How Many Cards Go in a Deck?

ThomasR

When building a deck one of the most controversial topics is the number of cards to include. Some players swear by 40, often you see lists with a handful more, and sometimes players really pile on the cards. How can you determine the right number? When is it okay to go above 40? Should you play an Upstart?

Upstart Theory

In "Road of the King" Patrick Hoban states that for any given deck there is a "correct" number of cards one should be playing. This, he notes, ignores the rules of the game, and is a number based only on the theoretical optimal deck size for any given strategy. In a tournament, however, we are limited to a range of 40–60 by the rulebook. Five-card Exodia decks wouldn't be much fun.

Hoban makes this statement to better explain his fondness for Upstart Goblin, which became limited after his successful campaign to justify its triplicate inclusion in most decks. The crux of his argument was that to play a 40-card deck without Upstart must suggest that 40 is the exact optimal number of cards for your strategy. If more cards were optimal, then you could play more, if fewer were superior then adding Upstart would at least get closer to that sweet spot. This theory does assume that there is no downside to playing Upstart, but even in modern day Yu-Gi-Oh! with its harsh end-of-match procedure, the 1000LP typically does not make a difference.


upstart goblin
"The legacy of Partick Hoban"

Why is it then that Upstart Goblin seems to be so much less frequently played in 2020 than it was in 2016 when Road of the King was published? Have people forgotten about it? I think that might be partly true. Another component may be the logical bias that it somehow feels "less worthwhile" to play only a single copy. Another important aspect, however, is simply that the optimal size for a deck has got larger.

Decks Gone Supersized

In 2016 it was very much the standard for nearly all decks to be exactly 40 cards, but just one year later everything would be flipped on its head by the release of That Grass Looks Greener. Initially overshadowed by Zoodiac in the same set, I believe that the now-forbidden spell card actually had a more significant impact on the game as a whole. Suddenly there was a real incentive to play 60 cards rather than 40. I think we owe a lot to the impact of Grass forcing players to properly investigate the implications of a larger deck count.


that grass looks greener
"This is a card that I really RATE!"

At the height of this revolution the 60-card decks had become so popular that other decks like Paleozoic Frogs were also playing 60. Often this was primarily as a meta call to prevent the blowout spell from being played against them by the Lightsworn-Predaplant-Zombie deck with which it was most associated. I recall a regional tournament that I entered with a 60-card Paleo deck, listing Grass in the side deck. I only sided them in against the few players who still opted for 40.

The most significant impact of this overhaul was that it taught players to respect the power of playing 50% more cards in their deck. The Lightsworn players were not only winning when they successfully resolved Grass. They were able to leverage all manner of other powerful engines, even with their corresponding Garnets, both literal and metaphorical. The beauty of 60 cards was that the players would draw the hands made unplayable by engine requirements half as often as in a 40-card deck. Yeah, that's right: half.

Time for Some Probabilities

This is an idea that I had first contemplated in early 2016, shortly after the release of Brilliant Fusion. I calculated the probabilities of opening with "Brilliant but not Garnet" in 40- and 60-card decks: 30.21% and 21.73% respectively. But I also calculated how the number of cards affected the chance of opening with Garnet: from 12.5% down to 8.33%. Some of the latter would be the absolute worst-case scenario of opening with both Garnet and Brilliant Fusion: from 3.55% down to 1.61%. When increasing deck count from 40 to 60, the chance of your best -ase outcome drops by just a quarter, but the likelihood of your worst case falls by more than a half.


chart 1
Some proportional improvements

These numbers become even more favorable for the larger deck size when you begin to incorporate more starter cards. Let's consider a deck with three Brilliant Fusion, one Garnet, three Predaplant Ophrys Scorpio, three Lonefire Blossom, and one Predaplant Darlingtonia Cobra.

In this case a favorable outcome is any hand which could resolve Brilliant Fusion; the unfavorable outcome is any hand which has either of the two engine requirement bricks but no other cards from the package; and the worst-case scenario is any hand which cannot resolve Brilliant Fusion and contains at least two of the cards listed above. For simplicity of maths, it is assumed that any hand will always have a monster card available to use for the effect of Scorpio.


chart 2
Even better results

In this case adding twenty more cards reduces the probability of the desired outcome by about a sixth, but still reduces the chance of the worst case by almost half. The more ways you have to access the combo pieces which you don't want to draw, the greater the marginal improvements from adding more cards to your deck will be.

Random or Controlled?

To take a non-numerical approach to the issue, you can consider every event where a card moves from your deck to be either "random" or "controlled." A random event is typically a card drawn or alternatively sending the top card of your deck to the grave. A controlled event would be anything where you look at your deck, choose which card to take, and then shuffle afterward. For random events having fewer cards in your deck gives the best chance of finding the best one at any given moment. For controlled events, however, having more cards in your deck means a lower chance to have already drawn the one you want to search for, as well as potentially making space for more search options.

Even if your deck contains no draw power, the fact that each game begins with five random draws heavily biases the advantage to a smaller deck size. Despite this, in recent years we have actually seen a number of decks reaching a critical mass of controlled events whereby the advantages of larger deck size outweighs the benefits of a more consistent opening hand. It's no longer uncommon to see decks maxing out the 60-card limit even now without Grass. Typically these decks revolve around cards like Cherubini, Ebon Angel of the Burning Abyss or Crystron Halqifibrax, and reliably feature Guardragon Elpy and Pisty.


guardragon elpy guardragon pisty
The usual suspects

With opening turns comprising dozens of moves, these 60-card combo behemoths are an extreme example, but middle ground certainly exists. My two most successful YCS decklists consisted of 50 and 48 cards and were built around the principle of playing many starter cards and diluting my engine requirements.

Deck Building

Next time you're building a deck I'd recommend that you look at the balance of controlled and random events in each game, as well as the number of engine requirement cards that you don't want to draw. If you have many searches and Garnets, then it may be time to consider adding more cards. If you don't search much at all, then you need a very good reason not to play 39 and one Upstart Goblin.


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



3 Comments

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Techgenus11(17.09.2020 22:07)

Nice one!

DavrK(14.09.2020 14:32)

Very useful and interesting article

TobiHenke(10.09.2020 10:13)

I really enjoyed this one.

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