Skilled players make good decks by considering the probabilities of drawing particular cards. Good decks increase the probability of drawing win conditions. Mathematics is always present when analyzing these probabilities. I'm going to attempt to explain simple mathematics that you probably know or may not know. My goal in this post is to reinforce the concept of mathematics so you, the reader, can create better decks.
I personally wasn't considering probabilities until I began practicing for Regionals and I was cautious of my probabilities while constructing the final draft of my deck. While it's true that you must include cards that cripple your opponents you must also include your winning strategies. Any card that searches and thins out the deck is useful. In conclusion it was with this build that I topped Regionals because it had enough deck thinning without removing the essence of the deck:
http://www.youtube.com/watch?v=OXjjtdbUs4w
Consider Upstart Goblin: Draw 1 and increase your opponent's life points by 1000. If you are playing a 40 card deck with 3 Upstarts you are essentially playing a 37 card deck with minor life point repercussions. That's simple math.
Pot of Duality is a similar card that's more expensive. Poor people play Upstart and everyone else plays POD if they choose. Some decks utilize 3 copies of both cards like Gravekeepers for example. I'll use Gravekeepers in my next example.
Gravekeepers play a 34 card deck if Upstart and POD are incorporated. Lets analyze the first turn though. You can only activate one POD once per turn therefore it's only a 36 card deck turn one (If you understand where I'm coming from). The main goal is to activate Necrovalley immediately. Most decks incorporate 3 copies of the spell along with 3 Gravekeeper's Commandant which searches the deck for Necrovalley. This is a total of 6 cards that activate Necrovalley in a 36 card deck first turn. Now that probability of playing Necrovalley: 6/36 = 1/6. This implies that it is simple and probable to open with Necrovalley. The secondary goal is to activate Necrovalley then activate Royal Tribute. Only 2 copies are allowed per deck currently. Here's the corresponding math: 2/36 = 1/18. That's the probability of opening with Royal Tribute first turn.
Anyway, in the Plant Synchro world I have started experimenting 3 Upstart Goblins in my builds. The explosiveness plants can unleash makes the 3000 maximum life increase by Upstart insignificant. My current goal is to include as many cards possible that thin out the deck in some fashion (Reborn Tengu, Sangan, Morphing Jar, Tuning, Tech Genus Hyper Librarian) without removing winning strategies and defense mechanisms (Effect Veiler, Mystical Space Typhoon, Solemn Warning). Currently it's proving to be a difficult challenge because I can only incorporate so much. I'm still unsure if I am going to Nationals or not but this type of build is what I'm planning to create nonetheless.
My final factor I wish to reinforce in this post is the importance of playtesting and drawing sample hands. It's crucial so you can realistically determine the probabilities of your deck when it matters. For example, I played 100 sample hands when I took on the challenge of building Six Samurai. 78 out of those 100 hands were capable of summoning Shi En first turn assuming there was no interferance from your opponent. Drawing sample hands provide you with information of your more probable plays outside of pen-and-paper mathematics.
Remember to include mathematics when constructing any deck. One card can make all the difference.
Mario
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