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Meme Magic: Probabilty and Deck Building

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»Satchmo    3221


"Ayy what up it's ya boi Mathman here, finna teach you some Meme Magic"


Over the years, one thing TCG players have always been aware of but rarely used was probability. This isn't exactly true at the highest levels of play, people usually calculate everything but you'll usually see the average and even above average player follow their gut rather than learn actual numbers to use to their advantage. "I played 2 because I wanna open it but 3 is cloggy", what the fuck kind of logic is that, honestly? Humans being a conflicting combination of logic and emotion on varying levels of the spectrum, we are almost conditioned to do what feels right less so than what is right. We can make that argument when talking about things that are subjective or abstract like morality. But when it comes to things that can be objectively proven better or worse, we still go with our own impulse. "I played one because I didn't want to not have an out game one but it sucks in the mirror". However, when you can quantify and see the actual consistency of each card in your deck, it will help you make better deck building choices. I do want to clarify that this is not the end all be all of deck building, you still need other knowledge to help you. At the very least, the articles and resources provided here will allow you to stream line your decks and hopefully it will be more beneficial than that.



I'll start off with the most important part, the actual calculators .


This is the simplest, most streamlined ygo calculator. It's incredibly simple in it's interface.

https://www.dropbox.com/s/p9qm7ko7lt0bis2/GYGO Combo Calc.zip?dl=0

This is a link to GlassgowYGO's program. This one creates slightly flawed calculations though, since it actually runs thousands of hands instead of giving you the exact probability by calculating the math. However, the fact that is actually draws test hands is pretty interesting as well. Here's a video tutorial by GYGO. Other information about the program:



Does not work on macs.
Known compatibility issues with Windows 7 & Avast, if you're having trouble running it and you match this here's instructions on how to circumvent it;
Avast - Click Cog/Settings - Active Protection - File System Shield Customise - Exclusions - Add - Browse to folder with the .exe in it. Should be good to go.
Some antiviruses, other than avast, may require an exception also to the .exe file.

If you're having technical difficulties, email details like your OS, anti virus and any other software details that might interfere with it to gygocombocalc@hotmail.com



This is a regular hypergeometric calculator. If you want to learn more in depth how to use one, try this but the results will be close to the same as yugioh.party.


This website is just a clunkier version of ygoparty in that it requires you to jump 3 pages to get the result/input the information. Also make sure you have www. or it will fail to reach the domain.


This one is very important, this is an overlap calculator. This will yet you check the probability of combos involving cards that can be both combo pieces. ie If you need to open Blazeman and Shadow Mist and have 3 E-Call in your deck as well.
This one made by our very own @citrus, you can find out more below in this thread.


Credit to @bilaterus and RustyWolf for ygoparty and the overlap calculator, @GlasgowYGO and Smelliot Toilet(?) for their calculator, Stattrek.com and whoever made dbtoolkit, I actually think it might've been Inexorably?




"You don't get any bonus points for making a couple of plays before you lose the game"

About a week ago, Mike Steinman wrote a tournament report about how he used math to fix some of the issues with Monarchs. It’s a very good article worth the read, so if you liked it be sure to give him some green internet points. Below in the spoiler are the math relevant bits to give those new to the concept an idea of what they are looking for.

However, I do want to draw special attention to how he categorizes cards, because that is a major part of how probability factors into modern yugioh. We aren’t just looking for how often we want to see Erebus, we’re looking for how many tribute summons we need to open, how many targets for tenacity, how many pantheism targets etc. This isn’t a new concept, Big BA decks always utilized “BA names” as opposed to specific BA monsters to get to Dante. Shaddoll needed a certain amount of LIGHTs, Fusion Spells and Shaddoll monsters to hit Construct more often. Which BA Names and Which LIGHT monsters you used are an afterthought to “How many of this type of card do I need?” With the advent of Pendulum monsters, I expect this to continue for the foreseeable future.




“The thickness of your deck is irritating me”

What actually sparked this article was Bilaterus himself, as he wrote a few articles explaining probability on an easy to understand level. He explains the Magic behind Meme Magic, So those will be in the spoilers below.

Something important to note here, just like in Steinman’s article, that Bilaterus introduces something important to factor in- Draw Spells. The Second Article will show you how to account for things like Trade-In and Pantheism when checking opening hand probability. Milling is done effectively the same way as draw spells.

I will also demonstrate how to aggregate percentages. There was at least one major yugioh application for this but I completely forgot what it was. I’ll update when I remember it. For this I’ll be using test results in stead.



Aggregate Percentage = x1 + x2 + x3 + .......+ xn / n x 100

First we need to determine what results we are aggregating. Let’s say 3 test results, out of 200 points. The 3 results are
1: 130/200
2: 140/200
3: 170/200

Next we add our scores together: 130+140+170=440.
Then we add the total possible result, so 200+200+200=600
Divide those 2, and we get 440/600=.7333, then .7333*100= 73.33, so 73.33%

When aggregating actual percentages like say 34% to open 1 of 3 Tour Guide, we’re dealing with fractions of a whole, so you can just say .34/1.



Your 34% concern suddenly becomes a lot more real when it's 100%”


If you flip a coin twice, will one result always be heads and one result always be tails? Probably not. You aren’t taking 50% of each result, each coin flip has a 50% to have one or the other result. The same applies to drawing random cards, 33.76% doesn’t mean you are guaranteed to open a Terrortop once a match but on average, you will. Sometimes you won’t see it once in 3 games sometimes you draw it every game for 8 rounds straight. There’s also a lot more of a human element to card games. When you draw through your deck and don’t properly separate cards when shuffling, you can get clumps of cards you used together from the previous game stuck together. So if you see all 3 Terrortops in 17 cards , and 13/17 cards are shuffled towards the bottom, guess who’s not drawing a Speedroid in the next game? And of course, just like double sided coins, cheating can be done in yugioh. No one wants to get stacked but you might (or you might be a scrum stacking other people) and suddenly 34% can be 0% without your control.




