A theoretical framework for two novel rule-variants for a popular trading card game

Abstract

A 3-person, probabilistic rule-set for the Pokémon TCG is described that aims to maximize fairness for all players. Several nuances are described and some tentative solutions are proposed. This rule-set was developed following experimental data. Additionally, a theoretical Strip-variant is proposed, but not practised here. This study adds to an unofficial database of alternative methods of trading card games, and hopes to receive input from others using the framework presented here in order to optimize 3-person Pokémon.


Cite: Asghar, M. (2018). A theoretical framework for two novel rule-variants for a popular trading card game. [online] cowopinion. Available at: https://cowopinion.com

Article history: Article accepted January 2018, available online 24 January 2018. Please note that the following article has not been through peer-review.

Keywords: Custom rules, Pokémon, trading card games


Introduction

Trading, or ‘collectable’, card games (TCG/CCG) have been pervasive in popular culture for the past 25 years. A TCG is one in which the player acquires, through purchase or trade, a sufficient number of cards (according to game-specific rules) in order to build a ‘deck’. This deck is then used to challenge other players in turn-based combat. There are a large variety of TCGs, with one source listing over 350 versions, including those that are no longer supported by their publisher. Some of the most popular include Magic: The Gathering, Yu-Gi-Oh!, and Pokémon.

IMG_20180124_173807
Figure 1. A coin from the Pokémon TCG.

Although TCGs have traditionally been a physical/tangible game similar to board games, e.g. Monopoly, recent digital TCGs have spawned a dedicated community following the contemporary rise of smartphones and facile internet access in the Western world; the most well-known example of this is Hearthstone, a standalone, initially free-to-play, smartphone game from the developers of World of Warcraft. Additionally, TCGs have been present as mini-games in some modern video games, for example, the card game Gwent in the Witcher 3. This digital revolution and the transcendence from niche players to the greater populace has spurned a resurgence in TCG popularity, supported by continuous publisher/developer support and ever-changing and evolving rules.

The Pokémon TCG

Following the release of the Pokémon video games for the Game Boy in the mid-1990s, the first generation of the Pokémon TCG was released in 1999 (English version, Wizards of the Coast). This ‘Base Set‘ was the first in a long line of 75 (to date) sets, spanning multiple Pokémon generations. While the fundamental rules have remained unchanged, various novelties have been added to the base games, such as the introduction of Pokémon-EX, BREAK evolution and more recently, Pokémon-GX cards. These additions usually mirror gameplay mechanics, albeit not exactly, brought about with each new iteration in the video game franchise.

A two player game, the Pokémon TCG operates on the winning condition of the player taking all 6 of his or her prize-cards – one is taken each time an opponent’s Pokémon is knocked out. Each player takes it in turn to draw cards, utilize ‘Trainer’ or ‘Item’ cards, attach ‘Energy’ cards to Pokémon, and evolve, retreat or put Pokémon into play. There are no official rules for 3-person games, i.e. a game in which the battle involves 3 players, each with their own decks, battling one another in a prescribed manner. Hence, the Pokémon TCG is limited in its extension to larger groups of friends. Here, we describe an unofficial ‘3-person Pokémon TCG’ rule-set, used successfully in human experiments.

In addition to regular card play, an alternative, erotic, method of ‘home-play’ exists amongst card players; usually performed with the standard set of playing cards (French suits), colloquially prefixed with the word ‘Strip-‘, e.g. ‘Strip-poker‘. The Strip variant of playing card games must include a fundamental rule whereby an item of clothing is removed following some pre-described win/loss condition. There is little information regarding adapting the ‘Strip’ condition to TCGs. Here, we describe a ‘Strip’ variant of the Pokémon TCG, and apply it, strictly theoretically, to a novel, unofficial, 3-person rule-set.

Methods

The following describes a framework for 3-person Pokémon TCG. These rules were implemented on an ad-hoc basis, and created by the author and two additional TCG game players, here anonymized as Emily and Jack. The personal pronoun will be used to denote the author’s action/intention, or referred to in the third person as Michael.

In the official, 2-person Pokémon TCG, each player draws 7 cards, and if both players have a ‘basic’ Pokémon in their hand, then the game may proceed (a mulligan is performed in the case of failing to draw a basic). A coin toss decides who goes first. 6 prize cards are then drawn and placed face down. If you knock out your opponent’s Pokémon, you may take a prize card. Your turn ends following attack, and thus, the game proceeds in rotation.

