Gamblers fallacy a fallacy?

Well_InTheory

No. This statement is exactly the gambler's fallacy.

You will win exactly 50% of the time.

The chances of BBBBBBBBBBB is the same as BBBBBBBBBBR. Pick any specific 11-long sequence and it will have the same probability of any other 11-long sequence.

Turning your thought-experiment around, you could also say you should bet on black, because BBBBBBBBBBR is a very unlikely result. Or "if you wait for BRBRBRBRBR then you should bet on R because continuing that sequence is unlikely", which is just as false.

Jocko Homo

This is the single most ridiculous thread I have ever seen on this forum...

There are many ways to think about the Gambler's fallacy. Here's a simple logical argument that shows that the Gambler's fallacy cannot be true:

Suppose you have a coin that has a 50% probability of flipping heads and that coin flipped heads n times in a row. What are the chances of flipping heads a subsequent time? If that probability is anything other than 50% then you are contradicting the initial supposition that you had a coin that "has a 50% probability of flipping heads," therefore the only logically consistent conclusion is that that is the true probability. QED

Jocko Homo

While one could determine the nature of this phenomena without a computer, it appears that you're the sort of person who needs one. Even if you think you don't, perhaps you can simply humour the posters in this thread by making the computer simulation... unless you secretly know that reality will not favour your theory...

Jocko Homo

You ask this question in many different ways in this thread:
The answer is simple: smaller strings are more probable than larger strings because there are less conditions to satisfy...

For example, let's suppose that roulette tosses are random and independent events. The reason why the chances of tossing 2 blacks are better than tossing 10 blacks is because, for the previous case, there are only two conditions to satisfy: that the first toss is black and that the second one is too. For the latter case, you have to satisfy all 10 independent conditions with the same odds for each toss. That will be much harder to do and consequently happens much less often...

Jocko Homo

Why do you say this? This makes no sense. How does micromass' statement imply what you're saying? If you were to try to construct a formally logical argument, you will find yourself unable to build the implication...

Jocko Homo

If you believe this then please describe for us how much more than 50% will you win? Care to calculate what you think the odds should be?

Ignea_unda

After sleeping on this for 2 nights, I think I am able to see where your brain is coming from. I still do not agree, but perhaps if I address this from another angle.

IF all the flips/tosses/spins etc. have already been made and you have a block of data, any number of sets, and you start randomly selecting data from the previously made set, and you select different lengths of strings, say 5 and 6, you will find, statistically, more strings of 5 than you will of 6 for any pattern you choose. HOWEVER, this is only because the likelihood of any specific 5-string is higher than any specific 6-string.

If you, on the other hand, start flipping/tossing/spinning etc., from scratch, and are not shown the results, would you not suspect that you have a 1/n chance of guessing right each time? Each selection is COMPLETELY unrelated to the previous ones.

However, I still think that you should create a computer simulation to verify your predictions. It could be a relatively short code (definitely no more than 50-100 lines).

DaleSwanson

As has already been suggested, I highly suggest you simply write a simulation program and test these ideas first hand.

In fact, you don't even really need a real program. Go here:
http://www.random.org/files/
Save one of the text files (warning they are about 2 megs each), open it up and search for the string '111111111', every time you find it check what the next number is. You will find it is equally likely to be 1 or 0.

Consider what would have to be true otherwise. The source of randomness (roulette wheel or radioactive decay) would somehow have to 'know' what the previous results were and be influenced by them. What if you looked at an entire casino's worth of roulette wheels at once, combining all the results into one giant stream of reds and blacks. However, someone else looked at just a single wheel. If the single wheel had a streak of blacks, but the casino as a whole was on a red streak, what would that individual wheel be more likely to produce? Now, what if you look at all the casinos on Earth? What if you come up with some complex method to combine the results (eg 10 from one wheel, 3 from the next, 17 from the next, alternating between wheels #4 and #5 for 20 choices after that, etc)? It should be clear there would be an infinite number of ways you could combine the data from many wheels. How could there still be a force influencing the results when the data could be combined to produce streaks in any different way?

To use an example I've seen before somewhere, imagine you had a standard fair coin, and flipped it until a long streak occurred (say 10 heads). Now you put the coin in a jar with many other coins and shook it up. Would that single coin still want to be tails? What if you chose another random coin, would it tend to be tails? What if you spent the coin, and a new person who knew nothing of this flipped it, would it still tend to be tails? What if you redefined tails as the side with a picture of a face, and heads as the side with a picture of a bird (or whatever it is)? Now would it tend to be tails (as you defined it), or the 'real' tails?

My point in all this is that when you start to think that sources of randomness are influenced by past events, it leads to many silly outcomes. There are simply too many systems you could use to combine events to produce random choices, and those systems would contradict each other if there were a force which tended to reverse long streaks.

Again, you really should just write a program to test this. You could also just use a spreadsheet. Or, you could actually get a coin and start flipping it. Every time a streak of 3 comes up make a bet against the streak continuing to 4. Keep track of you total winnings.

Volkl

It's nice to see that people are finally coming around. Does everyone agree that the computer simulation that you are all desperate for would reveal that 100 blacks in a row would be less prevalent than 10 blacks in a row? Then why wouldn't that same logic hold true for 11 blacks in a row being less prevalent than 10 blacks in a row? Staying within the 50,000,000 trials.

If these are true most humans would experience a higher probability that red would come up after 10 blacks in a row.

-----------------------------------------

Not that anyone mentioned it yet but the error with this logic might be that the 10 blacks in a row case should not be directly comparable to the 11 blacks in a row case, because, the ten blacks in a row case also comes within all large cases of blacks in row. This was not easy for me to see sorry for putting so much gusto into some of the earlier responses, or for frustrating the hell out of people, either way, I played baccarat this weekend and won, some how it varies at an even higher rate then roulette - but that's another theory for a different thread.

micromass

Nobody is claiming here that 11 blacks are as prevalent as 10 blacks. Everybody knows I would see 10 blacks more often than 11 blacks. That's not the point.

Evo

Please don't feed the troll. Please report threads like this.