Discussion Help me do some crazy Card Math of PAIN

Empoleon_master

Empoleon_master

I can stop watching Anime any time I don't want to
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I need this to see if a deck is viable or not. It was made for my dad so everything is dumbed down without names to make it less confusing for him. He says the odds are not in my favor (like the Hunger Games), I say this is due to him not being able to use math to calculate the rate of using VS Seeker and Battle Compressor at the same time.

Here's the math problem from hell.

I have 16 pokemon I can't start with 5 of them by the rules. I draw 7 cards at the beginning and I have to start with one of the 11 other cards. After that 6 cards are added to my prizes so I can't use them. When I start my first turn I draw one card.


I want to start my game with a pokemon I have 4 of. And then play a card I have 4 of to evolve my optimal starter, I have 3 of the evolution in my deck, this is a trainer card. I have 4 cards that allow me to draw 2 cards and discard one, this is to allow me to get that card to evolve sooner this is a trainer card. I also have 4 cards that allow me to look at the top 4 cards of my deck, chose one of the four in the event that it is one of 34 trainer cards and put it into my hand. It cannot get another copy of this cars via its effect. I have 2 of a card that can search for 2 energy cards in my deck, I can search out up to 8 different energy cards in my deck via this card. It is a trainer card. I have 2 of a card that will allow me to discard up to 3 cards in my deck. I have 4 of a card that allows me to use the card that allows me to instantly evolve my optimal starter if it is in the discard, it is a trainer card. I have 2 of a pokemon card that when put onto my bench via my hand allows me to draw until I have 6 cards in my hand. I have 10 total energy cards, only 8 can be searched for. The other two can only be attached to the pokemon that needs 3 energy to attack.


I have 3 of the pokemon I want to have my optimal starter evolve into. I need an energy card (any energy) attached to it to use its attack. Its attack searches for a pokemon I have 3 of, and 2 energy cards to attach to it. I have to add a third energy to the just searched for pokemon to attack. If I don't start with my optimal starter I have 3 cards to switch back into it should I start with anything else. I have two of a pokemon whose evolution must be in play when I have the pokemon with 3 energy on it ready to attack. I have two of its evolution. I can evolve it at any time using a stadium trainer card that is in play once I have it in my hand. And I can use the card that evolves my optimal starter to evolve it, but only on turns after I use it to evolve my optimal starter.


What is the percent chance that I can get my optimal starter evolved, attach an energy card to it, and get out the pokemon that needs 3 energy to attack + 2 energy cards via the evolved pokemon's attack on my first turn, then getting out the second evolving pokemon on my second turn?

I can go into specifics, with card names if you want me to to make this easier and less brain crying for you guys. PLEASE HELP.

Pokemon:
  • 4 Larvesta AO
  • 3 Volcarona AO
  • 3 Machamp EX
  • 2 Shaymin EX
  • 2 Ariados
  • 2 Spinarak
Trainers/Supporters/Stadiums:
  • 4 Wally
  • 2 Shauna
  • 2 Professor Birch's Observations
  • 4 Acro Bike
  • 4 Trainers' Mail
  • 4 VS Seeker
  • 2 Battle Compressor
  • 2 Professor's Letter
  • 2 Switch
  • 1 Escape Rope
  • 2 Muscle Band
  • 3 Fighting Stadium
  • 2 Forest of Giant Plants
Energy:
  • 7 Fighting Energy
  • 2 Strong Energy
  • 1 Fire Energy
 
It would definitely be easier to follow if you just posted the list of cards and counts, and what you're trying to do, instead of trying to get people to parse it. We know what Trainer's Mail is, Professor's Letter, Shaymin, etc.
 
