Treatise On Ratios

BONUS Question Of The Day: What's this I hear about ratios? What does MATH have to do with a children's card game?

Trading Card Game Referenced:

YU-GI-OH!

I am very glad you asked that, hypothetical new player! Ratios are very important when considering what cards to put in your deck, because they allow you to find the most efficient method of obtaining the kind of win condition you are searching for with the least amount of effort and the lowest chance of it horribly backfiring in your face.

BUT WHAT IS A RATIO, YOU ASK?

A ratio is a set of two numbers separated by a colon ( : <--- That thing) showing the relationship between the two of them, or rather how many times one goes into the other. For example, a 2:1 ratio means that, for every two of something, there is produced a single item of equal value.

To put this into game terms, let's go to one of our favorite pastimes from 2006; Yu-Gi-Oh!

Anyone familiar with this card game (and if you're not, i'll put it into easier to understand terms) knows about Mirror Force. This was a Trap card that you would activate when your opponent attacked. All of his monsters in Attack Mode (meaning, face-up, with the card vertical, and able to attack) when this card is activated would be absolutely destroyed. A player can have up to five monsters on the field at any given time. Now, best case scenario, he will have five monsters, all in attack mode. Mirror Force would destroy all of them. This means, in the best case, Mirror Force has a Benefit/Cost ratio of 5:1, meaning for a single card, you destroyed five of your opponent's. That means you used a single resource to rob him of FIVE resources. This is a huge deal!

Of course, this was an ideal situation. In most cases, he will have only one or two monsters on the field, or have four or five with only one or two in attack mode. That means, most of the time, it will average out to a 2:1 ratio, with the worst case being a 1:1 ratio where you save yourself.

How does this affect me and my deck building, you ask? It's actually quite simple! Most of the time, you want to maintain at LEAST a 2:1 ratio possibility with each card you put in your deck, meaning for every single card resource you have, you need to be able to either gain twice the resources for yourself, or rob your opponent of twice the resources (or, in special cases, give yourself a resource and take one from them). This is the balancing act of most decks. How do I manage to maximize the output of this card? In what way can I gain an advantage from this card other than just breaking even? This will drive you for most of your TCG career.

Now, sometimes you will need to put 1:1 ratio cards in your deck. It is unavoidable in some cases, in some decks. When that situation arises, you need to find a way to make the card gain synergy with the other cards in your deck to create a more favorable ratio. (We talked about synergy in our last lesson here.)

Again, going back to the YGO example, we look to one of the two Secret Rare cards in the Pharaoh's Servant booster pack series, Jinzo. He had 2400 attack, 1500 defense, and six stars, which meant to summon him, you either needed to sacrifice one of your creatures, or Special Summon him through other card effects. His effect was that he negated all Trap cards on the field, and prevented any new Trap cards from being activated, including yours. Assuming you summon him normally, that is a 1:2 ratio, where you spent two resources only to gain one, thus robbing yourself of a resource. (Being unable to activate your own Traps counts as losing a resource.) If you Special Summoned him, then it would still be a 1:2 ratio, as you expended the card to summon him which could have been used on someone else, AND you still lose Trap control.

"That sucks!" I hear you say. "Why would anyone give up the ability to use Traps for a card with mediocre attack, low defense, and blocking you out of your own cards?"

Because he represents a new kind of ratio, which I am about to explain, called the Potential ratio. Let's say you've activated all the trap cards you're going to for a while, but your opponent has plenty on the field (you think) to counter you. Summoning Jinzo would then lock him out of playing those cards. This would ALSO lock his Spell/Trap field with useless cards, preventing him from playing other vital Spells. If your opponent has no open Spell/Trap slots due to all of them being traps and being unable to activate any of them, he loses out on a lot of potential resource gains. You have effectively locked him out of 2/3 of his entire deck, with the only way to unlock it is to kill Jinzo with a strong enough monster, which if they do not have one out already, means you have entire TURNS of free shots to his face, very possibly ending the game. In this scenario, Jinzo would turn from a 1:2 into a variable, and almost incalculable, ?:2, with the ? being any number of lost potential incidents, lost potential spells cast, lost traps activated to rob you of resources, and of course all the resources you just gained from having absolutely no opposition.

Everything boils down to efficiency, and how much you can supply yourself with while depriving your opponent of the same opportunities. Ratios are very important to understanding the games themselves, and to tactics and strategy in general. Card games aren't just fun, they challenge your mind, make you sharper, more keen to noticing small details and thinking ahead of time. The better you understand the mechanics behind a game, the better you can use the physics of the world it represents to your advantage.

At the end of the day, all card games come down to mathematics. It's just a matter of how far you're willing to go, and let me tell you, with enough determination and a little tutoring, anyone can become sharp as a blade.

I hope this has been informative! Here's your homework for the rest of the night.

IT'S NOT ABOUT THE CARD, IT'S ABOUT THE ADVANTAGE THE CARD REPRESENTS.

Have a good night!