Pokémon TCG: Sword and Shield—Brilliant Stars

Pokémon and Math

Ooooo! There are so many things you can do! I just got out of bed from very little sleep, but here goes:

#1: Some say Pokémon TCG is luck-based and some say it's not so much luck-based. The latter group say that you'll always see the same good players rise to the top of the standings (i.e. there are a few good players that perform well consistently.) How much of this has to do with deck choices and how much of this has to do with the fact that they're "good"?

#2: Now here's one Unlimited Players are sure to love. Some say that there are decks that win consistently. There are some kinds of decks that win way more often than others (e.g. 30% of all decks that make it to the top 25% at a tournament have cards A, B, C, and/or D in them). What cards would you have to ban/restrict to create less uniformity in the kinds of decks that win tournaments?

#3: Some say that 30% of all the decks that make it to the top 25% (in the final standings) in tournaments have cards A,B,C, and/or D in them. Is there any value in making a deck specifically to counter those decks? Will that increase the odds of making this deck rise to the top 25% of players?.

How many people would have to play deck specifically built to counter the deck with cards A, B, C, and/or D, until such decks no longer take up 30% of the top 25%?

#4: Which tournament style yields the strongest players (i.e. the "best players" get 1st place)? I suppose you'd have to find some criteria to determine the strongest players.
Which tournament style yields the strongest players for the least effort/time (for the tournament staff). You could compare how well each tournament style yields the strongest players with how much time/rounds are required for the tournament.

-Swiss
-Swiss + Two More Rounds
-Accelerated Swiss
-Swiss + Single Elimination
-Single Elimination
-Round Robin
-Double Round Robin
-Egyptian
-Double Elimination

If you need any explanation as to what any of these are, let me know.

#5: Do the same players consistently win when you change the length of rounds?
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I have more ideas, but I have to get ready to go to league right now, so I will post more later!

EDIT:
-Swiss: See POP literature
-Swiss + Two More Rounds: Minimum number of rounds to yield one undefeated player and then an additional two rounds.
-Accelerated Swiss: After the first round, the TO intentionally pairs players of dissimilar scores in hopes that it will reduce the number of rounds until there is only one undefeated player. If players are forced to play other players with a higher score, they will win some of those matches, and that would reduce the number of players who are undefeated (or at least that's the idea).
-Swiss + Single Elimination: See POP literature
-Single Elimination: See POP literature
-Round Robin: Every player plays every other player.
-Double Round Robin: Every player plays every other player twice.
-Egyptian: There are no rounds. Players are given X hours to play. You may play anyone in the tournament you choose to play and may play the same player multiple times. The player whose rating increases the most at the end of X hours, wins.
-Double Elimination: Same as single elimination, but every plays until they lose to two opponents.
 
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ninetales1234, interesting ideas. I will consider them.

Elekid-kid, we already know the likely hood of getting a Level X in a box or tin.
 
I do not personally know, but the information is out there.

Yes, it would be too easy; I wouldn't get permission to do the project.
 
#6: Perhaps this is beyond your realm, but there has yet to be any decent AI that can play Pokémon TCG. There was a big thread about it here.
How about writing pseudocode for a program that is supposed to perform a specific task with certain success rate within the rules of Pokémon? For example, write a code for a program that can use a specific set of cards to set up a Dark Slowking [RR] to do 80 damage on the second turn with a success rate of 90% or greater. Or a program that can have Azelf lvX, Uxie lvX, and Mesprit lvX in play by the third turn with a success rate of 70% or greater.

#7: Analysis of cards that show up in in a great deal of decks. Let's say there is a commonly-used card that is overpowered or broken- for example, Luxray [LA]. It can do 100 damage for 3 energy. There is a mathematical component to this, to why it is too powerful: the value of its attack's damage and the value of the attack's energy cost.

How much would you have to reduce the attack value before the percentage of people using this card dropped below X%? How much would you have to increase the energy cost value before the percentage of people using this card dropped below X%?

(note: It is not necessarily my opinion that Luxray is a broken card, just the easiest example I could come up with at the moment)

#8: Mathematical evidence for why the outcome of a Pokémon TCG match relies less on luck than other TCGs.

Chromecatz said:
What is Egyptian?
Click to expand...
I edited my post to explain the tournament styles not listed in POP literature.
 
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As a general rule iwould adopt if i were you. Do a project that doesn't need more people than you and a few friends to be effective. There are things like what % of top players win their matches or w/e it was. How would you go about collecting data for that? Do some form of statistical analisis that is based soley on gameplay factors(shuffeling, setup, ect). If you took any statistic class you should know that there are alot of things you could do with just some simple data.
 
ninetales1234 said:
#6: Perhaps this is beyond your realm, but there has yet to be any decent AI that can play Pokémon TCG. There was a big thread about it here.
How about writing pseudocode for a program that is supposed to perform a specific task with certain success rate within the rules of Pokémon? For example, write a code for a program that can use a specific set of cards to set up a Dark Slowking [RR] to do 80 damage on the second turn with a success rate of 90% or greater. Or a program that can have Azelf lvX, Uxie lvX, and Mesprit lvX in play by the third turn with a success rate of 70% or greater.

