## Monday, October 21, 2013

### Calculating a Yugioh Deck's Turn Bias

So if you have been playing this game for anytime at all, you know that there is an advantage to going first.  You should also be aware that some cards are better when you go first and others when you go second.  For example, Thunder King Raioh is a great opening play.   Your opponent won’t be able to search and will have to expend some resources if they want to perform an inherent special summon.  Hand traps, in comparison, are better when you go second.

So here’s the question – does your deck have a first turn or second turn bias? In other words, does you deck win more often when you win or lose the dice roll?

This quality of your deck can be quantified in the following way.  Assign one of the following numbers to each card in your deck:

1 = If it is a good first turn card
3 = If it is a good second turn card
2 = If it really doesn’t matter

Now calculate a weighted average for the entire deck.  You can do this easily on a spread sheet by adding up the following:

Ʃ(B*n)/N
where B is the “turn bias” or the number you assigned the card, n is the number of that card,
and N is the total number of cards

By way of example, I have calculated this number for three of my Geargia decks.  The turn bias for each deck is given at the bottom of the table.

You may feel that the turn bias number B is arbitrary.  I wouldn’t disagree with you.  I assigned a number by simply thinking about my own reaction when I pick up 5 cards at the beginning of the game.  You may also doubt the validity of this metric.  Fair enough.  Though establishing validity would take a lot more testing, I can offer the following table:

As you can see, the numbers of good second turn cards increases as you look at these three decks from left to right.  As a result, the turn bias increases from 1.78 to 1.93.  You would think that a turn bias that was equal to 2.0 would be ideal.  My experience suggests otherwise.  My decks perform better when they are biased a bit towards the first turn.

This fun little exercise doesn’t really bring rigor to deck metrics.  However, it should get you to think about the ways that card choice plays out in the game.  You should also give this some thought when siding because you may be taken adding cards that pushes the deck’s bias in the wrong direction.  You would be better adding hand traps after a win and adding the purple cards after a loss.