Crunching the numbers: Game theory: Enhance your game with the power of math

[BulbaBot]

Crunching the numbers: Game theory: Enhance your game with the power of math

With Pokémon, as with a plethora of other games, one of the key ingredients for winning a battle is the ability to predict your opponent. Unfortunately, since the majority of us do not have telepathic mind powers, this can be a difficult task. It is due to the complex nature of prediction that mathematicians developed a theory on how people play games. We cleverly call this "Game Theory."

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[shadow the hedgehog6]

wow!

 

[yourlilemogirl]

I think my brain melted a little....

 

[Derier44]

Holy shit.......

 

[Axxonn]

Interesting! Love this column

 

[MegaCharr]

No wonder why I FAIL at Pokemon battles!!....arge!! More math I cant understand!!....

 

[Ghetsis-Dennis]

This looks all so confusing, I don't know where to begin.

 

[daniedeter]

If something's too confusing, please let me know how I can make it better. My goal is to make this understandable for as many people as possible, so if something doesn't make sense, I'm not doing my job correctly.

 

[Hector]

As a statistics guy (I'm an economics and computer science double major), I started reading this article and was looking forward to poking holes in your work. Sadly (for me), there were no holes.

This was an awesome read. I'm now looking forward to seeing what you can come up with for multiple turns and maybe even for an entire battle (problem is that, as I'm sure you know, the matrices would get incredibly complicated as you add turns and possibilities).

My one question for you would be how you would plan on changing the matrices if you don't know your opponent's entire moveset? I mean you could make assumptions, but you wouldn't know for sure. I know that would mess with the experiment and likely break it, but I'm curious to hear your thoughts on that.


Once again, great work and I hope to see more from you on this subject.

 

[daniedeter]

As a statistics guy (I'm an economics and computer science double major), I started reading this article and was looking forward to poking holes in your work. Sadly (for me), there were no holes.

This was an awesome read. I'm now looking forward to seeing what you can come up with for multiple turns and maybe even for an entire battle (problem is that, as I'm sure you know, the matrices would get incredibly complicated as you add turns and possibilities).

My one question for you would be how you would plan on changing the matrices if you don't know your opponent's entire moveset? I mean you could make assumptions, but you wouldn't know for sure. I know that would mess with the experiment and likely break it, but I'm curious to hear your thoughts on that.


Once again, great work and I hope to see more from you on this subject.

Happy to know you didn't find any mistakes
Now if only I could make it seem like I knew what I'm doing when I take my exams...

As for your question, as far as I know, Game Thoery unfortunately doesn't have a universal method to cope with incomplete information. My personal strategy in that situation is to list off every popular move for the opposing pokemon and to compare my moves against that. For example, with Alakazam I think Psychic, Calm Mind, Shadow Ball, Focus Blast, Energy Ball, and maybe Signal Beam, Trick, Taunt, and Enore. (I don't know if these are still popular. It's been a while since I've played competitively). This would result in a 4 by 9 matrix if we don't include switching.

I've also thought about comparing my moves against every possible move the opponent's pokemon can have. But I believe in the hands of an experienced player, that could actually make things worse instead of better (plus it's really impractical). That might make a fun science fair project to see if it actually is better though...

Hope I don't disappoint you in the future.

 

[Zekurom]

Now this is some real math.

 

[N-Pie]

I reported this in the report errors section, but I thought I'd post here too. I'm sure the cell where "HP Fire 70" and "Switch to Spiritomb" cross should read "0,70" because HP Fire 70 does 70 damage to Spiritomb and not 35. This means that switching to Gyarados is the superior choice if the opponent decided to use HP Fire, meaning you can't simply eliminate it like the article reads.

 

[daniedeter]

Oh snap, good catch.
Luckily, it looks like everything still works out the same way (since Shadow Ball is still better than HP Fire 70). I'll work on trying to get it fixed.
Have you spotted anything else? Now would be the time to tell me

 

[N-Pie]

Not that I can see.

 

[Bittersweet]

That's a really good article. I didn't have any trouble understanding it at all; seemed pretty straightforward.
Half the time these kinds of articles are just pointing out and explaining stuff that I was already doing in my head, but not REALISING I was doing it. THat's what makes it interesting.