One method to play 3-person Pokémon is to simply follow the same rules as the 2-person game but add an additional player to the rotation in a ‘free-for-all’ design. Thus, after your opponent attacks, your next opponent proceeds to attack. In this way, 2 turns pass before your next turn. There is a bias introduced here, whereby, given free will to choose whom players can attack, one may be ‘ganged up’ on, due to personal discrimination or through temporarily alliances setup to eliminate a powerful strategy/Pokémon. Naturally, this study decided against the above method; rather we opted for a probabilistic method.

A probabilistic framework

Each player rolls a die: the highest roll goes first, the next highest second, and so on. In the case of equal rolls, there is a re-roll until one player rolls higher. This decides the order of rotation.

Following the second player’s turn (note: the player who goes first may not attack on his or her first turn – this is part of the official 2-person game and applies here too), he or she will roll a die, or one may flip a coin, in order to determine the direction of attack: left or right, e.g. heads is left. We hypothesize that having less information regarding your attack opponent eliminates besieging a single player, complicates strategies against opponents, without complicating existing rules (which produces a more interesting game), and adds the additional thrill of chance.

The game proceeds thusly, until one player takes all 6 of his or her prize cards. For visualization, one may picture the players in a 3-person game as vertices on a triangle (see Figure 2), with turn-rotation proceeding clockwise or anticlockwise, and attack-direction proceeding randomly. All other 2-person rules, such as weakness, abilities, evolving and energy attachment, apply unchanged.

co_triangle
Figure 2. A simple 3-person setup. Each node represents a player. The grey arrow defines the turn rotation direction in this case

Strip-Pokémon

We also propose a ‘Strip’-variant of the Pokémon TCG, which abides by the probabilistic framework described above, with some additional rules. If a player’s Pokémon is knocked out by the attack, direct or indirectly, of any opponent, the defeated player must then proceed to remove one item of clothing. We define an item of clothing as a single, continuous article of material used to cover the person’s body; therefore, a pair of socks counts as two items. It is proposed that every player must only wear 6 pieces of clothing, and thus after each game, there is the possibility that one player may be fully nude (since there are only 6 prize cards). Note that, a player may win by knocking out 3 Pokémon from either opponent, whom will both be semi-nude. Additionally, for nuances involving Pokémon-EX or Pokémon-GX, where 2 prize cards are taken following their knock-out, we propose that similarly, 2 items of clothing should be removed simultaneously.

Experiments

In this study, we performed multiple 3-person games, with the same 3 players, across multiple days. Overall, eight 3-person games were played, utilizing the rules presented here. The Strip-variant was not practised, but was discussed excitedly.

On four additional occasions, a fourth player joined the game and we proceeded with a 4-person extended game, however, this soon proved quite tiresome due to long wait times before each player’s turn, and so the concept was trashed, much to the chagrin of the fourth player. A 4-person rule-set is not presented here.

Probabilities of multiple coin tosses are discussed in order to test whether the probabilistic method was fair for all players. A framework is set out including rules for special conditions as well. It was hypothesized that this method would lead to fewer biases than the ‘free-choice’ method (where one can decide whom to attack), however, the control condition was not performed, i.e. playing a ‘free-choice’ method n times compared to the ‘probabilistic’ method n times, and deciding on a fairness criteria/difference based on group responses.

Results

Here, we present an analysis of the probabilistic framework for 3-person Pokémon, developed following eight 3-person Pokémon TCG experiments.

The between-turns step (BTS)

The 3-person probabilistic method, and any 3-person method for that matter, brings up nuances that are otherwise trivial in a 2-person game. One such nuance is the answer to the question, “When is my between-turns step?”. The between-turns step (BTS) occurs between turns in a 2-person game, and thus the delay is symmetrical and fair between players. This is important since special conditions (Poisoned, Burned, Asleep and Paralyzed) are evaluated in this step.

Imagine a scenario where Jack puts Michael’s attacking Pokémon to sleep. In this setup, let’s suppose the rotation is anticlockwise, with Emily following Jack’s turn (see Figure 2). In a 3-person game, there must be 2 BTS’s before it is Michael’s turn again. The official Pokémon TCG rules state that, “Between turns, flip a coin. If you flip heads, the Pokémon wakes up, but if you flip tails, it stays asleep”. Thus, either, Michael will benefit from having 2 opportunities to flip in order to wake up, or, a rule must be added so that Michael is only allowed one flip before his turn.

