So you have this nifty idea for a deck. Great! You gather
the requisite cards, shuffle them up, and deal out six cards. Hmm, not bad.
Shuffle again, six more cards, and again … not bad. Maybe you’re onto to something. So you go through this drill five more times
and then on the eighth time you draw garbage.
At that point, you can pitch the deck and go back to your Dark Worlds,
conclude that the deck produces dead hands 12.5% of the time, or have the
statistical savvy to know that eight hands is not enough to fully assess the
deck’s potential. Hopefully, you believe
the latter.

There are 3,838,380 combinations of six cards in a 40 card
deck – well, actually less since there are duplicate cards, but you get the
point. To determine how often your new
deck will produce dead hands, you have to take a sample. It’s like political
polling where you gather opinions from a small number of people to make
statements about the whole group. In
this case, you want to look at a small number of random hands and assess them
as “Live” or “Dead”. The value of this
exercise depends on (1) the number of hands you look at and (2) your ability to
assess “Live” or “Dead”. In fact, the
latter is probably more important. The
reason that most of us struggle to top with a net deck by Billy Brake is that
he sees plays where the rest of us see dead.
If I knew the secret of that skill, you’d be reading about my latest YCS
top. Instead, I can give you the answer
to the sample size question.

I won’t go into all of the mathematics supporting these
ideas because that would drive away the small number of readers that I
have. Instead I will try to provide a handful
of principles and some useful numbers.

You could choose to analyze your deck by asking the following
question: “How many dead hands are in this deck?” This question sees the percentage of dead
hands as an inherent quality of the deck.
It is measurable like measuring blood pressure in the residents of a
group home. To determine how many of the
3 to 4 million hands you need to look at, you must pick a confidence interval
and a confidence level. The interval is
the plus/minus figure that often accompanies polls. If you choose a confidence interval of 5%,
you’re saying that your sample could have 12% dead hands but the deck could
have between 7% and 17% dead hands. The
confidence level is the percentage of times you will get the right answer if
you sampled the deck multiple times. For
example, if you and nine of your friends sampled the deck and measured the
number of dead hands, one would get the wrong answer if you were using a 90%
confidence interval.

So how many hands would you have to look at in order to get
an idea of the number of dead hands? For
a 5% interval and a 95% confidence level, you would have to look at

**384 hands**. You could back off on your assumptions and use a 10% interval with a 90% level. In that case, you would need to look at**68 hands**. The main conclusion that I draw from this analysis is that*players probably make decisions about their decks with insufficient information*(i.e. too few samples).
Common sense will tell you that you can get a good idea of
how good or bad a deck is long before you look at the 300

^{th}sample hand. The reason is that you are intuitively comparing the new deck with your experience and expectations with the old deck. You are, in a sense, performing a statistical test similar to a Chi Square test. Like many statistical tests, this one helps answer the question*Is my nifty deck different than my old deck?*The bigger the difference (i.e. the more dead hands your nifty deck produces), the fewer hands you will need to look at.
With that in mind, consider the following table that
compares your new deck with a deck that produces live hands

*90% of the time*. The first column is the percentage of live hands your new deck produces and the second column is the number of hands you need to look at to determine its inferiority. If your deck draws good hands only 50% of the time, you will be able to conclude the deck is*worse than 90%*in 6 hands (line 1). If your deck produces live hands 70% of the time, you’ll need to look at 24 hands to determine if the deck is worse than your old deck. If your new deck is 5% worse than your old deck, you’ll need to look at 370 hands.% of Live Hands | Total # | Live hands | Live hands |

in the Nifty Deck | of Hands | in the Old Deck | in the Nifty Deck |

50% | 6 | 5 | 3 |

55% | 8 | 7 | 4 |

60% | 11 | 10 | 7 |

65% | 15 | 14 | 10 |

70% | 24 | 22 | 17 |

75% | 42 | 38 | 32 |

80% | 93 | 84 | 74 |

85% | 370 | 333 | 315 |

I hope this sampling discussion helps you understand the
most common Yugioh complaint I've heard:

*I didn’t draw $#!^.*No, actually your deck draws much more*$#!^*than you realize. You simply haven’t looked at enough hands to know.
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