Terraforming the Harpies: Too Much of a Good Thing

Can you play too many searchers in a Yugioh deck?  Intuition would say probably not.  However, it’s not always a good idea to trust intuition.  

This question came up in the Pojo forum on Harpies.  In brief, Harpie players were arguing if it was better to play two copies each of Divine Wind of the Mist Valley, Terraforming, and Harpie’s Hunting Ground or some other ratio.  Initially, I opted for two Terraforming since deck thinning is always a good idea. Right?  Not quite.  As it turns out, playing two Terraforming increases the risk of a dead draw.  Here’s why –

Drawing the cards in sequence creates one permutation of these six cards.  For example: 

There are 6! or 720 of these permutations.  Most of these permutations are fine unless they end with Terraforming.  Drawing that card with no targets gives you a wasted draw.  Here are examples of two such permutations: 

Since you can get to these permutations by rearranging the remaining five cards in any order, there are a total of 5! or 120 such permutations.  However, the following permutation also gives you a dead card since the first Terraforming will select the last Hunting Ground: 

Rearranging the remaining four fields spells in any order produces 4! or 24 permutations that have Terraformings at space four and five. 

So, playing one Terraforming and five field spells generates 120 dead cards in 720 permutations or 16.7%.  Playing two Terraforming and four field spells produces 144 dead cards or 20.0%.  Therefore, playing one Terraforming will likely yield better results. 

There are valid reasons for wanting to play two of each card.  Drawing through all six cards may seem unlikely.  Having the flexibility to grab either Divine Wind or Harpie’s Hunting Ground is a plus.  However, Harpie players should remember their Queen

She can reduce the number of Terraforming targets so that you are almost guaranteed to have a dead draw.