Two BTS’s:

p(Awake) + p(Awake) = 0.5 * 0.5 = 0.25

p(Awake) + p(Asleep) = 0.5 * 0.5 = 0.25

p(Asleep) + p(Awake) = 0.5 * 0.5 = 0.25

p(Asleep) + p(Asleep) = 0.5 * 0.5 = 0.25

One BTS:

p(Awake) = 0.5

p(Asleep) = 0.5

From the above, it can be seen that the probability of Michael’s Pokémon being awake is 0.5 after one BTS, or 0.75 after 2 BTS’s (chance of p(Awake) = 0.25+0.25+0.25). The extra step therefore adds a 25 % advantage bias to awakening.

The same logic can be applied to the ‘Burned’ special condition. Similar to the Asleep condition, a coin is flipped in the BTS, with the addition of placing 2 damage counters on the Burned Pokémon. For 2 BTS’s, the afflicted Pokémon will receive double the damage compared to a single step, however, there is also a 25 % increased chance of flipping a head to remove the condition.

The ‘Confused’ condition is unaffected by 3-person Pokémon, since a coin is flipped before your attack, and so does not affect turn-rotation or attack-direction.

Similarly, when ‘Paralyzed’, the condition is removed once you have had a turn with the active Paralyzed Pokémon in play. The condition is removed during the BTS, but it does not matter in which step it is removed, i.e. after Jack or Emily’s turn.

Finally, the ‘Poisoned’ condition is severely worsened in a 3-person game with 2 BTS’s. In each BTS, a damage counter is placed on the Poisoned Pokémon. This would result in double the damage per step compared to a 2-person game, and is harsher than the Burned condition, since there is no chance of salvation via coin toss to remove the condition.

We suggest that a single BTS is fairer and less complicated than 2 BTS’s. This single step should be evaluated in the BTS directly preceding the player’s next turn.

Ten simple rules for Strip-Pokémon

While the Strip-variant of the 3-person Pokémon TCG was not performed experimentally, lively discussions between players brought up several interesting discussion points, 10 of which we will state here.

  1. In the winter months (November-February), 6 items of clothing may be insufficient, thus players may choose to wear some integer multiple of 6 and if their Pokémon is knocked out, proceed to remove the integer multiple number of clothes. For example, if Emily decides on a multiple of 2, then she must wear 12 articles of clothing. Then, after her Pokémon is knocked out, she will remove 2 items of clothing simultaneously – in this way, Emily will be fully nude if 6 of her Pokémon are knocked out (meaning someone has won the game) even though she wore 12 articles of clothing to start with. This ‘multiple rule’ need not be consistent between players, e.g. Michael may wear 6 items while Jack wears 24 items (6*4).
  2. It is agreed that ‘clothing’ does not apply to jewellery, accessories (e.g. glasses) or any other object that all players cannot unambiguously decide is clothing.
  3. Given the lengthy turn times in the Pokémon TCG, which are exaggerated even more so in 3-person Pokémon, it was suggested that a time-limit should be imposed to each person’s turn, such that, to quote one player, his or her “nipples don’t freeze off”. 1 minute was suggested, with the possibility of a linear reduction/reverse exponential, after all players have taken equal numbers of prize cards, e.g. if all players have taken 1 prize card, then the turn time is reduced to 50 seconds, after 2 prize cards, 45 seconds etc.
  4. Imbibing alcohol was suggested to counteract feelings of nerves/shyness, as well as to provide a devilish warmth, serving to combat chills as described in point 3.
  5. Players must be over 18.
  6. Paper towels or some sort of seat covers are to be provided if Strip-Pokémon is initiated.
  7. Strip-Pokémon can only be initiated if all players unanimously agree.
  8. Strip-Pokémon does not end until one person has lost. This is to prevent any ‘chickening-out’.
  9. Once a player has removed an item of clothing, they must, without fail, stand up and pivot 360°, at a rate no faster than 1.57 radians per second. There shall be no attempt by the player to cover up their nudity, nor shall any observing player be allowed to perform any sort of physical contact without consent.
  10. Finally, it has been advised that the Strip-variant of Pokémon should only be practised in sufficiently warm, private areas such as your own home, and that all players should not be in any sort of long-term relationship, as by social custom, showcasing your nudity to your fellow players may be frowned upon by your partner.

