Probability in Yu-Gi-Oh!: The Math of Going Over 40

When building a new deck, most people tend to stick to the minimum number of cards. After all, many strategies just want to draw a specific starter. But there are decks that don't need to stay at the minimum. There is nothing wrong with playing 40 cards, but with a little bit of math we can uncover other possibilities.


Why Would You Like to Play More Cards?

When talking about decks that play more than 40 cards in their main deck, in the January 2022 format, there are multiple to choose from. Players have access to cards such as and , and decks can play one or more engines in their decks. At the moment of writing this article, decks that run one or more of these engines are really popular, and the average number of cards in decks that play multiple engines tends to be closer to 60 than 40. For example, decks like Dragon Link and Cyberse Eldlich tend to play the biggest possible deck size.


Destiny HERO - Destroyer Phoenix Enforcer Rite of Aramesir

In some formats, playing more than 40 cards has rarely been a good idea, but with access to multiple small engines, deck building has become interesting. Next to the DPE and Brave Token engines, others such as Dogmatika and Rose Dragon are still rather popular. If you want to know more about the engines of the current format, I highly suggest checking out an article written by Sherif Lewis.

The Math Behind a 53-Card Deck

For this article, I use a 53-card Drytron deck as an example to demonstrate how adding cards doesn't negatively affect the balance of the deck. For those who are thinking about hand traps, we'll get to that, don't worry. For a deck like Drytron, there are usually two variants—the one that contains 40 cards and the second one that contains 50 or more cards. Apart from , the deck has many more ways to start their plays, such as , , and .


Drytron Alpha Thuban Cyber Emergency

In the 40-card variant, it's common to either play around sixteen cards that are Drytron monsters or search for them. This means the player starts with one of those cards 93.5% of the time and with two 67.7% of the time. For the most part, if you start with two Drytron monsters or cards that search for them, you are starting with at least a decent hand.

If the player wants to get the same numbers at a bigger deck size, they must obviously add more starter cards, such as . If one plays a 53-card deck, they have to play 21 starters to achieve a one-starter hand 93% of the time and a two-starter hand 66.7% of the time.

Another important thing in Drytron decks are ritual monsters. In a 40-card deck with five ritual monsters and three , the player draws one with 69% probability. With a 53-card deck, players have to play eight ritual monsters to achieve the same probability, which still leaves room for more cards of their choice.

If a player adds five starters and three ritual monsters to their deck, that allows them to add five more cards, be those more hand traps or other cards they see fit. In Drytron's case, this usually means more tech ritual monsters or hand traps, but in other decks, those slots can go to other tech cards or even a small engine. Playing more cards also reduces the possibility of drawing multiples of the same card, which, for example in Drytron decks, is a good thing most of the time.


53-Card Drytron Decklist
MonstersSpells & TrapsExtra Deck
  • 1
  • 1
  • 1
  • 3
  • 3
  • 3
  • 1
  • 2
  • 3
  • 3
  •  
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 2
  • 1
  • 3
  • 3
  • 3
  • 1
  • 3
  • 2
  • 2
  • 3
  •  
  • 3
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 2
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1

But What About Hand Traps?

The biggest downside of adding cards to the deck is that drawing hand traps gets harder for the player. In the current format, the usual amount of hand traps is between nine and twelve, but some decks run even more of them. A 40-card deck with nine hand traps draws one of them to opening hand 74% of time, while with 53-card deck, players would have to play twelve hand traps to achieve a similar probability. If a player decides not to add more hand traps and sticks to just nine, the probability of drawing one will drop to 62%, which is still a decent number.


Ash Blossom & Joyous Spring Forbidden Droplet Infinite Impermanence

Another thing to consider when adding cards to the deck is the side deck. In a similar fashion to hand traps, playing a larger deck requires a player to bring in more cards from the side deck to achiev the same effect. For example, while in one scenario, the player would only side , they might want to consider adding as well when playing more than 40 cards in their deck.

In Conclusion

When adding cards to the deck, the main thing to ask is, what is the goal of the deck. If you play a deck like Gravekeeper that wants to search as fast as possible, you most likely want to play as small of a deck as possible. However, for example when playing Drytron, the player wants to force their plays through as many hand traps and interactions as needed, and if everything else goes wrong, they can go for and Destroyer Phoenix Enforcer.

Some people like to add cards and draw test hands, and after they have drawn a couple of good ones, they end up thinking that playing a random number of cards is a good idea. For every Yu-Gi-Oh! player who likes to tinker with numbers, I would like to point them to this Deck Probability Calculator, which allows users to calculate chances of drawing specific cards to their opening hand. The same calculator has been used to calculate probabilities in this article.

Do you regularly use math when building your decks, or do you have another way to come up with your builds? Let us know in the comments below!

Opinions expressed in this article are those of the author and not necessarily Cardmarket's.