552190994315 6.454511764389678 7.173913043478261 8.191489361702128 9.166666666666666 10.10204081632653 11.0 100.0
KEEP 13.96078450479939
KEEP KEEP 12.96078450479939
KEEP KEEP KEEP 12.003669090726012
KEEP KEEP KEEP KEEP 11.053844056260159
MULL KEEP KEEP KEEP MULL 10.039303502385117
MULL KEEP KEEP KEEP MULL MULL 8.95756690575713
MULL KEEP KEEP KEEP MULL MULL MULL 7.929458724356424
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.127494652510505
nbLands = 12.......7.127494652510505
Quote:
Originally Posted by 13/61
13.90212855161999
13.024856394894622 12.448979591836734
12.239178376461219 11.358442208672866 12.244897959183673
11.538883655816313 10.282141254225328 11.0625 12.040816326530612
10.94642134995894 9.267871535298632 9.872340425531915 10.875 11.83673469387755
10.474347671601517 8.34581447673409 8.673913043478262 9.702127659574469 10.6875 11.63265306122449
10.12782226414573 7.559154179049331 7.466666666666667 8.521739130434783 9.53191489361702 10.5 11.428571428571429
9.896181847555026 7.073775934663424 6.5543778517696385 7.333333333333333 8.369565217391305 9.361702127659575 10.3125 11.224489795918368 100.0
KEEP 13.90212855161999
KEEP KEEP 12.902128551619988
KEEP KEEP KEEP 11.93910556703631
KEEP KEEP KEEP MULL 10.980451104616048
KEEP KEEP KEEP KEEP MULL 10.040275685360182
MULL KEEP KEEP KEEP MULL MULL 8.991614405384762
MULL KEEP KEEP KEEP MULL MULL MULL 7.95865770504603
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.125415278295165
nbLands = 13.......7.125415278295165
Quote:
Originally Posted by 14/61
13.913405820428626
12.974491242116585 12.708333333333334
12.12213936298278 11.57703838148019 12.5
11.35510400675849 10.456541041355017 11.297872340425531 12.291666666666666
10.69895768637167 9.390906920420159 10.08695652173913 11.106382978723405 12.083333333333334
10.170600152356341 8.410459578342486 8.866666666666667 9.91304347826087 10.914893617021276 11.875
9.780079202254562 7.559881858874402 7.636363636363637 8.71111111111111 9.73913043478261 10.72340425531915 11.666666666666666
9.520805699330339 7.008723329956298 6.664333915517355 7.5 8.555555555555555 9.565217391304348 10.53191489361702 11.458333333333334 100.0
KEEP 13.913405820428626
KEEP KEEP 12.913405820428626
KEEP KEEP KEEP 11.944931096392542
KEEP KEEP KEEP MULL 10.976417296708604
KEEP KEEP KEEP MULL MULL 10.024212297592934
MULL KEEP KEEP KEEP MULL MULL 9.0523931404312
MULL KEEP KEEP KEEP MULL MULL MULL 8.024932896214949
MULL KEEP KEEP KEEP MULL MULL MULL MULL 7.16132282854845
nbLands = 14.......7.16132282854845
Re: 61 or more cards in toolbox decks
The thing about a concept of a toolbox deck is... you need to get your hate in a perfect synergistic ratio between useful and useless. I am not saying that it wouldn't work to have more than 60 cards, but you are playing a metagame that is ever shifting every single moment. When playing at a tournament, it is a microcosm where a single player playing something different can change your ratios. So if you show up at a 60 person tournament where you have a psychological profile of every last player, their behaviors, and the probabilities of them drawing particular cards and then suddenly, someone shows up with Nourishing Lich, all that goes out the window. I'd rather stick to 60 cards and let the deck play out.