A fellow researcher also raised a point regarding the probability of a player being fully nude at the end of a Strip-Pokémon game. For example, if we take Michael as the frame of reference, then there are 7 different win conditions based on who has lost an item of clothing:

[0 6], [1 5], [2 4], [3 3], [4 2], [5 1], [6 0]

where for [x y], x is the number of items of clothes remaining for Emily, and y is for Jack’s clothes. There are 7 win conditions for Michael, and thus a 2/7 or a 28.6 % chance of someone ending up fully nude at the end of the game (if Michael wins).

Anecdotal evidence from experiments

We suggest that although imposing a probability rule to the 3-person variant of Pokémon removes personal biases, there is still a 25 % chance probability that a single player may be attacked consecutively, possibly nullifying deck strategies, and ‘ruining the fun’ of the game. It is therefore suggested that an attack limit rule is imposed: thus, the same player may not be attacked 3 times in a row. This is best described by example:

Let’s suppose that Michael’s turn ends, making it now Jack’s turn (see Figure 2). At the end of his turn, he flips a coin and since it has been decided that heads is left, Michael is attacked. It is now Emily’s turn. At the end of her turn, Emily flips and attacks Michael; who has now been attacked twice in a row. Following Michael’s turn, Jack knows that he can only attack Emily, regardless of who Michael attacks.

Although one who has been attacked twice in a row may find this unfair, a 3-times limit rule is better than a 2-times limit rule, since after every attack, the next attacker would then optimize an attack on the player he knows will attack next, reducing the efficacy of a probabilistic method and hence making the game seem more unfair. The 3-times limit rule has not been tested experimentally as of yet.

Discussion

In this study, we have demonstrated a plausible rule-set for playing 3-person Pokémon TCG. These rules provide chance-based attack-direction and turn-rotation, providing a fair method of play. Critics may suggest that an over-reliance on chance defeats any devised deck strategy, however, we propose that the fairness of a probabilistic attack outweighs the unfairness felt by one being ‘ganged-up’ on. We also suggest an additional, untested, ‘3-times-limit’ rule to prevent low-probability consecutive attacks on the same player, which also re-introduces a modicum of prescient strategy.

As part of our 3-person framework, we argue that a single between-turns step (BTS) for each player is fair and more consistent with classic 2-person Pokémon. A single BTS negates the additional 25 % advantage/disadvantage achieved by a second coin toss. Each player should consider their own BTS as the step immediately preceding their turn. For example, reusing the above example where Jack has put Michael’s Pokémon to sleep, Michael should ignore the BTS (Jack-Emily), and only evaluate the Asleep condition in the next BTS following Emily’s attack (Emily-Michael). With only 1 BTS per player in a 3-person game, all original 2-person rules fall into place neatly, without any complications resulting from doubling damage, or advantageous/disadvantageous bias from multiple coin tosses.

Finally, we suggest ten simple rules for a Strip-variant of 3-person Pokémon, which may also be adapted to the official 2-person game. Briefly, an item of clothing is removed following the player’s Pokémon being knocked out. Additionally, there is a 28.6 % chance of the winner causing one opponent to end up fully nude, increasing the thrill of the game. The author insists that this variation only be trialled in consenting adults.

Conclusion

Here, we have described a 3-person variant to playing the Pokémon TCG. We propose several alternative rules based on the fundamental principle that the game should be maximally fair for all players, without removing significant joy. A probabilistic method that entails coin flips and dice rolls to decide attack-direction and turn-rotation was acceptable to all players, with all expressing enthusiasm for more experiments.

We also provide a theoretical rule-set adaptation for a Strip-variant of the Pokémon TCG. This is based on removing items of clothing for every Pokémon that is knocked out. It is suggested that this method be practised in future studies.

Finally, we acknowledge that there are many more nuances that one may encounter following the 3-person rules described here, concerning Pokémon abilities, or ambiguous Trainer cards. We suggest that for now, these caveats be noted upon encountering, and dealt with on an ad-hoc basis. The author hopes that through more people playing 3-person Pokémon, an unofficial, but definitive rule-set will be established based on community collaboration and input.

Acknowledgements

The author would like to thank his two fellow Pokémon TCG players for their excellent advice, good sportsmanship and above all, for supporting the author’s slightly worrying addiction to the Pokémon franchise. Additionally, the author would also like to thank his loving partner, who allowed the above games and discussions to proceed without batting an eye at a hyper-excitable fully grown adult fawning over drawings of fictional monsters on pieces of card.

Also, the author wishes to express his gratitude to the people over at SixPrizes for inspiring this article.


Conflict of interest statement:

The author expresses no conflict(s) of interest.


Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s