Ultimate Deck Building Toolset (v 1.75)

[Dragoon]

ULTIMATE DECK BUILDING TOOLSET
GIVING YOU THE TOOLS YOU NEED TO BUILD A BETTER DECK

INTRODUCTION

Have you ever wondered what the chances were of drawing a certain card in your opening hand was?  Or maybe you wondered, on average, what turn you would have enough quanta to play that crucial card?  These things and more can be solved by using this toolset.  I tried to provide several tools that can help you better build decks so that you are not just haphazardly throwing cards in because you think it might help.  We should have a reason why we put cards in and reasons even for how many copies of a card we put in.  I hope that this toolset will help provide some of those reasons for you.

DECK BUILDING ASSISTER

EXPLANATION
The Deck Building Assister (DBA) helps you find out how many copies of a card you need to have a minimum draw chance.  For example, let's say you want to know how many copies of EQ you need to have to have at least a 75% chance of drawing 1 copy in your first 9 cards in a 30 card deck.  DBA would tell you that you need at least 4 copies to have at least a 75% chance of drawing 1 with those parameters.  It also tells you that the actual percentage is 78.16%.  The tool also tells you what your QI is for the cards listed and copies recommended.

HOW TO USE
To use DBA just type in the cards you want to calculate (or choose from the drop-down menu), enter how many copies you want and how many cards to draw through.  These don't have to be the same for every card.  Just make sure that the # of copies wanted is less than the # of cards to draw.  Then after that, enter the minimum percentage you want for those parameters.  Again, it doesn't have to be the same across all the cards.  Just right of center you'll see a yellow cell for your deck size; enter a number between 30 and 60.  At the top of the QI table is a place for you to choose your Mark.  This is to calculate the QI of your deck.

In the 2 gray columns, you will see the copies you need to fulfill your parameters as well as the actual percentage for the recommended number of copies.  All the way to the right is every element's QI based on the number of copies recommended.  Of course this is based on all the cards you list in the "Cards to Calculate" column.  Under the "Deck Size" area, you'll see how many card slots are left in your deck after adding up all the recommended number of copies for each card.  If all the copies add up to more than the deck size, it will warn you that your deck is not possible.  Below that area is the deck code for the cards you typed in and the recommended number of copies for those cards.

DECK ORDER GENERATOR

EXPLANATION
The Deck Order Generator (DOG) creates a draw order for your deck based on probability.  The main purpose of this tool is to give you a general idea of how your deck will flow.  Now realize this, though this may be the most probable and even fairly average draw order for your deck, it still is only 1 possible draw order out of thousands of possibilities.  Don't expect to draw your cards exactly as it is listed.  Again, what this does is give you a feel for your draw order as well as gives us an avenue to analyze our quantum generation and usage in other tools.  The tool only calculates 20 different cards out to 20 turns to save time and space.  This should be plenty enough information since the first half of the deck is the most important.

DOG works best with non-rainbow decks.  Rainbow decks have the inherent quality of having many cards with the same number of copies (usually 1, sometimes 2).  Because of this, DOG doesn't help too much because in the deck order, cards with the same number of copies are interchangeable.  What I recommend doing is grouping your cards by type (i.e. spells, creatures, weapons, etc.) and then having 1 card represent all the other cards of the same type.  Then you would just write in the total number of cards of that type in the "# of Copies" column.  This will give you a better feel of when you will draw types of cards rather than the exact cards which can still be pretty useful.

HOW TO USE
To use the DOG, you can either type in the names of the cards in your deck along with how many copies there are up to 24 (or choose the cards and number of copies from the drop-down menu in each cell), or you can paste your deck code into the appropriate cell.  But don't use both!  If you do, goofy things can happen.  So after deciding which one you want to use, make sure the other one is cleared.

Once you add your deck to DOG, then on the right you will see a list of cards.  This is the most probable order those cards will be drawn.  Remember, this is only 1 possibility out of many, but it should give you a good rough estimate of how your deck will flow.  Towards the center bottom, you will find a deck code for the cards that you manually type in.

CARD PROBABILITY CALCULATOR

EXPLANATION
The Card Probability Calculator (CPC) helps you to calculate the probabilities of drawing a certain number of copies of a card within so many cards.  For example, if you want to know what the probabilities of drawing at least 3 Pillars in your first 7 cards is, this tool can tell you.  Now this is the cumulative probability.  In other words, this will tell you the probability of getting the number of copies you want or more.

