Is Gambler's Fallacy Really True? Not according to my tests...

When a sequence of independent trials of a random process is observed to contain a remarkably long run in which some possible outcome did not occur (for example, when a roulette ball ended up on black 26 times in a row, and not even once on red, as reportedly happened on August 18, 1913 in the Monte Carlo Casino[277]), the underrepresented outcome is often believed then to be more likely for the next trial: it is thought to be "due".[278][279][280] This misconception is known as the gambler's fallacy; in reality, by the definition of statistical independence, that outcome is just as likely or unlikely on the next trial as always—a property sometimes informally described by the phrase, "the system has no memory".

List of common misconceptions

I remember learning about this back at school, but I recently thought to myself "is this really true". Common sense would seem to tell me that a change is more likely after a streak. So I put it to the test. I wrote a simple algorithm that did the following:

# continuously generate random numbers between (and including) 1 and 50
# when ever the random number is the same twice, check if the 3rd number has changed

The result was exactly as I expected. The ratio of changed to not-changed was 250:5 That means if you are betting on a number between 1 and 50, and the last two results were the same, the chances of the next result being the same as the last two is 50 times less than it changing. Maybe I'm just not understanding this gambler's fallacy thing properly, perhaps someone can explain these results logically.

I wasn't sure where to post this. I decided not to waste space on ATS and post in the off-topic section, because is more like a random question I was just interested in talking about. Feel free to move mods.

EDIT: Actually, I think the answer is staring me in the face. The result I got was probably 50 times less because the chances of picking the correct number in any instance is 1 out of 50. Of course picking one number has a 1 out of 50 chance compared to picking one from all the rest. Wow, I'm dumb.

There's lies, big lies, and then there's statistics.

My understanding is that a number between 1 and 50 coming up again when that single "flip" is taken into account, the odds are 1 in 50 just like before.

However, if one takes the entire sequence into context, the odds of having three flips in a row is 1/50x50x50.

only way to figure it out..

hit vegas....BABY!

reply to post by AnIntellectualRedneck

My understanding is that a number between 1 and 50 coming up again when that single "flip" is taken into account, the odds are 1 in 50 just like before.

Yeah, that's basically what the gamblers fallacy states. But check out my edit, I think I answered my own question.

However, if one takes the entire sequence into context, the odds of having three flips in a row is 1/50x50x50.

Yeah, that's correct. Seems a bit high though. I was getting lots of streaks higher than 2.

You are wrong, plain and simple.

How would common sense tell you a change is more likely after a streak? You are saying, if I see 5 reds in a row at roulette, that somehow the table has a memory and KNOWS there were 5 reds prior, and plans to bias towards a black on the next spin? So, it has a memory AND a personality?

That's absurd, sorry. Every spin of that wheel is independant of previous spins. The Gambler's Fallacy holds.

I'm not sure why you'd even need to write an algorithm, but if you did and you got those results, then your code and/or logic is at fault, not the tried and tested laws of physics.

Edit: Sorry, I see you noticed your error and corrected your post in the edit, in which case ignore my post.

reply to post by humphreysjim

Edit: Sorry, I see you noticed your error and corrected your post in the edit, in which case ignore my post.

Well I've already read it. What has been read cannot be unread!

Anyway, I did I better test. Instead of 50 possible numbers, I simply used two, so it was more like a coin flip. The results confirmed the gambler's fallacy. The ratio of changed to not-changed was 1:1 this time.

Originally posted by ChaoticOrder
reply to post by humphreysjim

 

Edit: Sorry, I see you noticed your error and corrected your post in the edit, in which case ignore my post.

Well I've already read it. What has been read cannot be unread!

Anyway, I did I better test. Instead of 50 possible numbers, I simply used two, so it was more like a coin flip. The results confirmed the gambler's fallacy. The ratio of changed to not-changed was 1:1 this time.

edit on 30-10-2011 by ChaoticOrder because: (no reason given)

To make it more interesting, if you see a coin flipped 10 heads in a row, the reverse of the Gambler's Fallacy is actually true, because there a decent chance the coin is biased

reply to post by ChaoticOrder


I have never ever ever believed in gambler's fallacy before. In practice, it's never right. It is only correct on paper. Unfortunately for many in the statistical mathematics community, reality doesn't play out on paper.

Originally posted by Cuervo
reply to post by ChaoticOrder

 

I have never ever ever believed in gambler's fallacy before. In practice, it's never right. It is only correct on paper. Unfortunately for many in the statistical mathematics community, reality doesn't play out on paper.

It should be easy to crack the casinos then, playing roulette with a Martingale type system.

I take it you're rich having done so?

That chance of getting heads two times in a row is .5 squared as is the chance of getting heads then tails because each has a .5 chance of occurring. The chance of getting heads three times in a row is .5 cubed which is .125 which is the same as a chance of getting heads tails heads heads heads tails tails tails heads so on and so forth. These situations have an equal likelihood of occurring. If you were to bet on any situation not occurring, your chances of winning are 1-.125. Drastic player favor because there is only one situation out of a plethora of possibilities which can happen as we push it to the 4th 5th and so on.

The chance of getting heads 5 times in a row then a head is .5^6 the chance of getting 5heads in a row then a tail is .5^6 CONFERMING the essence of gamblers fallacy. HOWEVER

There is a way arround this. Technically it doesn't matter what you bet on as long as

You keep betting on something using an advanced martingale system that increase the bet by 110% instead of 100%. This allows the statistical RISK to decrease per bet while increasing profit s far beyond traditional martingale betting. Increasing the bet by 111.1111% keeps the RISK linear.

The chance of losing 1 time in a row Is .5 the chance of losing 2 times in a row is .5 squared the chance of losing 5 times in a row is .5^5. You can bET ON ANYTHING so long as you keep betting double at least when you lose.

I work in a casino and have personally tried this out .

I also run simulation s and have made tons of vertual profit.

If you can find a roulette machine that base a min bet of 1 to 3 dollars, that is ideal. There are some around the casinos where I work.

Good luck

originally posted by: scaber
That chance of getting heads two times in a row is .5 squared as is the chance of getting heads then tails because each has a .5 chance of occurring. The chance of getting heads three times in a row is .5 cubed which is .125 which is the same as a chance of getting heads tails heads heads heads tails tails tails heads so on and so forth. These situations have an equal likelihood of occurring. If you were to bet on any situation not occurring, your chances of winning are 1-.125. Drastic player favor because there is only one situation out of a plethora of possibilities which can happen as we push it to the 4th 5th and so on.

The chance of getting heads 5 times in a row then a head is .5^6 the chance of getting 5heads in a row then a tail is .5^6 CONFERMING the essence of gamblers fallacy. HOWEVER

There is a way arround this. Technically it doesn't matter what you bet on as long as

You keep betting on something using an advanced martingale system that increase the bet by 110% instead of 100%. This allows the statistical RISK to decrease per bet while increasing profit s far beyond traditional martingale betting. Increasing the bet by 111.1111% keeps the RISK linear.

The chance of losing 1 time in a row Is .5 the chance of losing 2 times in a row is .5 squared the chance of losing 5 times in a row is .5^5. You can bET ON ANYTHING so long as you keep betting double at least when you lose.

I work in a casino and have personally tried this out .

I also run simulation s and have made tons of vertual profit.

If you can find a roulette machine that base a min bet of 1 to 3 dollars, that is ideal. There are some around the casinos where I work.

Good luck

Where I mention statistical RISK I'm talking aboutblack and red on a roulette table not coins my appologies in advance for any confusion