Determining Key Cards
For example, consider Joshua Schmidt’s Paleozoic Frog main deck, finishing second during December’s Yugioh Championship Series in Bochum:
| Joshua Schmidt’s Paleozoic Frogs | |
|---|---|
| Monsters | Dupe Frog x3 Maxx "C" x2 Ronintoadin x2 Swap Frog x3 |
| Spells | Pot of Desires x3 |
| Traps | Breakthrough Skill x1 Compulsory Evacuation Device x1 Dimensional Boundary x3 Paleozoic Canadia x3 Paleozoic Dinomischus x3 Paleozoic Leanchoilia x1 Paleozoic Marrella x2 Paleozoic Olenoides x3 Paleozoic Pikaia x1 Reckless Greed x3 Solemn Strike x3 Waboku x3 |
| Extras | ABC-Dragon Buster x1 Downerd Magician x1 Dante, Traveler of the Burning Abyss x1 Paleozoic Anomalocaris x2 Number 45: Crumble Logos the Prophet of Demolition x1 Todally Awesome x3 Sky Cavalry Centaurea x1 Daigusto Phoenix x1 Cat Shark x1 Paleozoic Opabinia x2 Number F0: Utopic Future x1 |
Here is a breakdown of his deck into distinct card groups to help illustrate the key cards in a typical opening hand, as well as what happens when Pot of Desires is activated.
Card Name | Paleozoic | Swap Frog | Other Frogs | Disruption | Draw Power |
Dupe Frog | Yes | ||||
| Maxx "C" | Yes | ||||
Ronintoadin | Yes | ||||
| Swap Frog | Yes | ||||
Pot of Desires | Yes | ||||
| Breakthrough Skill | Yes | ||||
Compulsory Evacuation Device | Yes | ||||
| Dimensional Boundary | Yes | ||||
Paleozoic Canadia | Yes | ||||
| Paleozoic Dinomischus | Yes | ||||
Paleozoic Leanchoilia | Yes | ||||
| Paleozoic Marrella | Yes | ||||
Paleozoic Olenoides | Yes | ||||
| Paleozoic Pikaia | Yes | ||||
Reckless Greed | Yes | ||||
| Solemn Strike | Yes | ||||
| Waboku | Yes |
The Expected Value
Using the formula for calculating the expected value helps to determine the most common opening hand, along with what cards are likely targets for drawing into, as well as banishing.
| Most Common Opening Hand | # Drawn | # in Deck |
Paleozoic Card | 2 | 13 |
| Swap Frog | 0 | 3 |
Other Frogs | 1 | 5 |
Other Disruptive Cards | 2 | 13 |
Draw Power | 1 | 6 |
Miscellaneous | 0 | 0 |
| Total | 6 | 40 |
It is important to note Schmidt’s deck has one too many cards dedicated to draw power, or any other group causing conflict with one another in a five-card opening hand. Instead of opening with an extra defensive card, Joshua may open with Pot of Desires, leaving whichever he may need to another element of chance, a move far more costly in nature. However, in this example, he will open second, drawing a full six-card hand, including a copy of Pot of Desires.
Pot of Desires? | ||
Card Group | Banished | Draw |
Paleozoic Card | 3 | 1 |
Swap Frog | 1 | 0 |
| Other Frogs | 1 | 0 |
| Other Disruptive Cards | 3 | 1 |
| Draw Power | 1 | 0 |
Some readers may notice only nine cards are banished instead of ten. Each of the expected values is set to round up or down to the nearest integer, as some were not of a high enough quantity for consistent banishment. In this case, it is possible for Pot of Desires to banish an additional card from one of the card groups.
The two cards drawn afterward will likely be from groups with the highest representation. In this case, activating Pot of Desires provides a boon for Joshua, as the deck features several redundant cards, as losing a few copies will not affect him. However, Pot of Desires hurts Joshua if he is in need of any specific card in the deck belonging to a group with lower representation such as Ronintoadin, as Desires will not only banish such cards but also not providing anything in return.