The CPC also has another section that will let you calculate the probabilities of drawing a combination of cards.  However, this multi-card combo section is under construction.  I hope to get it up soon.

HOW TO USE
Type or choose from the drop-down menu a card from your deck.  Choose the number of copies you want.  Choose the number of cards to draw through (7 being how many you draw in your opening hand).  It will then calculate the probabilities of drawing that number of copies or more within the number of cards you want to draw through.

The multi-card combo section is under construction.  I hope to get it up soon once I get some help.

QUANTUM EFFICIENCY TABULATOR

EXPLANATION
The Quantum Efficiency Tabulator (QET) is a tool to help you see what your quanta (Q) production and usage would be based on the draw order of your deck.  Basically, it works just like the game.  QET will add Q for each Pillar/Pendulum/Mark you draw.  It keeps track of how many you've drawn already and so how much Q you should be getting each turn.  It even does this with Pendulums correctly adding Q to the right element depending on your Mark and when it is played.  Also, it keeps track of every card that costs Q.  It takes all this information (and believe me, it's a lot), tabulates it, and then spits out a pretty graph for you to see your Q production curve in relation to your Q usage line.  The tool only calculates out through the first 20 turns, but this should be plenty of info to use.

Marks, Mark cards, Novas, Pillars, Towers, Pendulums, and U Pendulums are all calculated in this tool.  Supernova, Immolation, and Cremation are not calculated as those have other requirements to play them.

You will also be able to see every element's QI.  The QI is per element but does not include Other card costs (e.g. Short Sword, Animate Weapons, SoGs, etc.).  However it does divide up Quantum Pillars/Towers as .25 for each element.  It also subtracts the casting bonus of Towers (except Quantum ones), U Pendulums, and U Mark cards from an element's total casting cost.

However, I think the more important thing to take away from the tool is a deck's Quantum Equilibrium.  Quantum Equilibrium (QE) is the turn where your Q usage and Q production intersect.  In other words, this is the turn you have enough Q to empty your hand.  This is particularly important for aggro decks.  But this is also important for control decks because you often need to be able to gain control of the field quickly.  Many games are decided in the first 5 turns so making sure your deck has a good QE is important.  Determine your deck's ideal QE and then adjust the build of your deck accordingly.

HOW TO USE
All you need to do is type in the element your Mark should be or choose from the drop-down menu.  From there, you can see your Q production and usage in a nice big graph.

In the section to the left with all the elements, you can see total Q generators and total Q usage along with the corresponding QI for each element.

If you scroll right past the chart, you will find the user-defined Q modifiers for each element.  In here you can add when Supernovas, Immolations, and Cremations can be played.  You can also add things like recurring Q generation (Devourer, Brimstone Eaters, etc.) and recurring Q usage (Owl's Eye, Otyugh, etc.).  Just add all user-defined Q production and subtract all user-defined Q usage and put that total amount down in the proper element column and in the proper cells.

Further right you will see the table that the chart is based off of.  You can look here if you're having trouble finding exact numbers in the chart.

GUIDELINES

• Only fill in the yellow cells!  Everything else should be automated.  If you fill in anything else, you'll break it.
• When you type in the cards, you have to spell them correctly and without any plural endings (ie Antlion not Antlions) or abbreviations (ie Basilisk Blood not BB or Light Pillar not just Pillar).
• For upgraded cards that are exactly the same name as unupgraded cards add a U before it (ie U Wings or U Sundial).
• I'm open to other people helping.  So if you'd like to help, just let me know!
• I made a couple copies of the UDBT, so if someone is using one, try the other copy.  Also, if you have a Google account, you could always download your own copy of the UDBT.

BUGS AND FEATURES

The bugs are the features!  Just kidding.  There are things that still need to be fixed or improved.  Also, there are a lot of features that would be nice to add.  Here are some of them:

• Multi-card combo probability calculator- I'm in the process of finishing this.  QuantumT is helping me figure out the proper way of calculating this.
• Aggregate Damage Simulator- Calculates the ramp up and total output of damage for your deck.

If you find any other mistakes, please let me know!  Someone may have changed something or I may have messed something up.  Screenshots and descriptions of the problem help too.

SPECIAL THANKS

• Kael Hate for helping with the DOG Engine.
• suxerz for helping me with the Deck Code import feature.

