Test

> He makes the claim that shunsuke optimized his deck for going second, yet he ran 4 traps.

In terms of calculating the expected value, four traps represent the bare minimum of cards required to open with no more than one copy on average.

In a six-card opening draw, he has a 34% chance of opening with a single trap. Additionally, there is a 5.16% chance of opening with two traps. Essentially, one out of three duels, Hiyama can expect to see one trap. In fact, the expected value remains the same for a five-card opening hand.

For the remaining two duels, he will have no trap cards, which is ideal for an aggro play-style. For the one duel with a sub-optimal hand, why not try to slow the opponent down?

> You can't apply standard deviation to this at all because there's no mean in the data, just the expected values, and there aren't multiple data points to calculate the standard deviation from.

I explored the mean, variance, and standard deviation for each of the two-card combos in their decks, as such plays are essentially the “bread and butter” of a typical Blue-Eyes deck.

Here’s the results:

Play|Shunsuke Hiyama (Japan)|Erik Christensen (U.S.A.) :-:|:-:|:-: #1 (Two-Card Combo)|30%|19% #2 (Two-Card Combo)| 34%|34% #3 (Two-Card Combo)| 34%|35% Mean| 33%| 29% Variance| 0.000533333| 0.008033333 Standard Deviation | 0.023094011| 0.089628864

Christensen sacrificed two-card consistency to place more emphasis on stronger, three-card plays, such as dumping a Blue-Eyes monster with Trade-In and reviving, and Cyber Dragon Infinity. The lower variance and standard deviation illustrate how evenly distributed Hiyama's plays are in contrast to Christensen's.

I did not include this information because I thought it was fairly obvious for such a small sample of data.

> As for mathematical precision, none of the definitions fit. Precision can be seen as either the number of digits used in a calculation or how close repeated trials are to one another, such as throwing a dart repeatedly and having them all land close to one another

A 42-card deck represents the absolute maximum for Hiyama to keep his card ratios the same as if he were to use a 40-card deck, for a six-card opening hand.

It causes a one-percent drop in overall consistency from 66% to 65%, yet has no impact on what he can expect to draw. Essentially, he has two extra cards to work with without disrupting his opening hand.

I assume most duelists check their ratios by constantly drawing cards over and over to see how close the results are to what is desired, no? Well, knowing the frequencies short-cuts the entire process. Whether Hiyama mathematically checks his card ratios to find extra deck space is to be determined, it is impressive nonetheless.