Hello I am in a class right now and we are talking about common fallacy people about communication make I just want see if you think what I say is on the right path and if what the teacher said. This is on a fourm thing where we have to post and its worth 10% or grade.

Opening post by me:"Another fallacy I think people use quite a bit in their lives is the gambler's fallacy. I believe this because I hear people all the time say when their lives are going good that soemthing bad is proabally about to happen. And on the flip side when people are down they think good times will come around. When really events in our day to day life just happen by chance and how much work one is willing to put into something. So for example if you just got fired from your job, its not because you were at a high point of your life, theres a reason behind it, such as you werent doing your job."

Teachers response: "Well, with statistical regression (the tendency over time for things to average out) these ideas actually make sense. If you're having a run of bad luck, it's gonna get better. And if life's going great, sooner or later something not so fun will happen."

my response back to the teacher: "I guees I am a little confused on the gamblers fallacy then. The way I thought of it was past events do not play into future events. So for the most basic example, flipping a coin. For example if you have just flipped a coin 5 times and it cames heads each time its still going to be the odds of 50/50 that the next flip will be heads. While yes over the long run things do tend to average out to the mean past events do not affect the future outcomes in the gamblers fallacy. So while you have a good week it does not change your odds of having a good week the next week, as in past events have not affects on future outcomes. The odds of you having a good week are not affected by anyway of the past event of having a good week. So just because you just got your dream job does not change the odd of you next week and you are doomed to hell the next week. It is still going to be your normal odds of having a good or bad week. But with that being said life is not striaght foward as flipping a coin and your odds of having a good week do change from week to week, for example your mood changes, people come and go in your life, or you had to relocate your job. But the main point is that just you have a good or bad week does not change your future based off the fact that you have a good or bad week."

You were right...your prof is wrong (sort of). Provided that events are independent, then a run of bad luck is NOT more likely to be followed by good luck.

The regression to the mean comment is really only about what we expected to happen...but we can't draw conclusions about the future based on past results if the events are independent.

Ya I think you are both right. Gamblers fallacy and regression to the mean are both legitimate concepts.....the difference is time scales. It is wrong to assume what is going to happen in the short term has anything to do with what happened in the past, but it is correct to think in the long term things will average out.

As an example if you are flipping coins and you lose the first flip you can't anything about the likelihood of winning the next flip other than 50:50. Overtime though things will average out and your expectation value for all flips you ever take is to lose 1 (the one you just lost).

I think you both understand the math. The difficult part is when you bring human emotion into the equation. If you lose the first coinflip, are you upset because losing doesn't increase your chances of winning the next one, or are you happy because in the long run you'll regress to the mean?

It's easier when you only have to calculate expectation values and such. Humans are bad incorporating probability into their emotions in a sensible way.

I don't know anything about 'statistical regression' but I think your Prof is confusing the class at best.

"If you're having a run of bad luck, it's gonna get better. And if life's going great, sooner or later something not so fun will happen."

Can anyone argue that this statement is valid. It appears so blatantly wrong.

I think this is a question of literacy rather than math.

Will someone's luck change? - nearly always with a large enough sample (which I presume life is)

Will someone "starting running better"? - this is by no means certain

I think there is a sense in which the professor is right although it has nothing to do with statistics.

Consider this kind of bad luck:

A gambler has been betting on red in a casino and the last 10 times the ball has landed on black. He thinks the next spin of the wheel is more likely than usual to be favourable because of his run of bad luck. This is the gamblers fallacy and it is irrational.

But what about this kind of bad luck:

I lost my job, the bank repossessed my house, my wife left me, the dog got run over, I forgot to buy a lottery ticket that would have won the jackpot and my doctor tells me I have a year to live. There's only so many major events in my life capable of being that bad and I've got rid of most of them. My wife can't leave me again, nothing more can happen to the dog and so on. Isn't the next major event likely to be lucky rather than unlucky?

I think you have to be careful to identify whether or not events really are independent.

Nope...you could argue that you're more likely to be unlucky because the events may not be independent. The next major event could be your suicide or whatever.

