Pokémon and Math

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Paperfairy

Aspiring Trainer
Member
For those of you aware of what International Baccalaurate is, scroll down to the tl;dr.

For those who are not:

I have a huge math project coming up, spanning 2/3 of a year, in which I am required to collect data and analysis it. I can do the project on anything I like, as long as

- there is data to collect/has been collected
- I can analyze the data using mathematics and come to a conclusion

tl;dr: I am doing my Math Internal Assessment on the TCG


Now that we are all on one page, I want to analyze Pokémon, namely the TCG. Does anybody have any ideas as what may be good projects? A few ideas I had were:

- Is there a direct correlation between the amount of time spent shuffling and the number of Mulligans?
- What is the likelihood that an average deck will achieve its desired "set up"?
- In the current format, what is the likelihood that attacks like Baleful Wind will be successful?
- Is the condition of a win directly linked to the skill/ranking of the player?

Anything else?
 
Having your deck in order and 1,2,3,4,5,6 shuffling 6-7 times??? and your deck is back in order. Is that what you mean???
 
Paperfairy said:
For those of you aware of what International Baccalaurate is, scroll down to the tl;dr.

For those who are not:

I have a huge math project coming up, spanning 2/3 of a year, in which I am required to collect data and analysis it. I can do the project on anything I like, as long as

- there is data to collect/has been collected
- I can analyze the data using mathematics and come to a conclusion

tl;dr: I am doing my Math Internal Assessment on the TCG


Now that we are all on one page, I want to analyze Pokémon, namely the TCG. Does anybody have any ideas as what may be good projects? A few ideas I had were:

- Is there a direct correlation between the amount of time spent shuffling and the number of Mulligans?
- What is the likelihood that an average deck will achieve its desired "set up"?
- In the current format, what is the likelihood that attacks like Baleful Wind will be successful?
- Is the condition of a win directly linked to the skill/ranking of the player?

Anything else?
Click to expand...

1. I have to put thought to that, but I'm currently leaning towards no
2. That is all dependent upon the person setting up the deck, and their ability to utilize the correct ratios and available library, to create a deck that will be efficient at achieving it's desired "set up"
3. you will have to remind me what that does
4. To a certain extent, yes.
 
Shuffling depends on shuffling style. If you keep the cards in order e.g. cutting and stuffing it down the bottom, then it's probably a higher chance considering the same hand will probably occur every two cuts. Poker-style shuffling or cutting cards from the middle make it ridiculously annoying for people not in Uni.

The likelihood is dependant on the deck, but it tends to require approxiamately 2-3 energies, a starter, a Basic of the main line, a Candy, a maybe searcher or drawer. If we say energies are 18, which is 30% of the deck, there's an approxiamate 15%-10% or so of getting the energies, and even less so if you have specific energies for the deck. The starters are about 5% of the time, which is... 5%. Candies are probably about 5%, if maxed, and searchers/drawers take up possibly 12-18 spaces in a deck, or maybe more, I can't remember, leaving it around 20%-30% chance for it. I have no idea how to stack percentages.

Having a trainer in the opening hand is about a 50% chance, possibly 40%, and that would mean about 2-3 trainers a hand. So you have about a 40% chance of getting it?

No clue for this one.
 
I did not want answers to my questions, but rather: are the projects presented plausible ones?

DawnOfXatu: Define Draft Style?
 
Do they win or not. Do they pick the cards that are worth more money or do they pick cards that will win. Do they get the most trainers. Those are all plausible areas of draft style. The younger you are that I find the more you tend to get the cards that you think are "good in the metagame" yet when you become older you find yourself picking more trainers and cards that you think could win in the draft itself.

My younger brother at the LA draft picked up a 1-3-5 Bellossom line which honestly is rather bad in a draft. I on the other hand picked a 4/3/1 Castform line because Casty is a better card for a draft.

As another example however in that same draft my brother ended up collecting 13 more rares than I did because he has been taught to pick the cards that are "good" not cards that could win.

Using the same draft for a third example my brother ends up takeing around 5-8 less trainers then I do.

So therefore there are many different aspects in which you could see how a difference in age influences your draft style. I being older than my brother (and more practiced in drafts)
A. Get better decks and have top cut all but once (8 way 2-1 tie and I had the worst resistance)
B. End up taking less unneeded rare cards
C. End up getting more trainers and cards that can be used after the draft.
 
That would be a good one!! That is a great project.

how about: Link between collection# and how often it is pulled??
 
I'd give up on the shuffling. It's not easy to determine someone's shuffle style and therefore the odds involved, especially because most people perform several ways of shuffling (sorting in piles, then poker-style, then cutting is what I always see). It also depends on the way the cards were sorted before the shuffling. For instance, if it's right after a battle, that means that the discarded Pokes are still in their original line, probably with an energy or 2 right after them. But this also depends on whether they won/lost the battle, and how the actual battle went. So it's basically impossible to make a fair guess on this.

The Baleful Wind seems a cool one, even though the current format is not really reliable. Some decks play 20 trainers, some have the room for 35. This should be specified and you should pick a few (5-10) archetype decks and figure it out for those. Also, you should notice that the less setup time a deck requires, the more trainers it plays and thus the easier it is to BW one...or is it? There's also the factor involved that you might not even be able to BW from T1, but only from T2, because you miss an Energy. Then, they can play some of their trainers away before you can discard them.

The win condition is probably even tougher than that. Sure, skill also determines whether a deck is built reliably or not, but it's still very often that luckers can pull off a win because they have more luck and also a more luck-based deck (with, say, more Pokeradars instead of Bebe's). But with the 2-out-of-3 match system in place now, I think the conclusion of this should be yes. I'm not sure though...I just don't like the idea that the people ranked higher than me are complete idiots. xP
 
Paperfairy said:
I did not want answers to my questions, but rather: are the projects presented plausible ones?

DawnOfXatu: Define Draft Style?
Click to expand...

Not really. Like in Science there needs to be a constant, X, which cant be defined or proven in those questions.

All of this could be solved many, hundreds, if not thousands of ways. This could be a Scientific experiment, but no a math study.
 
@Gowk; There can be multiple solutions; as long as the project qualifies for the aforementioned, I can do it.

@trevorispro; Does not seem to have much mathematics or analysis involved.

@StealthAngel667; With enough tests, I believe luck would not be a significant factor. As for shuffling, I would not be using real life cards, but rather, computer generated randomization. Most of these tests will be taking place on Redshark or via randomization on a calculator. As you said, real people are unreliable, but yes, Test 1 is albeit shaky.

Sounds like numbers 2 and 4 are recieving the most support; I am leaning towards 2, seeing as how 4 could really depend on the deck. Rain Dance decks will almost always win differently than Honchkrow or Rain Dance.
 
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