#7: Analysis of cards that show up in in a great deal of decks. Let's say there is a commonly-used card that is overpowered or broken- for example, Luxray [LA]. It can do 100 damage for 3 energy. There is a mathematical component to this, to why it is too powerful: the value of its attack's damage and the value of the attack's energy cost.

How much would you have to reduce the attack value before the percentage of people using this card dropped below X%? How much would you have to increase the energy cost value before the percentage of people using this card dropped below X%?

(note: It is not necessarily my opinion that Luxray is a broken card, just the easiest example I could come up with at the moment)

#8: Mathematical evidence for why the outcome of a Pokémon TCG match relies less on luck than other TCGs.


I edited my post to explain the tournament styles not listed in POP literature.
Click to expand...

I could not do six for my project, but I plan to be a Computer Science major, so doing that would not be a bad idea.


I really, really, really, like seven.
 
You could find ratios for HP and retreat cost in Pokemon at different Stages and from different seasons, and figure out how much more broken they have gotten.
 
There is no correlation in the aforementioned. However, I have noticed a correlation between a Pokémon Base Speed in the games, and a Pokémon's Retreat Cost.
 
Keep it simple, it will make it hard. Which cards have the best damage/energy ratio.? You will have
to take into account all Special Conditions, Resistance, and attack effects (like healing) as well as
mandatory helpers, like Sceptile in a Grass deck, of course factoring in the likelihood that the helper
will be ready and able to help.... all weighted by effects of the metagame.

Can't wait for the report! Be sure and post it.
 
ninetales1234 said:
Ooooo! There are so many things you can do! I just got out of bed from very little sleep, but here goes:

#1: Some say Pokémon TCG is luck-based and some say it's not so much luck-based. The latter group say that you'll always see the same good players rise to the top of the standings (i.e. there are a few good players that perform well consistently.) How much of this has to do with deck choices and how much of this has to do with the fact that they're "good"?

#2: Now here's one Unlimited Players are sure to love. Some say that there are decks that win consistently. There are some kinds of decks that win way more often than others (e.g. 30% of all decks that make it to the top 25% at a tournament have cards A, B, C, and/or D in them). What cards would you have to ban/restrict to create less uniformity in the kinds of decks that win tournaments?

#3: Some say that 30% of all the decks that make it to the top 25% (in the final standings) in tournaments have cards A,B,C, and/or D in them. Is there any value in making a deck specifically to counter those decks? Will that increase the odds of making this deck rise to the top 25% of players?.

How many people would have to play deck specifically built to counter the deck with cards A, B, C, and/or D, until such decks no longer take up 30% of the top 25%?

#4: Which tournament style yields the strongest players (i.e. the "best players" get 1st place)? I suppose you'd have to find some criteria to determine the strongest players.
Which tournament style yields the strongest players for the least effort/time (for the tournament staff). You could compare how well each tournament style yields the strongest players with how much time/rounds are required for the tournament.

-Swiss
-Swiss + Two More Rounds
-Accelerated Swiss
-Swiss + Single Elimination
-Single Elimination
-Round Robin
-Double Round Robin
-Egyptian
-Double Elimination

If you need any explanation as to what any of these are, let me know.

#5: Do the same players consistently win when you change the length of rounds?
----
I have more ideas, but I have to get ready to go to league right now, so I will post more later!

EDIT:
-Swiss: See POP literature
-Swiss + Two More Rounds: Minimum number of rounds to yield one undefeated player and then an additional two rounds.
-Accelerated Swiss: After the first round, the TO intentionally pairs players of dissimilar scores in hopes that it will reduce the number of rounds until there is only one undefeated player. If players are forced to play other players with a higher score, they will win some of those matches, and that would reduce the number of players who are undefeated (or at least that's the idea).
-Swiss + Single Elimination: See POP literature
-Single Elimination: See POP literature
-Round Robin: Every player plays every other player.
-Double Round Robin: Every player plays every other player twice.
-Egyptian: There are no rounds. Players are given X hours to play. You may play anyone in the tournament you choose to play and may play the same player multiple times. The player whose rating increases the most at the end of X hours, wins.
-Double Elimination: Same as single elimination, but every plays until they lose to two opponents.
Click to expand...
Well, I'd say #1 is more to do with the same decks making the top table; ie. Net Deckers without a good idead of their own, but it would be an interesting idea to explore...
 
The second one, you should choose a specific deck.
and its very easy to figure out. Theres a simple formula that i use to figure it out personally.
But since its your math project im not about to reveal my formula, as simple as it is.
If you're taking a statistics or math 101 class then you should be able to figure it out.

Also the skill of a player cannot be measured mathematically, and everyone shuffles differently so I wouldn't choose those.

Try figuring out the chances of a specific card being prized.
The chances of not getting a basic in your hand first turn.
The average damage output per Energy Card attached. (IE Bibarel does 60 for 2 so the average output on that attack is 30 per energy) do this for every pokemon and find the amount of damage a single energy provides.

You just have to find something that can actually be measured.
 
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