Will the downsides of Desires change if Joshua decides to play more cards? For example, consider Joshua decides to add twenty more cards while keeping his original ratios for everything else the same. Here is the result of activating Pot of Desires on the first turn using the same deck with twenty more cards:
Pot of Desires? (60-Card Deck) | ||
| Card Group | Banished | Draw |
Paleozoic Card | 2 | ? |
Swap Frog | 1 | ? |
Other Frogs | 1 | ? |
| Other Disruptive Cards | 2 | ? |
| Draw Power | 1 | ? |
| Miscellaneous | 3 | 1 |
As shown, Pot of Desires has a ravaging effect upon card groups disproportionate with the largest groups. Adding more cards to the deck compounds the negative effect further when the deck is unbalanced among the groups.
How valuable is Pot of Desires mid-duel? Somewhere around turn five or ten? For example, continuing with the original 40-card deck, however, it is turn eleven and both players have drawn five cards each since the draw phase. Furthermore, Joshua activates Reckless Greed, drawing two more cards, and ends up with one copy of Pot of Desires. Therefore, in total, Joshua has drawn 13 cards from the deck.
Provided Joshua did not play any cards capable of dumping traps or monsters to the graveyard, here are the expected cards remaining in a 27-card deck:
Group | Remaining |
Paleozoic | 9 |
Swap Frog | 2 |
Other Frogs | 3 |
| Disruption | 9 |
| Draw Power | 4 |
| Total | 27 |
Pot of Desires? (27 Cards Remaining) | ||
Card Group | Banished | Draw |
Paleozoic Card | 3 | 1 |
Swap Frog | 1 | 0 |
| Other Frogs | 1 | 0 |
| Other Disruptive Cards | 3 | 1 |
| Draw Power | 1 | 0 |
Surprise! Activating Pot of Desires achieves the same results mid-duel as activating it on the first turn. It will banish most cards from groups with the highest representation; however, all card groups will lose a minimum of one card. Therefore, if Joshua has not drawn into a Ronintoadin by turn eleven, he is fine. However, if he has drawn into it, he may have banished his remaining copy. This is what makes Pot of Desires such a polarizing card. It will not increase the odds of drawing into underrepresented targets. It does the reverse.
Ten cards represent the bare minimum of cards in a group a duelist may have and receive a respective card when activating Pot of Desires. However, this total varies proportionally with the total deck size. Therefore, cards belonging to a specific group need to represent at least 30% of the total deck to survive banishment and provide a chance of being drawn. Anything outside of these groups is subject to banishment and Desires will provide nothing in return. In fact, 30% of a deck is the required minimum to see an expected value of one card per two cards drawn.
After considering the expected values of drawing into such cards when using Desires, is it worth using? Better yet, is general draw power worth playing in a deck? It depends. If the duelist meets the bare minimum for Pot of Desires, there is still only a 50%-55% chance of drawing the card. This applies to all effects capable of drawing two cards from the deck. However, a group needs only representation of 25% of the total deck for other effects drawing two cards, such as Trade-In.
However, for cards representing such a large percentage, the duelist will draw more than one of such cards in their opening hand on average. This leads to the conclusion of draw power benefitting decks capable of affording redundancies in high quantity. Generally, decks with such redundancies are very powerful with simple, yet explosive plays.
A Small Consistency Boost
Lastly, cards providing draw power do not provide guaranteed results. Therefore, it is inadvisable to invest more than 10% of the deck to it in hopes filling inconsistency gaps. Draw power works best when viewed as a means to mulligan undesirable opening hands. For example, consider a deck has an opening combo rate of 66%. Which leaves 34% of the remaining opening hands undesirable. The deck includes three copies of Pot of Desires, which the user may draw into 34% of the time as well.
Calculating the odds of obtaining an undesirable hand and Pot of Desires is as follows:
34% * 34% = 12%
Pot of Desires has roughly a 50% chance of drawing at least one target card upon activation, thus continuing the equation here:
(34%*34%) * 50% = 6%
Furthermore, if the user requires two cards from two separate groups meeting the minimum, the chance is 3%, effectively half. So three copies of Pot of Desires will increase a deck’s overall consistency by a minimum of three percent, and at most six percent. This is great for high power decks with barely enough consistency by competitive standards (66% and above).
Conclusion
In conclusion, cards providing draw power is not for everyone. Furthermore, Pot of Desires definitely is not for everyone. Pot of Desires will do far more harm than good to decks with many moving parts. Conversely, Pot of Desires will provide an indisputable benefit to decks with plenty of free space to spare and do not rely on cards of limited quantity. In fact, effects providing draw power do not guarantee desired results, thus deck builders should consider such effects as icing on the cake and not part of the main meal.
