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Thread: Pokemon, Randomness, and You

  1. #1
    cabd's Avatar
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    Pokemon, Randomness, and You

    Pokemon, Randomness and You:

    Clearing up Some Misconceptions

    Introduction:

    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:
    1: Lose
    2: Lose
    3: Win

    Now assume you switch:
    1: Win
    2: Win
    3: Lose
    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.

    Selective Memory

    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.

    In Closing

    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.
    The Yanmega Guy
    Fresno, California; Masters
    Yeah, I work for 6P

  2. #2
    An interesting read that embraces the slightly less reported psychological and mathematical side of the Pokemon TCG, I loved how you were able to successfully use the Monty Hall problem in relation to the Pokemon TCG. A great article.

  3. #3
    Good read. Are there any other logical fallacies that relate to Pokemon?

  4. #4
    Quote Originally Posted by cabd View Post
    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:
    1: Lose
    2: Lose
    3: Win

    Now assume you switch:
    1: Win
    2: Win
    3: Lose
    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. .
    They did something exactly like this on mythbusters
    Quote Originally Posted by QD4U View Post
    "Pokémon EX rule"? What is this? Oh so Darkrai EX gives up two prizes when he dies. WELL THAT'S JUST GREAT.

    1/10 would give it 0/10 but art is cool so.

  5. #5
    Excuse me, but what do you mean with magby having a 75% chance? maybe it was a typo or why is that the right number?

  6. #6

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    Dude, I have no idea what you are trying to say in your Monty Hall scenario. I think it is your scenario that throws me off. If you energymite, you probably take you last 2 prizes that turn. Even if you have to pass that turn and I draw the wrong prize, I still have to KO a Pokemon to draw the J/A in order to get to 2 prizes and have the 50/50 chance, which means you still have 2 turns to get the ko while it takes me 3 turns to get to use the J/A...but, the logic flow has so many break downs, even if I try to ignore what I've stated above, I still cannot follow it.

    One "fallacy" that you addressed improperly is your nats side event scenario. While your opponent did have the same 50/50 chance of hitting heads, you DO still have to calculate ALL probability associated with the scenario. How many times did he go for the Reversal? Lets assume he had 2 reversal and 2 J/A in hand. He wiffs on both reversal, J/A's, wiffs again...should he J/A again? By your logic, no. And, while I don't necessarily disagree with you (personally, would NEVER run reversal), you haven't calculated all possible outcomes. There is no gamblers falacy in making the assumption that numbers will level out eventually. If your opponent flips 4 coins, the probability of all 4 being tails is pretty low. The probability that he hits tails in every scenario after going 0/3 is (impossible) pretty low. STATISTICALLY SPEAKING, your opponent made a good decision. Your assumption that he assumed it was better than 50/50 (which, he may have assumed) is the fallacy that it was a bad decision. Even if your opponent assumed it was higher than 50/50, it was still a good decision STATISTICALLY speaking, even if he made the fallacy to think his probability SHOULD have been higher. If we make decisions based on probability, I J/A for that reversal every time. And, if you don't J/A for the reversal, you aren't making decision based on probability (or, randomness, as your thread suggests) in the first place, thus the "fallacy" that you are buying into gamblers fallacy actually becomes the fallacy.

    Edit:
    Let me clarify the above paragraph: if you decide to NOT Junk Arm because you ONLY have a 50/50 chance, and thus are taking gambler's falacy into account, you are making the WRONG decision statistically speaking. STATISTICALLY speaking, you will hit the Reversal 1 out of 2 times more often then not. EVEN IF you do make that decision and assume it is higher than 50/50, you still make the right decision, even if for the wrong reason.

    If you aren't going to take ALL of probability into account, don't run flippy cards. Its all about playing the odds....and, one thing I have learned about playing the odds from watching poker, more often than not (most of the time, in other words) that which SHOULD happen, happens unproportionally more than that which shouldn't. In other words, if you watch poker on TV, if it says a player has a 51% chance of winning, they usually win more than 51% of the time...in other words, ALWAYS JUNK ARM FOR THAT REVERSAL, even if you miss, you still make the right decision.
    Last edited by chrataxe; 12/26/2011 at 03:06 PM.

  7. #7
    Quote Originally Posted by chrataxe View Post
    Dude, I have no idea what you are trying to say in your Monty Hall scenario. I think it is your scenario that throws me off. If you energymite, you probably take you last 2 prizes that turn. Even if you have to pass that turn and I draw the wrong prize, I still have to KO a Pokemon to draw the J/A in order to get to 2 prizes and have the 50/50 chance, which means you still have 2 turns to get the ko while it takes me 3 turns to get to use the J/A...but, the logic flow has so many break downs, even if I try to ignore what I've stated above, I still cannot follow it.

    One "fallacy" that you addressed improperly is your nats side event scenario. While your opponent did have the same 50/50 chance of hitting heads, you DO still have to calculate ALL probability associated with the scenario. How many times did he go for the Reversal? Lets assume he had 2 reversal and 2 J/A in hand. He wiffs on both reversal, J/A's, wiffs again...should he J/A again? By your logic, no. And, while I don't necessarily disagree with you (personally, would NEVER run reversal), you haven't calculated all possible outcomes. There is no gamblers falacy in making the assumption that numbers will level out eventually. If your opponent flips 4 coins, the probability of all 4 being tails is pretty low. The probability that he hits tails in every scenario after going 0/3 is (impossible) pretty low. STATISTICALLY SPEAKING, your opponent made a good decision. Your assumption that he assumed it was better than 50/50 (which, he may have assumed) is the fallacy that it was a bad decision. Even if your opponent assumed it was higher than 50/50, it was still a good decision STATISTICALLY speaking, even if he made the fallacy to think his probability SHOULD have been higher. If we make decisions based on probability, I J/A for that reversal every time. And, if you don't J/A for the reversal, you aren't making decision based on probability (or, randomness, as your thread suggests) in the first place, thus the "fallacy" that you are buying into gamblers fallacy actually becomes the fallacy.

