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Doomkaiser Dragon
Card# CSOC-EN043
Doomkaiser Dragon's effect isn't just for Zombie World duelists: remember that its effect can swipe copies of Plaguespreader Zombie, too!
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 This week, I’ll discuss the basic math behind our favorite game and why some decks seem to do better than others. The deck of choice to illustrate my point, of course, will be the Dark Armed Dragon deck piloted by Jason Holloway at Shonen Jump Championship Nashville
Built on a Framework of Simple Math Principles
The Yu-Gi-Oh! TCG is not a complicated game in a mathematical sense. It’s like poker in that it forces you to be conscious of probabilities involving your hand and deck. You also have to think about your opponent’s hand and decide plays based on that. Obviously, our game goes a bit deeper than hoping to get a lucky draw or figuring out what cards are being held out of the usual 52. Not that poker is predictable. Those 52 cards represent a considerable number of combinations. However, those 52 cards pale in comparison to the 8,000+ in our game. Can you imagine the number of card combinations you can come up with for a deck? (It’s a large number, I promise you.)
Our game also adds more reliability to the usual probabilities of your typical card game. We have cards that can search for others, cards that allow you to get more cards from the deck, and cards that synergize with other cards to make your draws more consistent. Keeping that in mind, it’s easy to see how complex this game can get when you start to consider the math behind it. But it’s actually much simpler than you think. It’s basic probability. If you’re reading this and you’re already familiar with basic probability concepts, then please excuse the re-hashing of high-school algebra.
Since the Yu-Gi-Oh! TCG can be thought of as a series of individual probability experiments, it’s helpful to understand some basic terminology related to probability theory. An "outcome" is the result of a single trial of a probability experiment. A "sample space" is the set of all outcomes of a probability experiment. An "event" usually consists of one or more outcomes of the sample space. Now that you know the definitions, let’s go over just how you determine the probability of a given event:
Formula for determining the probability of an event "E" --> P(E) equals the number of outcomes contained in the event "E" divided by the total number of outcomes in the sample space.
I don’t like that explanation. Let’s make it easier to understand:
Formula for determining the probability of an event "E" --> P(E) equals the number of favorable outcomes divided by the total number of outcomes.
Lastly, there are some ground rules about classical probability that need to be understood:
1) The probability of any event will always be a number from zero to one.
2) When an event cannot occur, the probability will be zero.
3) When an event is certain to occur, the probability is one.
4) The sum of all probabilities of all of the outcomes in the sample space is one.
5) The probability that an event will not occur is equal to one minus the probability that the event will occur.
Putting It All Into Practice
I know, I know. This seems like a basic math lesson, but let’s apply what we’ve learned to dueling. Let’s say that you are Jason Holloway and you have your 41-card deck sitting next to you on your play mat. It’s testing time and you’re curious about the odds of drawing certain cards in your deck. You want to know what the probability of drawing your Elemental Hero Stratos from the top of your deck is. Using the basic formula (# of favorable outcomes / total # of outcomes) we can write it out as such:
P(Stratos) = 1/41 or 0.024
That decimal can be expressed as a percentage by multiplying it by 100 to get 2.4% From the looks of things, the chance that you’ll draw Stratos is very slim on the first try. Now let’s figure out the chance of drawing one of your two Light and Darkness Dragon cards using the same scenario:
P(Light and Darkness) = 2/41 or 0.049
Expressed as a percent, this turns out to be 4.9%. Again it’s hardly an impressive number, but you have to put things into perspective. If you look carefully, you’ll notice that a 4.9% chance is a bit more than double the original 2.4%. If you wanted to draw one of your three Dark Armed Dragon cards, then your probability becomes 7.3%—a little more than three times the probability of drawing a Stratos. The obvious conclusion to be made here is also one of most basic principles of deckbuilding: the more copies you have of a card in your deck, the higher the likelihood of drawing a copy of that card. I know what you’re probably thinking by now: "Okay Bryan, this is all fine and dandy, but you’ve proved, mathematically, something I already knew intuitively." That’s an excellent point, but there’s a bit more to it. Let’s get a little more complex. Imagine that you want to draw both a Dark Armed Dragon and a Stratos. The order doesn’t matter much, so say you want to draw Dark Armed Dragon first:
P(DAD and Stratos): 3/41 x 1/40 = 0.002 or 0.2%
 A few things are easily noticeable. First, the probability that you’ll draw both in a row is extremely low. Second, the denominator changes as you add more cards to your hand (I’ll explain why in a bit). Third, as your hand size gets larger, the odds of drawing a very specific hand are also extremely unlikely. The reason why the denominator changes as you proceed is because the deck size is changing given that certain events are occurring. These are not independent events because the size of the deck changes as you meet the first condition. In probability theory, this is expressed mathematically as: P(A and B) = P(A) x P(B|A). What all that gibberish means is that you are determining the probability that event B occurs given that A has already occurred. This makes sense since you drew a card to get that Dark Armed Dragon: your deck size has been lowered by one. You no longer have 41 total outcomes, you only have 40. Let’s say that you are curious about the probability of drawing two copies of Destiny Draw as your first two cards. This is expressed as such: 3/41 x 2/40 = 0.004 or 0.4%. Given that you drew one Destiny Draw as your first card, you’ll have only two of them left in a 40-card deck. The keyword for multiplying the probabilities is "and." Simple enough.
Another method for calculating the probability of an event is when the word "or" appears. For example: a card is selected at random from your 41-card Jason Holloway deck. Find the probability that it is a spell or trap. The probability of drawing a spell in Jason’s deck is 14/41 and drawing a trap is 7/41. These two events are mutually exclusive. They cannot occur at the same time in this scenario. In this case we have to incorporate the first addition rule:
P(A + B) = P(A) + P(B) --> P(spell or trap) = P(spell) + P(trap) --> 14/41 + 7/41 = 21/41 or 0.51
Your chances are 51% that you’ll draw a spell or trap. Those are nice odds. Thinking through this backward, the chances of not getting a spell or trap are 49%.
Implications and Further Practical Use
There are a few implications to ponder:
1) Deckbuilding is more clearly defined with numbers.
2) These simple calculations can help you during any game.
3) The game is suddenly not so complicated and is good for practicing your basic math skills.
Being able to perform these simple calculations can tell you a lot about how to adjust your deck during the design and test phases of deckbuilding. You’ll be better able to gauge the chances of drawing into a certain card. This knowledge gives you the ability to structure your field according to the likelihood of a favorable draw. This is better known as "playing to your odds." If you can shape the game state in a way that will make an Allure of Darkness draw a spectacular game-altering event, then you are well on your way to the big leagues. Think about that. When you start performing your calculations, be careful not to be fooled by the numbers. They may be small, but they are relative. As I mentioned earlier, the difference between 2.4% and 4.9% is staggering: more than double!
You can throw wishful thinking and fuzzy logic straight through the window. Basic probability is only the beginning.
Thanks for reading!
—Bryan Camareno |
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