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  1. "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. RESOURCES I'll start off with the most important part, the actual calculators . http://www.yugioh.party/ 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: http://stattrek.com/online-calculator/hypergeometric.aspx 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. www.dbtoolkit.com/ 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. https://jscalc.io/calc/XXJbvsNuHPUbtG8A 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? FIELD EXAMPLE "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.http://yugioh.tcgplayer.com/db/article.asp?ID=5786&writer=Mike+Steinman&articledate=6-21-2016 "HOW CART?" “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. https://ygorganization.com/maths1/ https://ygorganization.com/maths2/ 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. VARIABLES “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. THE EVOLVING ARTICLE “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