Thread: Probability Fallacy - help?

Originally Posted by thegnome54

It's when someone claims that a certain (realized) outcome is very unlikely by assuming that a near-infinite amount of other outcomes were possible and/or equally likely.

With the near-infinite amount of other outcomes, there is also a near-infinite amount of time, and a near-infinite amount of scenarios with possible outcomes. Saying there are too many outcomes doesn't apply to the universe, there are too many infinites to consider.

Originally Posted by thegnome54

"It's really improbable for the earth to be perfectly suited to life, therefore God did it"

I don't think it is the earth that was perfectly suited to life, but rather, life adapted perfectly to the earth. I think it's actually quite arrogant to assume that god created the earth for us humans, having also created the entire universe. What makes us so special? We're actually in the process of destroying this planet, that doesn't seem like something a race modeled after a god would do.

A good analogy to earth being perfectly suited to life, is a hole being the perfect shape for the puddle in it. It is shaped to the exact form of the puddle, what are the chances of that!?!

I was curious, so I poked around. You might be describing Lindley's Paradox.

Or it might be closer to Berkson's Paradox.

Originally Posted by skysaw

I was curious, so I poked around. You might be describing Lindley's Paradox.

Or it might be closer to Berkson's Paradox.

No, both of those are too statistically "deep" - this is even simpler than conditional probabilities and such.

It's really a matter of ascribing significance to an outcome after it has happened, and then claiming that it is unusual for it to have occurred because there were so many other "non-significant" outcomes. In reality, if any of the non-significant outcomes did occur, then they would be considered significant.

It's not actually a fallacy really, although incorrect deductions can be made from it.

Let's take out the factor of consciousness. For example,

There is a bag with 1000000000000 marbles in and a bag with 10 marbles in. You are give a marble and told it is from the small bag.

Naturally you call the person a liar, certainly if this is the first trial. There's absolutely nothing wrong with the maths.

What you're essentially doing though is adding consciousness as a key factor, and asserting the anthropic principle is true. Thing is, not everybody believes that the anthropic principle is logically sound.

The first quote of yours is mine, and it's completely valid. It's just a way of refuting the traditional view of 'current time' as being something which moves from point time 0 to time x irregardless of me or you like a vehicle travelling along a straight road at the same speed constantly which at certain times happens to be between specific points; that our 'nothingness' has been 'waiting' for a few billion years, and now that nothingness is consciousness, and soon it'll be nothing for a few more billion years (so to speak). That view is improbable to the extent that it is impossible, for the above reason: treating time like an impartial vehicle which by a sheer coincidence is on 'your inch' on a road which is a million miles long is clearly incorrect.

The fact that I am conscious now and that the universe is so old does give me faith in the endurance of consciousness, but probably not in the traditional sense of reincarnation into other animals in this universe upon death. See, gnome, nobody knows what consciousness is, nobody has any idea why it arises, nobody knows the nature of reality, in fact we cannot even yet get our observed universe to make sense yet, and nobody understands the nature of time or causality or possibly even logic. That's why the anthropic principle is so dodgy, I personally think it's a cop-out in some respects.

The second quote; well at face value that is wrong because evolution is true. But I'm of the opinion that the universe is fine tuned; I'm guessing there's no need to explain that to you. And then of course you evoke the anthropic principle... yeah, again there's a bit of a problem about making any assertions because we have no idea about the ultimate structure of reality. I'm personally of the view that we are part of a multiverse simply due to its brilliant elegance as a solution (although the multiverse theory still does nothing to explain why it should be there in the first place), but there are some people who reckon it's due to some kind of deity and I respect that opinion to quite a large extent.

Welcome back by the way, you were a very good poster... how's the neuroscience thing working out? I'm looking at a maths degree at the mo before specialising in computational neuroscience research, but I'm still unsure.

Originally Posted by thegnome54

No, both of those are too statistically "deep" - this is even simpler than conditional probabilities and such.

