#theknapsackproblem

Recently I’have been playing too much Pokemon: Emerald,  raising my Pokemon for transfer to the illustrious Diamond and Pearl. Having long played the franchise I thought I would share one of my favorite ways of looking at the game. It involves a fairly basic math puzzle: The Knapsack Problem.

A knapsack problem is one of the more interesting ways to understand how someone’s mind works. Essentially you have a set number, like the space in a backpack. The goal is to fill the backpack as optimally as possible. It has implications in all fields of gaming: in World of Warcraft it can help determine the optimal raiders for a dungeon, or the best items to take going into a certain area. In Strategy games it can help determine the optimal use of the food/unit limit. But since I’m playing Pokemon that is what I am going to use as an example.

If your unfamiliar with Pokemon you should find most of the terminology similar to other RPGs. If your unfamiliar with gaming slang… try to keep up; I will try to keep the language clear.

In a Pokemon battle the trainer is allowed 6 Pokemon with 4 moves each. That is 24 moves total. What is the most effective use of moves? The enemy could literally choose from millions of possibilities for his team design. When you take moves into consideration the number pushes past anything I care to try to quantify and while it is possible to account for all the type combinations it would spread your team woefully thin.

I prefer to think of gamer's as falling into two categories in this area: Greedy and Paranoid. Lets give each type of gamer a Swampert and see what they do with it.

A greedy gamer wants to optimize his teams power; He decides to give his Swampert Earthquake and maximizes his attack statistic. Although Earthquake is a very powerful move but has no effect on flying enemies. Luckily Swampert learns Ice Beam. (Very effective against flying Pokemon ) Because the greedy gamer put all his stats into attack his earthquake is extremely powerful but his ice beam is next to useless.

The paranoid gamer on the other hand wants to minimize his chances of being caught off guard; coincidentally this is the category I fit into most often. I would take that same Swampert and give it balanced stats with Ice Beam. It’s true that damage output is lower then the greedy gamer  but to compliment it I am useful in more situations. The majority of gamer's fit into both categories and sway between them by circumstance. It is a weakness in psychology that can be exploited with sharp eyes.

Lets take a look at one of my most powerful Pokemon as an example. The beautiful and sturdy: Milotic. The proper way to display him among competitive gamer's would look something like this:

Milotic (M) @ Leftovers Trait: Marvel Scale (50% higher defense when suffering) EVs: 58 Special Def / 252 Special Attack / 200 Def Modest Nature (+SAtk, -Atk) -Ice Beam -Surf -Recover -Mirror Coat

This is a pretty standard build for Milotic. Mirror Coat reflects special attacks back, recover makes up for the damage sustained in those attacks. Aside from that move he has very little versatility, he does pack a water move for extra damage and an ice move for taking out Grass/Flying/Dragon types.  His defenses are top-notch (Thanks to marvel scale and a naturally high Special Defense) and his modest nature gives him incredible special attack. (At the loss of attack, but he has no moves that use attack.) Combined with Recover he can take an incredible amount of punishment before going down.

His power comes at expense of his versatility however; and it was a choice I make gladly, under the right circumstances Milotic can finish off two-three enemy Pokemon without fainting. Under the wrong conditions he is a deadly liability. The stunning lack of versatility can be made up on other parts of my team. Remember this is 1/6th of the Pokemon I have and uses 4/24th of the total moves I have available.