Pokemon, Randomness and You:
Clearing up Some Misconceptions
As much as we players dislike it, probability and luck are very prominent parts of the Pokemon Trading Card Game. Some decks aim to eliminate it as best as possible; others choose to embrace the flips, such as Sharpedo Lock. And even outside of flips, probability plays a vital role in mechanics such as opening hands and topdecks. Sadly, the human brain is not wired to perfectly understand some of the trickier parts of this logic. Hence, I’m here today to clear that up.
The Gambler’s fallacy
The Gambler’s fallacy is simple: the belief that if deviations from expected behaviour are observed in repeated independent trials in a random process, future results will favour deviations in the opposite direction. But what does that mean in layman’s terms? Try reading it like this: a coin that flips 10 tails in a row will favour heads afterwards. Sounds a bit silly, doesn’t it? And yet, this logical fallacy is how the casinos and gambling parlours of the world make their money.
Our minds are trained to accept this fallacy as truth. We have what is called “Representativeness Heuristic” that makes us think that way. It’s an area of study in psychology even to this day. The Representativeness Heuristic is a heuristic wherein we assume commonality between objects of similar appearance.But how does it apply to the Pokemon TCG? Well, when people have long chains of bad coin flip luck, they expect “Oh well I’ll hit heads now, I have to” even though their chance is still 50-50. A good example of this was observed when a player chose to Junk Arm away his only draw supporter for a fourth chance at reversal at the free play area in Worlds this year. I was amazed he did it, and yes, he did hit tails.
Odds are always static
Another way to state that the above is that odds are never dynamic. If you learn more information about something, the odds change. This is where the famous Monty Hall Problem can be adapted to the Pokemon TCG:
You have three prizes left. Two of them are energy, and one of them is a Junk Arm. I use Energymite on Electrode Prime. If you get the Junk Arm, you can win the game by grabbing a Catcher and OHKO-ing my RDL. If you get an energy, I’ll be able to take my last two prizes with RDL. Since we’re playing casually, I offer you a little help: You will pick one of the three prizes without looking. I’ll then reveal an energy card in one of the other two prizes you didn’t choose. You may then keep your prize, or switch to the other prize. Which do you choose?
Naturally, our minds tell us we now have a 50-50 shot at getting the right prize. But that’s wrong! You should always switch prizes. Here’s why:
At first, you had a 33% chance of picking the Junk Arm.
There’s three possibilities of the cards:
1: Energy, Energy, Junk Arm
2: Energy, Junk Arm, Energy
3: Junk Arm, Energy, Energy
Assume in each case you pick the first prize, and keep your choice instead of switching:
Now assume you switch:
So as you can see, you have a 2/3rds chance of winning by switching. Don’t believe me? Test it a few times for yourself, and record your results. It’ll even out to 2/3rds in the long run.
Another more realistic scenario came up with the validity of Magby as a Gothitelle counter. Many people believed it to work 50% of the time when in fact it worked 75% of the time.
The Coupon Collector’s Problem
This is another fallacy: in a selection of numbers, people observe that a result that has yet to happen is more likely to happen than normal. This is mostly visible in dice rolls and coin flips. If you hit the numbers 1, 3, and 5 on eight dice rolls, most people tend to believe that the next roll will return a 2, 4, or 6. But that’s still a 50-50 chance.
This is the simplest, and we’re all guilty of it: we tend to remember negative outcomes of a probability-based event over positive outcomes of the same event.
Ever heard of a player saying “My coin luck is horrible”? Lots of people do it. But it’s wrong. Very wrong. Everybody is guilty of this one. Remember the HS-BW format we had at worlds? Everyone remembered how many reversal flips they missed, or how many times Cleffa woke up going into their opponent’s turns. But few could tell me how many times the coin or dice went their way. It’s just human nature. To illustrate that, keep track of your coin flips on a notepad for your next 50 games. You’ll be surprised how close to even they actually are.
I hope that this helps you be a little more aware of your odds and statistics. Pokemon may be marketed towards kids, but there’s a lot of grown-up logic and mathematics going on behind the scenes.