Monday, January 12, 2015

Putting Your Deck on a Diet

As a cancer doctor, one would think I would be protected from discussing dieting with patients.  After all, cancer is associated weight loss and not obesity, right?  

Figure 1
Not so.  In fact, many of my patients survive their cancer only to face the same weight problems they had before their diagnosis.  As a result, talking about dieting has become a part of my normal practice.  Fortunately, dieting for a Yugioh deck is much easier as long as you think of deck thinning as a form of deck dieting.  

Deck thinning is the process of increasing your odds of drawing a card by decreasing the pool of remaining cards in your deck.  This naturally happens when you search for a card.  Not only do you get the card you want, but you increase the chances of drawing one of the remaining unsearchable cards. Some cards serve no other purpose but to “thin the deck.”  Upstart Goblin remains popular though there are others like Jar of Greed. 

How much advantage is there to deck thinning?

This analysis will compare decks that search often to a deck that has no search cards.  The latter deck will be called the Fat One because you can call a deck fat without being thought of as insensitive.  Like a good economist, I must make a few artificial assumptions: 

  1. The output will be the chances of drawing an unsearchable, limited card like Raigeki.
  2. All decks except for the Fat One will open with a search card. After that, the decks will draw into a search card every x number of turns. This variable will define the other decks.  We will look at decks that draw a search card every 3, 4, and 5 turns.  

This analysis shows that “deck thinning” has rather modest benefits (Fig 1).  For example, the Fat Deck gives you a 25% chance of drawing into your Raigeki by turn five.  These odds increase to 26.3% if you play a deck that searches with every third card.  In other words, if you have between 13 and 14 search cards, you will increase your chances of drawing a limited card by 1.3%. By turn ten, your odds will increase by 4.2% (Fig 2)
Figure 2
Of course, real life is more complicated.  The current top decks have cards that search multiple times.  Qliphart Scout can search every turn.  Still, the advantage of this card is in what it searches for and not the amount that it thins the deck.  

Here are my conclusions:
  1. The advantages of “Deck Thinning” are relatively modest. 
  2. Deck thinning only improves your odds late in the duel.
  3. Cards that do little more than “thin your deck” are not worth playing.  This includes cards that search for cards you don’t need.  

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