#pokemaths

[premachu]

Pokemaths: The difference between probability and statistics explained

Probability is starting with a trainer and figuring out what Pokemon they will have

statistics is seeing a Pokemon and guessing the trainer.

Probability is easy. You see the trainer. You record where they’re from and their level and deduce what Pokemon they will have. “Here’s Bug Catcher, he’s from Veridian Forest and has no badges, so will have Pokemon like this”. In other words “We flip a fair coin ten times, here are the possible outcomes”

Statistics is the opposite. We record the Pokemon and guess the trainer. A Pikachu, it’s an electric type and found in forests. What’re the chances it’s Misty’s? Or “we flip three heads and two tails, is it a fair coin?” Record the Pokemon! Each piece of data is a point in “connect the dots”. The more data, the clearer the shape (1 spot in connect-the-dots isn’t helpful. One data point makes it hard to find a trend.) One water-type Pokemon? Could be a few people. 3 water-types? Probably not bug-catcher. Measure the basic characteristics. Every Pokemon has a level, type, and habitat. Every data set has a mean, median, standard deviation, and so on. These universal, generic descriptions give a rough narrowing: “The Pokemon is level 8: a beginner trainer, or a gym leader?” Find the type of trainer. There are dozens of possible trainers (probability distributions) to consider. We narrow it down with prior knowledge of the system. Surrounded by lakes? Think water-type trainers, not rock-type trainers. Dealing with yes/no questions? Consider a binomial distribution. Look up the specific animal. Once we have the distribution(“gym-leaders”), we look up our generic measurements in a table. “Six water type Pokemon, all over level 80 is most likely owned by a water-type gym leader, like Misty”. The lookup table is generated from the probability distribution, i.e. making measurements when the Pokemon is captured. Make additional predictions. Once we know the trainer, we can predict future behavior and other traits (“According to our calculations, Misty will defeat all trainers under level 20 and have a rare-water type.”). Statistics helps us get information about the origin of the data, from the data itself.

The inspiration for this post and layout is based on a article from betterexplained.com linked here.

[premachu]

Poke-maths: L1 - Probability.

WF Learn maths through Pokemon!

Probability is the chance of something happening when it’s random.

What is random?

If you've played the Pokemon games you’d be use to the idea of an random event. For example, every time you walk through tall-grass full of wild Pokemon. You can’t decide which Pokemon you’ll bump into, so we call it random. Something else which is random is finding a shiny Pokemon. Once again, we can’t influence our chances of finding a shiny Pokemon, so we call it random. 

The easiest way to figure out if something is random is to ask: Can I control it? Can I decide what happens?

If you answer no to those two questions, you’re probably looking at a random event!

While random events are in god’s hands, we can still have a good idea of what could happen in a random event. We do this through probability....

Probability: fortune telling. 

Probability could be thought of as really good fortune telling, one who can do all sorts from predicting the future to knowing your past. 

To be a great fortune teller all you need to know is the following things...

1. Know all the possible outcomes.

2. Know the chance of each outcome.

3. A crystal Pokeball to look through. 

And that’s it! (ok we can omit the crystal Pokeball, if we must). Now let’s fortune tell in Pokemon world using just these two things.

I choose you

It’s finally time! You get to choose your first Pokemon and begin your Pokemon journey. 

However, you can’t decide between three rare Pokemon. So you decide to pick at random. 

Let’s use figure out the probability of choosing a starter Pokemon to see what we end up with!

1. Know all the possible outcomes. There are three outcomes. Charmander, Squirtle and Bulbasaur. 2. Know the chance of each outcome. You’re just as likely to choose any Pokemon. So the chance of each outcome is equal.  We can write this as a one-over-three chance or 1/3. 

Using this as our basis, let’s look at some more examples.

You have two Pokeballs. One with a Charmander and one with a Squirtle. If you throw a Pokeball at random the chance of either Pokemon is 1/2 or 50%.  

Now let say there’s two trainers. Green and Red, who both have a fire-type and a water-type each. Green has a Vulpix and Squritle, Red has a Charmander and Poliwrath. Let's list all the possible outcomes of their throws by type. WW, FF, FW, WF.

WF

FW

WW

FF

If each of trainer throws a Pokeball at random the chances are as follows...

1. The chance that both Pokemon will be different types is 2/4 (50%).  FW, WF.

2. The chance that both Pokemon are water-type is 1/4 (25%).  WW.     3. The chance that at least one Pokemon is water-type is 3/4 (75%).  WW, FW, WF.

Viridian Forest - Encounter rates

We're already use to the idea of "random" events, such as encountering wild pokemon. Now, let's say you're leaving Pallet Town and walking through the grass. What are the chances you will bump into a Pidgey? Let's look at all the Pokemon within the grass (all possible outcomes). A pidgey, ratatta, ekans and Pikachu. If all the Pokemon are just as likely as each other, then the chance of bumping into a Pidgey is one out of four. Add up the Pokemon by types and see what type is most likely. normal: pidgey, ratatta. 2

Poison: ekans. 1 Electric: Pikachu 1.  Theoretically normal type is most likely. However in reality you could walk through the grass and only meet Pikachus. The more times you walk through the forest, the more grass pokemon you're likely to encounter. So in the long term, what you observe will be close to the theoretical observation, even if it differs in the short term. Which is how casinos in Goldenrod city make their money, because even if you win in the short term, the chances are stacked in their favour over the long term.  To check if this is actually true, we can run a simulation, which I’ll save for the next lesson!