    Edit:
    Let me clarify the above paragraph: if you decide to NOT Junk Arm because you ONLY have a 50/50 chance, and thus are taking gambler's falacy into account, you are making the WRONG decision statistically speaking. STATISTICALLY speaking, you will hit the Reversal 1 out of 2 times more often then not. EVEN IF you do make that decision and assume it is higher than 50/50, you still make the right decision, even if for the wrong reason.

    If you aren't going to take ALL of probability into account, don't run flippy cards. Its all about playing the odds....and, one thing I have learned about playing the odds from watching poker, more often than not (most of the time, in other words) that which SHOULD happen, happens unproportionally more than that which shouldn't. In other words, if you watch poker on TV, if it says a player has a 51% chance of winning, they usually win more than 51% of the time...in other words, ALWAYS JUNK ARM FOR THAT REVERSAL, even if you miss, you still make the right decision.
    Whew... quite a response there! Lets see if I can give some insight.

    First, in the case of the Monty Hall problem, go read the original scenario and see how it works before coming and saying that the logic is wrong. Here's a link for you! ( http://en.wikipedia.org/wiki/Monty_Hall_problem ) Assume prizes would be tied with 2 left each after the Energymite but RDL can't get into the active position because a retreat has already been done this turn (or whatever reason you'd like, it doesn't matter). If you pull the Junk Arm as the prize, you can Junk Arm for a Catcher and pull up RDL to KO him for the win. If you pull an energy, you miss the KO on RDL and lose because he's about to KO your active for 2 prizes. The scenario is showing how relative probability works. If you are shown a wrong answer, you should switch your pick because you picked at a 1 in 3 chance and the alternative offered is now a 2 in 3 chance. It's quite complex and most people don't understand and will argue for hours. If you still don't understand, go read the link and hopefully that will clear things up.

    Second, in the case of the Worlds Side Event, the scenario would need to be more fully explained to make a judgement call on whether the player made the right move. If all he needed was a heads on reversal to win the game and there is no chance of any others in the deck, the draw supporter does him no good and he should go for the Junk Arm. But this is rarely the case. Typically there is something left in the deck that could help win the game. Also, it's not typically a matter of "if I get this heads, I win, if I miss, I lose." Though, in that format, it was unusually common. If the scenario was that KO would put the player in a much stronger position but not give you the win, throwing away your last draw supporter is not something I would do for a coin flip. It's still 50/50. While statistically it will balance out, random numbers have strings of repeated flips. Because it's 50/50, you will eventually get to a 50/50 result, but you may go through 20 tails in a row before getting there.

    The biggest thing that I believe you're missing in both scenarios is the game state that is implied. In the first, if you hit the Junk Arm, you win but if you miss it, you lose. It's a scenario with extremely specific constraints. You can't "work out" a better solution because that's not what the scenario is about. It's about the chances on switching your choice or not which is a difficult logical scenario to wrap your head around. In the second, the fact that the player basically threw away the game by discarding his only draw power is a bad decision. He based the entire game on a coin flip and that's still a 50/50 chance regardless of the previous coin flips.

    BTW, love the article cabd. Can't wait to see more.
    David Griggs
    South Carolina PTO

  8. #8
    Shen's Avatar
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    The luck factor of Pokemon has always, to me at least, meant that we need to play more rounds. The more rounds we play, the greater chances we have for our "odds" to settle out. For example, say we play against a deck twice with a 50-50 match-up in swiss, and we lose both times. In the long run, we should be able to win every other game. However, two games isn't a large enough sample size to represent the outcome of the match-up accurately. Of course, player skill comes in to play and so forth... but at the highest level of play, when people are very close in skill at the top tables, we need more games to determine a true winner.

    I think you've shown several great examples of how luck plays a role in Pokemon, and you've used the terms "in the long run" and "time(s)" several times yourself. In order for these scenarios to play out with greater accuracy, we simply need more games (or "times," to play out the "long run") . This also solves the first turn rules, in that we're more likely to go first 50% of our games in the long run.

    Great read, would love to see more!
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  9. #9
    Quote Originally Posted by cabd View Post
    Selective Memory

    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.
    People often say, "I hit so many red lights coming home from work!" yet ignore all the green ones they went through.

    http://en.wikipedia.org/wiki/Availability_heuristic
    6th place MD States 2007, 48th place US Nationals 2007, 8th place Stafford CC 2010, 6th place Mid-Atlantic Regionals 2011, 2nd place Leonardtown BR Spring 2012, Winner Ditto ex CaC Contest
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  10. #10
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    As a person who works to model and manage risk for a living.

    Random can be described and modeled, but can't really be controlled.
    Random can't be contolled because Random isn't fair.
    <)))))><
    Theorem: One can do just about anything, but not everything.
    Corollary: One can afford just about anything, but not everything.
    The worst thing you can do for someone you love are the things they could and should do for themselves. - John Wooden, Legendary UCLA Coach

  11. #11
    That isn't the standard coupon collector problem. Which is how many tries (buys) you have to make to compete a set.

    You need to be very careful with your assumptions. If a player flips heads ten times in a row then I'm much more likely to want to check that the coin is fair than believe that the odds of heads next flip are 50-50.

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