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The mathematical trap known as the "Gambler's Fallacy"

Location Coney IslandPosts: 259 Amazing
edited September 2013

We got into a discussion buried within another thread about the "Gambler's Fallacy", but it is an interesting enough topic to warrant its own thread as it may come up in your life at some point.

Scenario:

1) I hold a fair coin in my hand and ask you, "what are the mathematical odds that I flip 5 heads in a row?"

2) You do the math and say, "a 1/32 or about a 3% chance". and, you would be correct.

3) I proceed to flip 4 heads in a row, then stop and ask you, "what are the odds that this last flip is a heads again?"

Here is where a mistake can be made if you don't keep your eye on the ball.

If your answer is "1/2 or 50-50" then you are correct and did not fall for the "Gambler's Fallacy" as it is known.

However, if you thought to yourself, "well, it is the same conditions as it was before; it is still trying to get 5 heads in a row which is a 1 in 32 chance." And your answer was "3%", then you got Jedi mind tricked. (*thanks to Popinski for idea on re-wording this section)

So how did you answer?

Here is the issue of Gambler's Fallacy explained on Wikipedia: en.wikipedia.org/wiki/Gambler%27s_fallacy

Location beyond the Black HolePosts: 1,938 Fantastic

RNG is fake anyway...

ever tried to play the same 400 mp3s in winamp in shuffle mode with the random song button on? after listening to the same list in the same mode over and over again, starting with the same song in the list, the order which should be "random" turns out to only play the same few songs over and over again, so you look through the list and see a bunch of Songs you haven't heard in weeks or months and some that keep running like every other hour.

what if i told you, there is no RNG? it is all a pre defined pattern, your sample size is just o small to see it.

but i have yet to witness Winamp playing the same song 4 times in a loop while set to shuffle.

hands out tinfoil hats

True BelieverPosts: 451 Amazing

The gamblers fallacy isn't someone saying you have a 3% chance to flip the coin on the 5th time. gamblers fallacy is seeing patterns when there is none. The people who think they found that lucky slot machine. Or they swear by there being a higher chance of getting uniques if they swap to their level 1 before they start a terminal.

Your example has the "gambler" not noticing a pattern which is the exact opposite of what the fallacy is. Of course in this game it is hard to tell between an actual gamblers fallacy or a possible bug. For all we know there might be some big bug effecting drops and RNG.

Posts: 73 Mighty

There are different kinds of randomness. In games they usually use a more evenly distributed "randomness" formula, so it will keep players from complaining about getting the same thing twice in a row and it should be like that, else it would be chaos (even so, sometimes it happens).

@ZEROBANG said: RNG is fake anyway...

ever tried to play the same 400 mp3s in winamp in shuffle mode with the random song button on? after listening to the same list in the same mode over and over again, starting with the same song in the list, the order which should be "random" turns out to only play the same few songs over and over again, so you look through the list and see a bunch of Songs you haven't heard in weeks or months and some that keep running like every other hour.

what if i told you, there is no RNG? it is all a pre defined pattern, your sample size is just o small to see it.

but i have yet to witness Winamp playing the same song 4 times in a loop while set to shuffle.

hands out tinfoil hats

Winamp even has a slider for "randomness" so it's obvious it has a pattern to not play the same songs over and over again, except if you rate them, then it will have a higher chance of playing the songs that you like more. It's actually a formula for that.

I thought these things were obvious to begin with...

Even if you flip a coin, the side it ends up on is governed by the laws of physics.

Posts: 1,788 Fantastic

To be fair, technically, nothing is random due to cause and effect. The only issue is that some things are effectively random because the cause cannot be adequately ascertained.

Posts: 432 Amazing

@ZEROBANG said: RNG is fake anyway...

ever tried to play the same 400 mp3s in winamp in shuffle mode with the random song button on? after listening to the same list in the same mode over and over again, starting with the same song in the list, the order which should be "random" turns out to only play the same few songs over and over again, so you look through the list and see a bunch of Songs you haven't heard in weeks or months and some that keep running like every other hour.

what if i told you, there is no RNG? it is all a pre defined pattern, your sample size is just o small to see it.

but i have yet to witness Winamp playing the same song 4 times in a loop while set to shuffle.

hands out tinfoil hats

I don't know how winamp does it but many music players on random will randomize the list you have given it and play each song once until all songs have been played before repeating. Other media players will weight their decisions based on stats of how often you have decided to play a particular song. If Winamp is using a rating system you might have to go in and manually rate all of your songs the same if you want a more even distribution or see if it has different setting for how it randomizes your music.

