When will I draw my card?

Special summoning against your opponent’s set backrow is a little like walking onto a newly frozen pond.  You proceed with a bit of tenuousness. 

Step: Normal summon … please, no Bottomless …

Step: Special summon … please, no Solemn Judgment …

Step: XYZ summon … please, no Tor

Opponent: Torrential Tribute!

Through the ice you go with all your imperious monsters. 

So here’s the question Sid Crosby: What are the odds of your opponent drawing an out with each turn? 

The following graph shows the percentage of drawing a card as a function of the number of draws. Each line represents the number of copies of the card in the deck.  Given the search power of most decks, I have included values for more than three cards.  For example, Yamato can be searched by Tenki and Peacock giving the player nine ways of finding the little general.  I should add that this analysis does not take into consideration what has already been played.  If your opponent has played Torrential, the chance of drawing Torrential is 0.  I also do not account for decking thinning as the result of a search.  Nevertheless, I do believe it is illustrative. 

Good players probably intuit what this graph demonstrates.  For the rest of us, a table may be more practical. The numbers in red are the turn in which your opponent has more than 50% or 90% chance of having a particular card. For example, your opponent has a 50% chance of having Dark Hole by turn 15.  He has a 90% chance of having it by turn 31.  

Number of Cards	1	2	3	4	5	6	7	8	9
Turn for > 50%	15	7	4	2	1	1	1	1	1
Turn for > 90%	31	22	16	12	9	7	6	5	4

What can we learn from this little analysis?

1. Fear not the one of’s.  I certainly don’t want to advocate reckless play.  Going minus four to Dark Hole is a quick way to descend to the lower tables.  On the other hand, one can play too conservatively.  In fact, conservative play is often punished by the speed of most decks.  In a meta of unprecedented searching power, drawing Dark Hole is a relatively rare event.

2. Don’t rely on two or three side deck cards.  Putting in three Light-Imprisoning Mirrors is not enough to beat Bujins.  You will have to wait four turns to have a 50% chance of having that card while the Bujin player will have an 80% chance of opening with Yamato.  While I agree that LIM is a great card and one that I will side, you should consider ways of playing around that deck without it. 

3. Keep these numbers in mind when facing certain archetypes.  I’ve pointed out in a previous post that there are more similarities than differences in deck builds.   For example, Fire Fist decks typically play only one or two traps that hurt you when attacking.  Holding back an attack in fear of a Mirror Force, Dimensional Prison, or Magic Cylinder makes little sense.  Your opponent will need six or seven turns to have a 50% chance of having one of those cards. 

Coming up next: The Road to YCS Atlanta

My posts and play over the next two weeks will be dedicated to getting ready for this event.  This is the first big event after the introduction of Legacy of the Valiant.  It should be entertaining.