# Gamblers fallacy a fallacy?

1. ### Volkl

39
If I was a serious gambler there is a small chance that I could place 50,000,000 bets physically at a casino. Pretending that the game we are playing offers fair odds, the chances of one particular outcome coming up 1000 times in a row within the set compared to the same particular outcome coming up 100 times must be much less. If this is true the probability of 20 particular outcomes in a row must be less then the probability that 10 of the same particular outcomes can come up. Doesn't this prove that there is a tendency towards randomness meaning that there is a tendency to have less of the same particular value coming up in a row. To me, this logic proves that the gamblers fallacy is in itself a fallacy. Or do you believe that all 50,000,000 could be the same value for anyone living on earth? I had a roulette wheel with no greens in mind.

Last edited: Sep 22, 2011
2. ### micromass

19,211
Staff Emeritus
No, let B=black and R=red. Then the probabilities for

B R B R B R B R B B B R B B B R R R R B R B R B R B B B R B R

are exactly the same as

B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B

These two events have exactly the same probability because each roll of the Roulette wheel is independent.

3. ### Volkl

39
So again, your one of those that believes that a human could in reality experience 50,000,000
black outcomes?

4. ### micromass

19,211
Staff Emeritus
The chance would be very small, but the chance is the same as any other outcome.

This is very easily checked with a computer. Just let a computer spew out random outcomes and see if there is any outcome that occurs more than another. Probability doesn't lie, my friend.

5. ### Volkl

39
I agree with the chance being small, so much so I'm betting on it. Please explain why you believe the chance is small? Do you beleive the chance of ten in a row being black is much larger?

6. ### micromass

19,211
Staff Emeritus
Whatever betting strategy you have, run it on a computer first. You'll see quickly if there are any fallacies.

7. ### Volkl

39
The logic here does not require a computer. The point is that there is a higher probability that smaller sets of like numbers occur than larger sets of like numbers, so there is a tendency for the next value to oppose the previous string of like values.

8. ### micromass

19,211
Staff Emeritus
I know that seems believable to you, but the logic is inherently flawed. A value does not depend on previous values.

There is only one way to settle this and it is by practical experimentation. You will see in practical experiments that what you are saying is false.

9. ### Volkl

39
I guarantee that 1000 blacks values in a row would be found less than 100 black values in a row. Another way of saying it would be that there would be more sets of 100 blacks in a row then there would be 1000 black sets within the 50,000,000 sample size within all of the samples/trials any human could simulate in a lifetime.

10. ### micromass

19,211
Staff Emeritus
Yes, of course. But this does not mean that if you have 100 black values in a row, that the chance on a red is somehow higher than the chance on a black...

11. ### Kevin_Axion

921
Micromass is right, there is only a variance in the probability if they are removed from the system.

12. ### Volkl

39
Since there is always more smaller sets of like numbers in a row then there is compared to larger sets of like numbers in a row - I believe it does. If not, you would not have said of course below.

13. ### Volkl

39
This system is simply 50,000,000 spins of a wheel though-Kevin.

14. ### micromass

19,211
Staff Emeritus
This conversation is pointless. We can never convince each other in any possible way. So I suggest you go and try some practical experiments. Do it on a computer or in a casino. You'll see that what you say is false.

15. ### Volkl

39
How can the probability for 1000 blacks in a row be less than a hundred in a row if there was no tendency towards randomness?

16. ### micromass

19,211
Staff Emeritus
I don't see what you're getting at here. The system is random.

17. ### Volkl

39
I'm trying to get agreement on the "tendency" towards randomness.

18. ### Ignea_unda

133
Each time you have a 50% chance of guessing right. There is ZERO impact from the choice before it.

19. ### Kevin_Axion

921
Then there is no variance in probability. Each time you spin the wheel the probability of getting a number in your set $\mathcal{S}$ is one over the cardinality of your set: $\frac{1}{\left|\mathcal{S}\right|}$.

20. ### Volkl

39
I'm trying to get agreement that there is a "tendency" towards randomness when comparing strings of like outcomes to other strings of like outcomes. I.e. Shorter strings of like outcomes are more prevalent then longer strings of like outcomes.