Your example of the gamblers fallacy is correct, but you can also use it to illustrate the professor's point about regression to the mean. I'll use the simple example of flipping a fair coin (probability 0.5 of landing heads and 0.5 of landing tails) -- to more clearly illustrate the "luck" aspect I'll stipulate that every time you land heads, you get $1 and every time you get tails you get $0. In other words, your expected value from flipping the coin n times is $0.50*n.

Supposing under these conditions you flip 5 coins and land heads 1/5 times and tails 4/5 times. You will have been "unlucky" to only land heads 1 time, but this does not mean that your probability of landing heads has increased -- that would be the gambler's fallacy. However, it is true that your expected value over 5 flips is $2.50, so you're correct in saying that you're likely to run better in the future -- that is regression to the mean.

Edit: And, obviously, each coin flip is independent.

Yes, I agree if you think of this stuff as causally related. My wife left me because I lost by job and now I'm going to kill myself because my wife is gone (ignoring that being purposeful rather than unlucky).

But can you not think of it as similar to the type of probablity puzzle where you take balls out of a bag without replacing them? The next one is more likely to be green because the last one was red.

I now know more about statistics than I did 5 minutes ago - thanks

This isn't actually correct...DUCY?

Regression takes infinite time...an infinite number of flips.

Edit: And, in that infinite number of flips, you can have any number of H or T in a row...you can have 1trillion H in a row...so is it more likely that any of the next trillion flips will be biased towards T? No! You could just as easily have the next trillion be H in a row too!

Not sure if I articulated that poorly or what, but that's not what I meant. My point is that over your first 5 flips, you won $1. Your expected value over 5 flips is $2.50. Consequently, you will probably "run better" over your next 5 flips than over your first 5. I think the point of confusion is this: I'm saying you'll "run better" relative to your first 5 flips, not relative to your expectation.

It depends on what you mean by "you will probably run better" on the next 5 flips.

We can calculate the odds of only winning $1 on the 5 flips. Since it's <50% prior probability, we can OBVIOUSLY say that the odds of winning >$1 on your next 5 flips is >50%...but this isn't BECAUSE you ran poorly on the first 5.

The events are independent.

Not what PtMx said imo. He's saying if you have one trillion H in a row then it's likely that the next one trillion flips will contain more T than the first one trillion.

I'm not sure this is that difficult.

That's what I said...and that's false. It's not more likely...the events are independent...geebus.

The mistake you people are making is taking the "probability as frequency" interpretation of flipping a coin being 50% probable T vs H.

lastcardcharlie flips a fair coin 1 trillion times. He lands H 1 trillion times and lands T 0 times.

lastcardcharlie -- exhibiting extraordinary patience and thumb stamina -- intends to flip the coin 1 trillion more times. Now, lastcardcharlie ponders: "am I likely to get more T than I got last time?" In other words, if we let #T be the number of times we land tails over our next 1 trillion flips, is P(#T > 0) > 0.5? Notice that the reason we use P(#T > 0) is because we landed T 0 times over the first trillion flips.

If lastcardcharlie had landed T x times during his first trillion flips, we would have considered P(#T > x). Does this make sense, or are we still talking past each other?

He's more likely to win more in the second 5 flips than in the first 5 flips AFTER SEEING THE FIRST FIVE FLIPS SUCKED. He's not more likely to win more in the second 5 flips before he starts flipping at all. I'm 100% sure ptmx is discussing the former.

oh my god people, this is like the nth time we've defined regression to the mean.

If we have a series of poor events occur in our lives that are truly by chance, and the chance events are distributed with a normal probability, we are running pretty bad and therefore more likely to run better in the future (than you are currently running). There is no causation between past and present events in this scenario...just a statement about the nature of normally distributed chance events.

Correct. Here is another way of looking at it. Rather than flip a coin, suppose we roll a fair die. If you roll a 1 (consider that a "bad" life event), then we can state precisely that odds are 5-1 that the next roll will be higher (i.e. near future life event will be "better"). There is nothing about that which violates statistical independence.

Unless life is rigged.

If you bet tail, and flip a coin 5 times and it's all heads. Then you flip this coin 100000 times. At the end the most probable result is that it is 50000 tail, and 50005 heads.

But if you run so badly, the tendency is to things to get better, because it's hard to be worse than losing all the coin flips!

Is 49999/50006 or 50001/50004 the same probability as 50000/50005?

no need to bring infinity into it.

ur post count is rigged