It's really a matter of ascribing significance to an outcome after it has happened, and then claiming that it is unusual for it to have occurred because there were so many other "non-significant" outcomes. In reality, if any of the non-significant outcomes did occur, then they would be considered significant.

I was afraid that was the case... just hoped it might start the search for you. I'm sure there is a simple term for it.

Still can't find a good term for you, but here's someone else's writing on this exact topic:
http://goodmath.blogspot.com/2006/05...le-is-not.html
and
http://goodmath.blogspot.com/2006/05...ble-redux.html

On a slightly related note, I absolutely hate when anyone uses probability to refer to something that has already happened. If something has occurred, the probability of it having occurred is 1. It already did happen. Probability is an approximation tool used for predicting future outcomes and doesn't apply to past events.

This also sounds like it is somehow related to the gambler's fallacy; but not exactly the same.

Originally Posted by Xaqaria

On a slightly related note, I absolutely hate when anyone uses probability to refer to something that has already happened. If something has occurred, the probability of it having occurred is 1. It already did happen. Probability is an approximation tool used for predicting future outcomes and doesn't apply to past events.

This.

I agree with the sentiment here. Using probabilities for past events is just plain silly.

Originally Posted by bluefinger

This.

I agree with the sentiment here. Using probabilities for past events is just plain silly.

For the most part, yes. But it depends on whether you include a complete reference timeframe. It is sometimes useful to go back to calculate the probability of something, but only if you have a specific point in time you are referring to, as well as a pretty good knowledge of what variables are in play.

Example: I won the lottery! What were the chances of that happening?

There are two correct answers. One is 100% (from today's reference point), and the other is 0.000001%* (from yesterday's reference point). As long as you include the reference, it's not really all that silly.

*or whatever the actual odds for that lottery

Originally Posted by skysaw

For the most part, yes. But it depends on whether you include a complete reference timeframe. It is sometimes useful to go back to calculate the probability of something, but only if you have a specific point in time you are referring to, as well as a pretty good knowledge of what variables are in play.

Example: I won the lottery! What were the chances of that happening?

There are two correct answers. One is 100% (from today's reference point), and the other is 0.000001%* (from yesterday's reference point). As long as you include the reference, it's not really all that silly.

*or whatever the actual odds for that lottery

That is if you include such perspectives when using probabilities. However, when people use probabilities in such ways to evaluate past events, they often fail to take into account those two perspectives. Because of this, they go on to making rather fallacious conclusions, not necessarily fallacious calculations.

Originally Posted by bluefinger

This.

I agree with the sentiment here. Using probabilities for past events is just plain silly.

But wait I thought....I mean...my biology teacher told me that if you flip quarters 100 times you'll come really close to getting 50 heads and 50 tails.


And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

Originally Posted by Sandform

But wait I thought....I mean...my biology teacher told me that if you flip quarters 100 times you'll come really close to getting 50 heads and 50 tails.

And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

Depends on the perspective... if you see it on the perspective of you flipping quarters and recording a sequence, it would be

half -> half -> half -> half -> etc

Which could end up with:

Heads -> Heads -> Tails -> Heads

But from the perspective as a whole, such a sequence would only have a chance of one sixteenth of happening, even though the action only has a probability of one half from being either heads or tails.

Originally Posted by Sandform

And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

A double 6 is unlikely in general, but not any more unlikely if you just rolled one. It's 1/36 every time you throw 'em.

And what about rolling dice. Doesn't rolling a double 6 with two dice make the likelihood of rolling another double 6 unlikely? (right after)

Ohhh dear, warped view of reality there.

Originally Posted by Xei

Ohhh dear, warped view of reality there.

So if you have two rolls...and you roll a I dunno...3 and a 4, then you are just as likely as before to roll a 3 and a 4 the next time right after?

Originally Posted by Sandform

So if you have two rolls...and you roll a I dunno...3 and a 4, then you are just as likely as before to roll a 3 and a 4 the next time right after?

You are correct, sir!

Yep, probability of 1/36 each time. You really thought that the dice somehow change?

Well fuck Mark Twain lied to me.