Below are the links for the Ultimate Deck Building Toolset.
Remember, only fill in the yellow areas!!!

UDBT 1 (https://spreadsheets.google.com/ccc?key=0AvzXeWJKVKrsdDBxcUkwdF9VbW1fZHJldURpNTZaN0E&hl=en&authkey=CNbL2eYL) | UDBT 2 (https://spreadsheets.google.com/ccc?key=0AvzXeWJKVKrsdHl0dFRxRDBIZUg5U3JxNHlOT1JyS2c&hl=en&authkey=CPuM1pkO).

[Malduk]

Well... props for the huge amount of work.

I'd love to say that I love it, but actual probabilities mean more than all the numbers and graphs from that tool. Possible order of cards from the deck is not nearly as useful info as draw chance of your needed card. With evenly distributed rainbows, DOG is useless. With redundant decks like 18-6-6 deck, you really dont need any tool.

[Dragoon]

Well... props for the huge amount of work.

I'd love to say that I love it, but actual probabilities mean more than all the numbers and graphs from that tool. Possible order of cards from the deck is not nearly as useful info as draw chance of your needed card.

The problem with just knowing the draw chance of your needed card (eg Hypergeometric Calculator) is that it does not let you know if you'll have enough quanta to play said card.  You know you'll have it, but having it doesn't mean you can play it.  But that's what QI is for right?  Well, QI is a separate tool that helps you balance your Q production and usage but it doesn't consider draw probability.  So you may have a balance of usage in the long term, but it doesn't help you if you can't play the card when you really need to.  Solving this problem was the goal of the UDBT.  Originally I had tried to create a deck order by probability.  The problem is that Pillars were the most probable card for any individual draw because of their proportion to the deck.  So since it isn't possible to build a deck order by probability (at least that I know of), I tried to build a deck order by proportionality which seemed fairly representative of the average draw order.  The chances of this exact draw order being done is actually not very big, but it gets pretty close to what an average draw order would be if you played a bunch of games.  And with this, you can see your Q flow.

With evenly distributed rainbows, DOG is useless.

As for rainbows, yes DOG is less useful for Rainbows than for Monos and Duos.  This is because of the inherent problem that most Rainbow decks have the same number of copies of differing cards (ie 1 or 2).  So because all cards with the same number of copies are interchangeable, it really doesn't help you know when you're going to draw a specific card.  Again HC is the better tool for solving that specific problem.  However, a better way of using DOG with Rainbow decks is to pick a card that represents all the other cards of the same kind.  In other words, if you have 1 Lightning, 1 Shockwave, 1 Freeze, and 1 BB, instead of writing those 4 cards with 1 copy, write 1 of those cards with 4 copies (ie Lightning 4).  Then when you look at the DO and you see Lightning, you can assume that you will have drawn a CC card of some kind.

With redundant decks like 18-6-6 deck, you really dont need any tool.

Yes, redundant decks like that are pretty simple to calculate on the back of a napkin (which is what I have done a lot before).  But when you start doing things like 13-6-4-3-3-2 decks, then the tool is handy to calculate those things for you.  Plus then you can also see your Q flow with QET.  That's something that would be hard to do on the back of a napkin. 

[Dragoon]

v 1.1 Update

• I added a Hypergeometric Calculator to the UDBT.  Unfortunately, it's not cumulative yet.  I'll have to fiddle with the formula more to add that.

[Malduk]

I get how it works and what you're saying. I just dont find it useful. Or useful enough to actually use it. I started writing a long post about why guessing one draw that will actually happen in minority of your games is not that useful, but I dropped it as I think you understand my point.
About having quanta to play it, that is not really a big issue in deckbuilding. Most players have a good feeling about their quanta usage, and simple tests against AI3 can give you faster answers. And you cant really tweak the deck to "perfect quanta production to quanta usage ratio" as your quanta production relies on draws. And by draws, I dont mean order of draws, but by probability to draw what you need in first 8 cards.

Finally, when games are decided in several turns, no one cares what will be drawn from there till the last card, as the game is already over, so deckbuilding goal should be to build deck that has a fast enough setup, not the deck that has good draws from turn 15 to turn 23.