Card counts

Pokemon

4 Larvesta AO
3 volcarona AO
3 Machamp EX
2 Shaymin EX
2-2 Spinarak Ariados

Total 16 pokemon 11 basic 5 evolution

Trainers

4 Acro bike
4 Trainers mail
4 VS seeker
2 battle compressor
2 professor's letter
2 switch
1 escape rope
2 muscle band

Total 21

Supporters

4 Wally
2 shuana
2 Birch's observations

Total 8

Stadiums
3 Fighting stadium
2 Forest of Giant Plants

Total 5

Energy
7 fighting
1 fire (in the unfortunate event of Beautifly)

Total 8

Special Energy
2 Strong energy

Total 2

Total 60

The goal, assuming you go second is to rush Volcarona out via Wally, attach an energy card that's not Strong Energy, then use Solar Birth to get out Machamp EX with 2 basic energy, preferably fighting energy, then next turn get a third energy onto Machamp EX, along with Ariados, something to add 20 damage to Machamp EX, then use Crazy Hammer for 180 damage.
 
^ That was sooooooooo much easier!

I know what you're trying to do, so let me tell you now there's so much math involved, that you'd be a lot better off play-testing and determining the chance that some scenario will occur through observation. It would be extremely useful if you could calculate an accurate percentage because if you can quantify it, then you can optimize it. I actually came up with a multi-variable formula written in summation notation that would have calculated the odds of getting any combination of cards off of the top n cards of the deck, but I tested it, and when n = 60 (you have your whole deck in hand), it came out to something greater than one. (I believe it was around 1.6.) So it obviously was 100% accurate. And it didn't even take into account the stuff like playing an Ultra Ball for a Shaymin, playing Juniper, or the fact that you can only play one Supporter per turn. I came a little closer another time, but I had to write out all of the possible permutations of five items, then six, then seven, and so on until I could establish a pattern, and I didn't have the time for that at the time.

So that probably went way over a lot of people's heads, but if anyone else understands multi-variable calculus, and has a fancy calculator, maybe you can figure it out.
 
I wonder if it would be possible to (with the right math) build a thing where you could just copy your deck list in and it will spit out the percentage chances? Or is that the kind of project you need a six figure budget, professional coders and mathematicians?
 
Draaka said:
I wonder if it would be possible to (with the right math) build a thing where you could just copy your deck list in and it will spit out the percentage chances? Or is that the kind of project you need a six figure budget, professional coders and mathematicians?
Click to expand...

It's just time, as long as you have access to the equations used
 
I'm still on Algebra two and damn I will now save this topic for any idiot that says that pokemon is simple or some crap. This is also why I really wish TCG one or play TCG would update their card lists so I can test this stuff. As I don't have 3 macahmp yet, nor do I have the 4 larvesta and third volcarona. FML.
 
Draaka said:
I wonder if it would be possible to (with the right math) build a thing where you could just copy your deck list in and it will spit out the percentage chances? Or is that the kind of project you need a six figure budget, professional coders and mathematicians?
Click to expand...

I've wanted to write a program that would take a decklist as an input and give some kind of "score" as an output for the longest time, but I don't have that kind of free time on my hands.
 
@Empoleon_master I do like your approach. As a former math major, @TheStrictNein suggestion of starting with that particular website is a good one - very cool idea. Understanding the probability of your maximizing your initial setup is important, because you can increase your chances of creating that "ideal" initial setup with key cards (like you have) like card search/draw Items. However, game "reality" will eventually kick in, for example, will you have sufficient resources left in your deck after the initial setup? So, play-testing will help you balance your deck for the game realities. Also, your opponents will most likely not "cooperate" during your setup either.

Although I have not tested your variation of this Machamp-Ariados deck, I have tested Landorus as my starter, and this Pokemon performs that roll quite well, IMO.

Mora said:
I've wanted to write a program that would take a decklist as an input and give some kind of "score" as an output for the longest time, but I don't have that kind of free time on my hands.
Click to expand...
Years ago, I actually developed a spreadsheet that "computed" a "battle rating" for each Pokemon. It was an attempt (albeit poor) to develop decks through the combination of the most "battle-worthy" Pokemon. It was a fun exercise; I identified a double-digit number of key attributes that each Pokemon has and used these in my analysis.

So, when you do get that extra time, go for it; it will be enjoyable.
 
Empoleon_master said:
I'm still on Algebra two and damn I will now save this topic for any idiot that says that pokemon is simple or some crap. This is also why I really wish TCG one or play TCG would update their card lists so I can test this stuff. As I don't have 3 macahmp yet, nor do I have the 4 larvesta and third volcarona. FML.
Click to expand...

