Monday, August 19, 2013

The Power of the Draw

To understand why the last format devolved into a two-deck slugfest, you need to understand the impact Super Rejuvenation and Spellbook of Judgment had on their respective decks.  Without these cards, E dragons and Spellbooks are good decks.  E dragons would still be tier one while Spellbooks would likely return to its pre-JOTL quirkiness.  However, add Super Rejuv and Judgment and these decks get propelled into the Yugioh pantheon of “The Best Ever”.  The reason becomes obvious when you consider how much an extra draw gets you.

Let’s say you have a 45 card deck and want to draw into one of three power cards.  Your odds of doing so are about 35.6%.  If you work hard and eliminate five cards, you can increase your odds by about 4%.  However, if you draw an extra card without lowering the total card count, your odds of drawing your power card is 40.5 %.  Draw two extra and the probability increases to 45.2%.  In other words, drawing one additional card makes up for the sloppiness of having five cards over the minimum deck size.  

Compare these numbers with the advantages of adding Pot of Duality to your deck.  In my mind, this card is the equivalent of reducing your deck by three cards. So going back to our 45 card deck, adding one PoD increases your odds to 37.8%.  If you add three PoD, your odds increase to 43.1%.  In other words, three Pot of Dualities underperforms two extra draws.  

Of course, draw power was only part of the E dragon/Spellbook monopoly.  These decks also had search power.  I see cards that search as “equivalent” to the power cards.  So if you add a searcher, you now have four chances to draw your power card.  This increases the odds to 44.8%.  Thus, adding a card that searches is the most efficient means to getting to your power cards. 

Do these numbers shed some light on why your quaint little Samurai deck didn’t stand a chance against E dragons?  If they played three gold sarcs, three reactant, and three Redox and if they drew four cards with Super Rejuv, their chances of getting to Redox was 93%.  

The rest of us never had a chance.

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