[TimerClock14]

gah! you ninja'd me to this
but, this is far better than mine
props for the effort put into this, looks very nice

[Dragoon]

Finally, when games are decided in several turns, no one cares what will be drawn from there till the last card, as the game is already over, so deckbuilding goal should be to build deck that has a fast enough setup, not the deck that has good draws from turn 15 to turn 23.

Yes, I agree with that totally.  That's why I say determining a deck's QE (eg when you can empty your hand) is more important than determining a deck's QI (eg the ratio between Q production and usage).

I get how it works and what you're saying. I just dont find it useful. Or useful enough to actually use it. I started writing a long post about why guessing one draw that will actually happen in minority of your games is not that useful, but I dropped it as I think you understand my point.
About having quanta to play it, that is not really a big issue in deckbuilding. Most players have a good feeling about their quanta usage, and simple tests against AI3 can give you faster answers. And you cant really tweak the deck to "perfect quanta production to quanta usage ratio" as your quanta production relies on draws. And by draws, I dont mean order of draws, but by probability to draw what you need in first 8 cards.

I appreciate your perspective and agree that that's how I've mostly built decks too (and probably will continue to do so in the future to a good extent).  I suppose some of these tools may not be as useful to veterans who have a very perceptive intuition that's been developed through many hours of deck-building.  But I think for people not at that level, the visuals and deck order can give them a rough feel of how their deck will flow.

However, your comment did get me thinking about some different things.  I think I can improve on how the DOG generates the deck order.  I thought that probability was out, but now that I know that Google Docs can do Hypergeometric Calculations, I think I've found a way to create a deck order by probability.

Basically it takes each draw and determines which card gives the highest probability taking into account how many cards have been drawn and which cards have already been drawn.  For example (13 Pillars, 6 Phoenixes, 4 RPs, 3 Deflags, 2 Fahrenheit, 2 Crimson Dragon):

Draw 1: Pillar - Pillar (1/1=43%), Phoenix (1/1=20%), RP (1/1=13%), Deflag (1/1=10%), Fahrenheit (1/1=7%), Crimson Dragon (1/1=7%)
Draw 2: Phoenix - Pillar (2/2=18%), Phoenix (1/2=33%), RP (1/2=24%), Deflag (1/2=19%), Fahrenheit (1/2=13%), Crimson Dragon (1/2=13%)
Draw 3: Pillar - Pillar (2/3=33%), Phoenix (2/3=9%), RP (1/3=32%), Deflag (1/3=26%), Fahrenheit (1/3=19%), Crimson Dragon (1/3=19%)
Draw 4: RP - Pillar (3/4=18%), Phoenix (2/4=15%), RP (1/4= 38%), Deflag (1/4=32%), Fahrenheit (1/4=24%), Crimson Dragon (1/4=24%).
And so on . . .

I dont' know how much different this would be from what I already have, but it would be the most probable draw order for a deck (even if the probability of drawing that exact draw order is fairly small).  Something like that may be more useful to people since it's based on probability and the probabilities of drawing one card verses another.

Another idea that came from your comment was a way to help people build a deck based on the probability of drawing X card within Y turns.  It'd be a Probability-based Deck Creator.  So the idea is this:

1. You type in the size you want your deck to be.
2. You type in the cards you want in your deck.
3. For each card, you type in what the minimum probability you want to draw X number of that card in Y number of turns.
4. You type a QI (or better yet QE) range that your deck should be.
5. The formula would then generate how many copies of each card to satisfy all those variables.

Anyways, it's an idea.  I don't know if it's possible.  And it's definitely nothing that I'm going to be doing for a while since I'm busy with life and the Trials.  But it'd be pretty cool I think.

gah! you ninja'd me to this
but, this is far better than mine
props for the effort put into this, looks very nice

Thanks.

[Malduk]

<cut>

I'm glad you didnt perceive my comments in a negative way, and that it gave you some new ideas for the tool (which look good!).
Good luck with it!

[918273645]

Holy shit!
+ Karma
+ Bookmark

[ddevans96]

Holy crap. This is amazing.

[Ekki]

I think I love you Dragoon 

+Karma for this

[Dragoon]

Thanks for the compliments and karma.  And +Karma to Kael for helping me with this.
v 1.2

• The Hypergeometric Calculator is now cumulative.  You type in the card you want to look up, how many cards you want to draw through, and how many copies of that card you want to have within the cards drawn.  It then tells you the probability of drawing that number of copies or more for the amount of cards you want to draw through.
• Some general bug fixes.