Strong 5 to a Light 6”


I’m going to continue updating this thread with resources as I find them and new things you can utilize to calculate other things in this game and others. CFV is not one of those games, because calculating how likely you are to do anything other than ride correctly requires you to have gone through multiple turns and 9+cards in your deck. But most CFV players suck anyway, so you should just be at a natural advantage if you’re from duelistgroundz. The first thing I’m gonna do is figure out how to utilize aggregated percentages in ygo. There will be a changelog at some point

change log
6/26/16- Had to remove all the article text to fix the formatting.
1/20/17- added Citrus' calculator

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»Satchmo    3221

forum fucked the article up at first

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»Satchmo    3221

p(A or B) = P(A) + P(B) - P(A and B) <<< adding percentages

these are things I've been meaning to add to the article I'm always either just busy or lazy

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mark    3105

pinned this because math in yugioh will always relevant

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mark    3105

link to Goldfish calculator etc. as requested

we can make this the yugioh math thread, and put all math relevant stuff in here (the conclusions, still make separate topics for questions)

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citrus    21

I don't mean to toot my own horn, but please add mine as well:

As far as I've tried, none of the existing calculators can do what mine can do.  For example, let's say I'm playing Ice Barrier Frogs, and I want to find the probability of opening Toadally Awesome in my first 5 cards, after resolving Upstart Goblin and Pot of Desires.  Swap Frog and any water monster fulfills this requirement, but so does any two Ice Barrier cards (from Prior, Medallion, and another L2).  Both of these criteria produce the same outcome, but none of the above calculators properly finds the odds of one or both combos occurring.  (That is, subtracting the intersection between Swap + Water and 2 Ice Barriers is very messy.)


My calculator will tell you that the probability is 57.23%, because it produces every possible hand, counts how many times each unique hand occurs, and finds how many of the unique hands contain one or more of either criteria (Swap + Water or 2 Ice Barrier) so there's no double counting.  It then divides the total occurrence of all unique criteria-meeting hands by the total occurrence of all unique hands to provide the true probability.


My calculator can also print out all possible unique hands into a neat text file, although it takes some to do while resolving draw effects in its current implementation.  Its current use is also a bit difficult if you're not familiar with programming, but I think it has very high functionality.

Edited by citrus

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mark    3105

I haven't looked into it yet, but can you make 'complicated' calculations with it as well, such as Pot of Desires/Brilliant Fusion and using Upstart Goblin before/after deckthinning etc. If you knew a list of the hands and the order of the cards you play, depending on the hand you have? Also stuff such as Magical Mallet? 

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citrus    21

Strictly speaking the program doesn't do "complicated" calculations because the end result of resolving draw effects is the same, but I can implement some kind of balancer for Desires (e.g. reduce occurrence probability to compensate for  banishing all Garnets).  Generalized searching is not implemented, but the program can treat searchers as the combo pieces that they search for (e.g. treat E-Call as Shadow Mist and Bubbleman at the same time). Shuffle and redraw effects are not implemented because their resolution is functionally trivial. For instance, the entire outcome space of resolving Reload or Magical Mallet consists entirely of ally hands that could have opened Reload or Magical Mallet, except without Reload or Magical Mallet. I can implement this as a check that just removes Reload or Magical Mallet from each hand they're drawn in. 

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mark    3105

I think that, while there may be value in knowing the effect of Desires, the point is that in builds with Brilliant+Desires you'd always want to activate Brilliant before Desires if you draw both, but if you draw Brilliant off of Desires, you now want to know if you have banished your targets yes/no. There's also drawing the target yes/no. The searchers and drawcards thing is less relevant, I'll admit that, and of course we can treat a deck with 3 Terraforming 3 Field spell 1 Upstart 3 Into the Void as '36 card deck with 6 Field spells', but with the decks I'm currently testing the problem is that a lot of it depends on technical play, so for example, you'd activate Brilliant before Desires/any draw cards, or any other deck thinning mechanics. You'd sometimes want to activate your draw cards before activating your engine cards, but sometimes after, depending on whether you want to draw what you search/send yes or no. (say, your hand is Brilliant Fusion + draw cards, and you play 2 Garnet, now normally you'd want to Brilliant first, then use the drawcards, to minimize odds of drawing Garnet, but if you want to draw the Garnet for some reason, say you need a monster in hand to activate One for One, or you want him to normal summon for a rank 4 play, now you'd want to activate the drawcards before activating the Brilliant, and while this is a minor interaction, in complicated decks such as Omega synchro spam or stuff like that, it's very relevant. I'm currently using 'draw 50 hands on ygopro' to decide the odds, but that's inaccurate as fuck, because if you hit 5 of these hands better or worse than average, then that's already a 10% deviation. The problem is that with theory and basic math I can already see what would be good and what not. So the only times I'd actually resort to using math, is with very difficult problems where the difference will only be 1% at most, but these are the exact kind of situations that are too complicated to calculate with math or with programs. I mean if this is not solvable then nevermind, I guess the best solution to this is just using a lot of theory + math till you've find the right answer, but I was just wondering if it was possible with the program. 

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