@PlNK

I prefer the Monty Hall problem. People always get that wrong.

Posts: 181 Incredible

@Kimimi said: To be fair, technically, nothing is random due to cause and effect. The only issue is that some things are effectively random because the cause cannot be adequately ascertained.

Agree. Cause and effect=everything. That's what Lambert said to Keanu (and he didn't understand).

Anti-HeroPosts: 1,192 Fantastic

How can anyone answer 3%? Lol.

Location Look at my profile for a link to free random hero box keys!Posts: 1,180 Fantastic

@Bijyu said: The gamblers fallacy isn't someone saying you have a 3% chance to flip the coin on the 5th time. gamblers fallacy is seeing patterns when there is none. The people who think they found that lucky slot machine. Or they swear by there being a higher chance of getting uniques if they swap to their level 1 before they start a terminal.

Your example has the "gambler" not noticing a pattern which is the exact opposite of what the fallacy is. Of course in this game it is hard to tell between an actual gamblers fallacy or a possible bug. For all we know there might be some big bug effecting drops and RNG.

You are completely wrong. Gambler's Fallacy has nothing to do with superstition. It's a misunderstanding of probability. It's thinking that a coin is "due" to flip tails because it just flipped heads 4 times in a row. It's thinking you "used up" your good rolls because a unique dropped on your level 5 toon.

Location Coney IslandPosts: 259 Amazing

@Popinski said: You worded that completely wrong, but yeah, that's sort of right.

The wiki page has everything on the subject of course, but here is a relevant quote:

"While a run of five heads is only 1⁄32 = 0.03125, it is only that before the coin is first tossed. After the first four tosses the results are no longer unknown, so their probabilities are 1. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses, that a run of luck in the past somehow influences the odds in the future, is the fallacy" en.wikipedia.org/wiki/Gambler%27s_fallacy

I got it right. So I don't know where the "completely wrong" you wrote is coming from. All I did was put the same information from the wiki page inside a conversational form to make it easy to follow.

Location Crazy Town, Banana Pants Posts: 3,752 Cosmic
edited September 2013

@PlNK said: The wiki page has everything on the subject of course...

I am not saying you are wrong, but Wikipedia can be edited by anyone. While it does have a large amount of correct information and a lot of people put effort into making sure it is correct and that it stays that way. It also has an alarming amount of incorrect information. So it is not always an airtight reference source.

Love the thread, interesting read. just thought I would throw that out there.

Location Coney IslandPosts: 259 Amazing

@Bijyu said: The gamblers fallacy isn't someone saying you have a 3% chance to flip the coin on the 5th time. gamblers fallacy is seeing patterns when there is none.

Please go read the wikipedia page about "Gambler's fa> @Scorpiodisc said:

Love the thread, interesting read. just thought I would throw that out there.

Thanks. And of course I agree with you. Anyone who as done at least one research paper in the past few years knows that Wik will not fly as a source. But I felt for such a lightweight subject and for easy reading I would go with the Wik.

If I had to get serious about it, I would site this instead: mansci.journal.informs.org/content/39/12/1521.short

What is creepy though, is even when wording my example like you would talk to a child to make it simple, and giving a reference, some will come back and post that I have no idea what I am talking about.

True BelieverPosts: 451 Amazing

@MattMinus said:

Both of those examples are the person thinking there is a pattern in the randomness. So you just confirmed what I said. We seem to be agreeing on what the fallacy is so why are you disagreeing?

AssembledLocation My happy place...Posts: 1,296 Fantastic
edited September 2013

Statistics is really not that hard. It's just that people are often counting the wrong sample space 90% of the time.

Posts: 809 Amazing

I tend to suffer more from confirmation bias - if it works (0% RIF and 56% SIF) and generates excellent results over time (4 uniques, >10 cosmic, >30 artifacts) I'll keep doing it.

I did level up colossus with pure +RIF, but my opinion is there's a bug as I tend to get better rewards with 0% RIF.

Location ĠėńőšĥãPosts: 1,542 Fantastic

Is it really RGN when uniques are set to a 0.01% drop rate and Chthonic Idol Artifacts are at 99% drop rate.

Location Coney IslandPosts: 259 Amazing
edited September 2013
Posts: 809 Amazing

@PlNK said: AloisHammer

Disagree with this:

I'm extremely confused. To my knowledge, said person hasn't posted in this thread or participated in this discussion.

Location CardiffPosts: 212 Amazing

Is'nt the answer to everything 42 anyway!

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