Gambler's Fallacy and Pokemon: Are you gambling too much?

[Mrobinson587]

Pokemon is a game of math. Understanding key concepts is crucial to being a good battler. Today I want to bring up the issue of "Gambler's Fallacy"

http://en.wikipedia.org/wiki/Gambler's_fallacy
The first paragraph should give you a good idea of where to start with how you should start thinking.

Edit: This situation does not have repeated trials as pointed out by ColinJF. Not a good example. Sorry
Today on the UU later I was faced with a situation where it was Gallade Vs Gallade. I run Jolly and as I later found out my opponent did as well.

I Shadow Sneaked while they Sword Danced. Next turn I Shadow Sneaked again and won the speed tie KOing Gallade and consequently allowing Gallade to KO his last Pokemon and win the match.

This is a perfect example of misapplying math. My opponent felt he had a 75% chance of winning the speed tie next turn and exclaimed "You are so lucky". Many of you may think that he might have had a 75% chance to win as well but it is STILL 50%.

This concept can be applied to almost everything in pokemon, but should be most notable with things like Jirachi's Iron Head or Garchomp's Sand Veil.

Well I really just wanted to get this conversation started and make people aware of what might be a common mistake. If you need more explaining I will do my best to help you understand. The wikipedia article explains it pretty well and should be read first before asking please :D

 

[Cathy]

You misunderstand the gambler's fallacy.

Losing a speed tie toss up twice in a row is more unlucky than losing it once in a row and winning it the next time. The chance of losing two in a row is 1/4; the chance of losing just one is 1/2. A quarter is less than a half.

Let's suppose that you and your opponent faced off in 10 consecutive speed ties. The expected number of speed ties for either player to win is 5, since the chance of winning any given one is 50%. Hence, if you win less than five, you could say you got "unlucky".

In general: losing n speed ties in a row is less likely than losing n-1 speed ties in a row. This is not a fallacy.

The correct interpretation of the gambler's fallacy is that the chance of you winning the speed tie is independent of whether you won the last one, which is pretty obvious, and not what people are getting at when they claim to have been unlucky.

 

[Objection]

The first round in that Gallade example wasn't even a speed tie so even if somehow the odds of losing a speed tie were dependent on how many you'd lost before, that number would be zero in that example and the chance would be 50% anyway.

 

[Cathy]

True, the original post scenario doesn't even involve repeated trials, so it doesn't have much to do with the gambler's fallacy. That said, I wanted to clarify the actual gambler's fallacy.

 

[The Plant]

The fallacy, I think most often comes up when trying to get a critical hit or freeze on a defensive stat upper.

 

[Mrobinson587]

Saying you got unlucky and what you choose to do are 2 different things. You get Flinched by Iron Head 3 times in a row. You will die in two more attacks but you have a chance to KO jirachi with 100% accurate Earthquake the next turn. What are you chances of KOing Jirachi?

Obviously 40%

You can't feel like "because I got flinched 3 times in a row i'm due to not get flinched this next turn" which is what is more what I wanted to get across. I have a feeling that many people don't think how they should when facing situations like this.

 

[scorchedsky]

The fallacy, I think most often comes up when trying to get a critical hit or freeze on a defensive stat upper.

What people seem to forget is how frequently critical hits actually happen, and this is a good point: In 16 consecutive ice beams, the odds that NONE are critical hits is (15/16)^16, which is only 35.6%. 16 ice beams without a freeze is even worse, (9/10)^16, which is only 18.5%. You're actually very lucky if you stall out 16 ice beams without being crit'd / frozen.

 

[Tangerine]

I honestly don't see a productive discussion coming from this. If you really want, I will recommend that you write a Smog article regarding the subject - but there really isn't much to discuss here.

 

[X-Act]

Saying you got unlucky and what you choose to do are 2 different things. You get Flinched by Iron Head 3 times in a row. You will die in two more attacks but you have a chance to KO jirachi with 100% accurate Earthquake the next turn. What are you chances of KOing Jirachi?

Obviously 40%

You can't feel like "because I got flinched 3 times in a row i'm due to not get flinched this next turn" which is what is more what I wanted to get across. I have a feeling that many people don't think how they should when facing situations like this.

I know the thread is locked, but I'd like to say something about this.

It is true that if you get flinched 3 times in a row by Iron Head, the probability that you'll get flinched in the fourth turn is still 60%. However, as Colin pointed out, the probability of Jirachi flinching 4 times in a row is only 12.96%.

This is akin to coin flipping. Each and every coin flip has a 50% chance of landing heads or tails, whether it is the first flip, the fifth, or the hundredth. However, long streaks of heads and long streaks of tails are rare. The probability of getting 10 heads in a row on a (fair) coin is only one in 1024. It is not zero, which means that it IS possible, but it is unlikely. In fact, you can show that if you flip a coin 10 times, getting 5 heads and 5 tails is the most common outcome (of course, not necessarily in that order).

That means that I DO expect Iron Head Jirachi not to flinch me 4 times in a row, with about the same probability as I expect a Pokemon not to critical hit me at a crucial moment of the battle. The fact that these things DO happen though is usually why 'hax abuse' Pokemon tirades happen.