I always think it's sad-funny when I hear about people who track the winning lottery numbers looking for patterns. They talk about certain numbers being "due" because they haven't hit in awhile.

Losers all. (In more ways than one.)

Originally Posted by skysaw

I always think it's sad-funny when I hear about people who track the winning lottery numbers looking for patterns. They talk about certain numbers being "due" because they haven't hit in awhile.

Losers all. (In more ways than one.)

See I knew that it wasn't right it was just that in the case of the quarters and the case of the die I had heard two people who I thought knew what they were talking about say something opposite of what I thought was true so I just figured they were right about all the other crap in this particular field I might as well agree...

Quarters - biology teacher. I even pointed out to her that it was unlikely to get 50/50 in reality and she said "well it would be really really close." She was talking about the punnet square and probabilities in what the offspring would have and I asked her is that in total (so if you have 4 babies at different birthing periods and there is a 1/4 chance of blah blah, 1/4 blah, 1/4 blah blah, 1/4 bloo blah) you will have one of each, or is that only in one birth. She left the room to confer with another teacher and came back and said something but by that time I didn't care...hehe.

As for the dice, Mark Twain had some story about it that I heard in passing so I figured he knew what he was talking about too.

Originally Posted by Xei

Yep, probability of 1/36 each time. You really thought that the dice somehow change?

No...but Mark Twain told me so...=(. Or maybe he was purposely making a false statement to make a point...


Hmm, "no" probably isn't the best word to use there...more like yes in spite of a nagging feeling that it wasn't true?

Originally Posted by Sandform

Quarters - biology teacher. I even pointed out to her that it was unlikely to get 50/50 in reality and she said "well it would be really really close."

Tread carefully here...

It is true that if you flip a quarter 100 times, the number of heads is likely to be near 50. But this is a totally different notion than believing that the chance of a heads coming up has anything to do with how many times it has already come up. Again, this comes back to the time framework you are referencing. Here's how you should look at it.

Given a typical (non-trick) quarter and 100 typical flips:

At the start, each flip has a 50% chance of being heads, so you will likely have in the neighborhood of 50 head flips.

After you flip it 50 times, they have all been heads! But the chance for each remaining quarter is still 50%. You will likely have a total of around 75% heads, because you are "starting" with 50 heads, and will probably get around 50% heads on the remaining.

Now you have flipped it 99 times and they have all been heads! But the chance of the last one being a heads is still only 50%. You now have a 50% chance of having them all be heads.

After the final flip, you see you have a perfect series of heads... 100%! There are no more chances to calculate, only a history of what happened.

Originally Posted by skysaw

I always think it's sad-funny when I hear about people who track the winning lottery numbers looking for patterns. They talk about certain numbers being "due" because they haven't hit in awhile.

Losers all. (In more ways than one.)

I've used that strategy in keno at a casino. It actually worked really well. Although not exactly the same strategy. I'd watch a few games and see what number hasn't came up in a while. Then I'd bet on that number. If it didn't come up, I'd double my bet, and bet on the same number until it did come up. By the time it finally comes up, I'll win all the money back I've bet and then some.

In this game, 20 numbers are drawn out of 80, and you can pick anywhere from 1 to 20 numbers to bet on. With picking only 1 number, you have a 25% chance it'll come up, and if it does, you get 3x your bet in winnings. I figured if a number hasn't come up in a few consecutive games, it's bound to come up eventually, so I pick that one to bet on the whole time.

I always walk away with more money than I come in with, but I do fall into that loser category

Originally Posted by Schmaven

I've used that strategy in keno at a casino. It actually worked really well.

That's great. Winning money is always fun, and I'm glad it's worked well for you so far. I just hope you realize that the chances of it working better than a random pick are exactly 50%.

Well your strategy is completely wrong. You could have betted on any number, it would still have had 25% chance of turning up each game, irregardless of previous games. If you walked out with more money after several games then you got lucky.

I don't understand people who think reality works like this... like some kind of magical power is somehow affecting deterministic events.