...the origins of the term "TecH" stem from how during the early part of the game's life players far more skilled with probability than myself did indeed set up formulae to calculate what should and shouldn't work. One such player noticed a discrepancy in that sometimes a single copy of a card that should cause the deck to lose more because it damaged reliability running this singleton instead of another copy of something else instead caused the deck to win more. Looking at what was happening, this player realized that taking a hit to overall reliability was justified when said single card offset a particularly bad match-up: multiple copies proved overkill but that single copy won more matches than it lost for a net gain. This player dubbed it "technical advantage" and as was the style of the time, shortened it to "TecH" with the odd capitalization.

I don't know about the original writings, but I actually can cite a reference: an older, returning player that then went by the screen name "0bsol33t" (I knew him before that as "bondiborg") wrote an article explaining this and a few other useful bits of Pokémon jargon here. The article is from nine years ago: not as authoritative as if it were from when this first went into effect (it was a pretty common term online by 2002; I didn't join the online scene until late 2000), but a lot better than just "Well, I remember reading/hearing/seeing...". ;)
 
TuxedoBlack said:
@Empoleon_master I do like your approach. As a former math major, @TheStrictNein suggestion of starting with that particular website is a good one - very cool idea. Understanding the probability of your maximizing your initial setup is important, because you can increase your chances of creating that "ideal" initial setup with key cards (like you have) like card search/draw Items. However, game "reality" will eventually kick in, for example, will you have sufficient resources left in your deck after the initial setup? So, play-testing will help you balance your deck for the game realities. Also, your opponents will most likely not "cooperate" during your setup either.

Although I have not tested your variation of this Machamp-Ariados deck, I have tested Landorus as my starter, and this Pokemon performs that roll quite well, IMO.


Years ago, I actually developed a spreadsheet that "computed" a "battle rating" for each Pokemon. It was an attempt (albeit poor) to develop decks through the combination of the most "battle-worthy" Pokemon. It was a fun exercise; I identified a double-digit number of key attributes that each Pokemon has and used these in my analysis.

So, when you do get that extra time, go for it; it will be enjoyable.
Click to expand...

I might try. I remember I mathematically constructed the perfect Heatmor deck forever ago. I found the optimal balance between the essential Trainers and Energy (I believe through lagrange multipliers, iirc). It was a bit of number crunching, but what made it doable was the fact that the deck didn't play any draw. It only played Skyla to search out Ether; the rest of the deck had to be Energy so that you could reliably use its attack for maximum damage. In fact you could set it up in such a way that you only have one variable. Say 4 Heatmors (constant), x Trainers, and 60 - x Energy But there's really not a whole lot going on in that deck. I'm not sure exactly how I'd quantify a few things such as drawing additional cards. Maybe I'll sit down and think about it again in the near future.
 
Mora said:
I might try. I remember I mathematically constructed the perfect Heatmor deck forever ago. I found the optimal balance between the essential Trainers and Energy (I believe through lagrange multipliers, iirc). It was a bit of number crunching, but what made it doable was the fact that the deck didn't play any draw. It only played Skyla to search out Ether; the rest of the deck had to be Energy so that you could reliably use its attack for maximum damage. In fact you could set it up in such a way that you only have one variable. Say 4 Heatmors (constant), x Trainers, and 60 - x Energy But there's really not a whole lot going on in that deck. I'm not sure exactly how I'd quantify a few things such as drawing additional cards. Maybe I'll sit down and think about it again in the near future.
Click to expand...
I'd love to see the Heatmor list, I've been trying to make an Ampharos-EX deck that just relies on the first attack for acceleration, or an Entei deck similarly.
 
tototavros said:
I'd love to see the Heatmor list, I've been trying to make an Ampharos-EX deck that just relies on the first attack for acceleration, or an Entei deck similarly.
Click to expand...

I'll have to dig it up; it was ages ago. In fact since the new site went up, I'm not even entirely sure if it's still around :/

Also, I think I'm going to edit the deck list into the OP for convenience.
 
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