Many beginners of the game (I used to think this way too) have the mindset that more cards is better. Looking from one standpoint, having more cards in a deck means you have access to more resources, and keeping advantage wins duels. However, these are the people who have either not studied probability and statistics to a proficient level, or who play casually.
The thing about a 40 card deck is that even though you have less resources, you get access to those resources quicker. It's a simple probability problem really. Let's pick a generic card like Mirror Force. If your opponent is swarming you with monsters, it sure would be nice to draw that Mirror Force and turn the game around. Let's also consider that the duel has already progressed several turns.
In a 40 card deck then, it would have ~25 cards mid-game, while a 60 card deck would have ~45. Let's do the math:
1/25 = 0.0400
1/45 = 0.0222
So in the 40 card deck, you have a 4% chance of drawing the life-saving card, while in a 60 card deck, it reduces to 2.2%. The difference is somewhat minute, but that small difference can mean a match.
Let's try a more practical example. In every deck, there are key cards which a duelist will want to have in their hand so they can begin their combos. Since my main deck is Fortune Chaos, then the top 5 cards I would want as an opening hand would be:
1) Future Visions (3) / Terraforming (2)
2) Fortune Lady Light (3)
3) Compulsory Evacuation Device (2)
4) Gold Sarcophagus (2)
5) Allure of Darkness (1)
6) Fortune's Future (3)
I would explain the combo I pull off with these in this post, but those of you who play me frequently would be aware. The point of this post is to emphasis the importance of the 40 card minimum.
The number in brackets next to the card name indicate how many of that particular card I have in my deck, either because of ban list restrictions, or by personal preference. Let's start with my #1 most important, Future Visions.
For Future Visions, I have 3 copies of the card in my deck. Terraforming is a "floater", which is a card that searches for another card in your deck. So in my 40 card deck, I have 3 copies of the card I need, and 2 copies of a card which searches for the card I need, which in the end accomplishes the same thing. However, not only does Terraforming get me the card I need, but it also "thins" my deck, which lowers the total number of cards. As I showed previously, a lower number of cards in the deck result in a higher probability of drawing what you need.
5/40 = 0.125
5/60 = 0.0833
So in the 40 card deck, I have a 12.5% chance of drawing Future Visions, while in the 60 card deck, it is an 8.3%. Of course this is assuming I only draw one card. But at the beginning of the duel, each player draws a hand of 5 cards, and on their first turn, they draw an additional card. So by your first turn, you will have 6 cards in your hand. Let us now see the percentage of drawing Future Visions, assuming that after each draw, you still don't have it in your hand.
40 Card Deck:
5/40 = 0.125
5/39 = 0.128
5/38 = 0.132
5/37 = 0.135
5/36 = 0.139
5/35 = 0.143
Total = 0.802
60 Card Deck:
5/60 = 0.0833
5/59 = 0.0847
5/58 = 0.0862
5/57 = 0.0877
5/56 = 0.0893
5/55 = 0.0909
Total = 0.522
Difference: 0.802 - 0.522 = 0.28
That's a total of 28%! Now is the time to remind you that each event is not additive; in other words, if you repeat the process in the 40 card deck until you reach a total of equal or greater than 1, that does not mean you will draw that card after that many attempts. These events are independent of each other, except for the fact that after each event, you remove one card from the total number of cards. So a more realistic calculation would be the average of the attempts:
40 Card Deck Average:
0.802/6 = 0.134
60 Card Deck Average:
0.522/6 = 0.087
Difference: 0.134 - 0.087 = 0.047
So each draw, in a 60 card deck, you lose ~4.7% of getting the card you need. In the end, that can really add up.
Finally, I will dissuade you from putting 41 or 42 cards, just because you think 1 or 2 more cards won't be that big of a deal. True that if you repeated the calculations above with a 41 denominator, the difference in percentage would not be significant, but remember that these calculations only encompass drawing ONE card you need. What if for example, to do a perfect combo, you needed all 6 cards listed above. I hope you remember your probability rules from high school.
In this example, I will go from least likely (Allure of Darkness because there is only 1 copy of the card) to most likely (Future Visions / Terraforming). That would make the order of Compulsory Evacuation Device and Gold Sarcophagus, as well as the order of Fortune Lady Light and Fortune's Future arbitrary, as they the same number of copies. Also assume that each draw draws the card in question, so that the number of copies of other cards are not affected.
40 Card Deck:
Allure of Darkness = 1/40 = 0.025
Compulsory Evacuation Device = 2/39 = 0.0513
Gold Sarcophagus = 2/38 = 0.0526
Fortune Lady Light = 3/37 = 0.0811
Fortune's Future = 3/36 = 0.0833
Future Visions / Terraforming = 5/35 = 0.143
Rule of multiplication: 0.025 * 0.051 * 0.052 * 0.081 * 0.083 * 0.143
= 6.52 x 10^-8, or 0.0000000652, 0.00000652%
41 Card Deck:
Allure of Darkness = 1/41 = 0.0244
Compulsory Evacuation Device = 2/40 = 0.0500
Gold Sarcophagus = 2/39 = 0.0513
Fortune Lady Light = 3/38 = 0.0789
Fortune's Future = 3/37 = 0.0811
Future Visions / Terraforming = 5/36 = 0.139
Rule of multiplication: 0.0244 * 0.0500 * 0.0513 * 0.0789 * 0.0811 * 0.139
= 5.57 x 10^-8, or 0.0000000557, 0.00000557%
Difference: 6.52 x 10^-8 - 5.57 x 10^-8 = 9.50 x 10^-9
Now that is a significant difference in chance of getting the "perfect" hand. If you do the same for the 60 card deck, it will be a ridiculous percentage. In short, ALWAYS RUN 40 CARD DECKS.
The probability data presented above assumes that the deck is entirely random; that is, no cards are intentionally placed together. This can happen unintentionally when a duelist combines their current field with their deck while starting a new game. In another post, I will go over Biased Shuffling, which essentially makes the perfect hand easier to obtain, since no form of shuffling is completely random.
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