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2 easy ways to disprove the gambler's fallacy

Gaming_Debater
Posts: 233
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11/24/2014 6:43:42 PM
Posted: 2 years ago
Gamber's fallacy- the mistaken belief that something will occur in a "balance" of frequency depending on how frequently it happens now.

Way #1: rolling a die

Let's say you roll a die 6 times per experiment for 2 experiments. If the fallacy is true, then each number should be rolled no more or less than twice total as each number has a one in six chance of being landed on. Multiply that by your two experiments and you get a two in twelve chance. The results for the first one are as follows:

1- 0
2- I
3- I
4- II
5- 0
6- II

If the gambler's fallacy is true, then there should be two rolls for 1 and 5 each, one roll each for 2 and 3, and NO rolls for 4 or 6. These are the results:

1- 0
2- III
3- I
4- 0
5- II
6- 0

The total results are:

1- 0
2- IIII
3- II
4- II
5- II
6- II

Do the rolls add up to twelve? Yes. Were the rolls "balanced?" no.

IE you can disprove the gambler's fallacy just by playing monopoly.

Way #2: With this argument:

P1) If chance operated in a closed system, an event would occur less frequently later if its frequency were higher than normal now as an act of balance and vice versa.

P2) Chance does not operate in a closed system

C1) Therefore "balances" of frequencies do not occur

C2) Therefore the gambler's fallacy is false.
Mhykiel
Posts: 5,987
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11/30/2014 12:05:48 PM
Posted: 2 years ago
At 11/24/2014 6:43:42 PM, Gaming_Debater wrote:
Gamber's fallacy- the mistaken belief that something will occur in a "balance" of frequency depending on how frequently it happens now.

Way #1: rolling a die

Let's say you roll a die 6 times per experiment for 2 experiments. If the fallacy is true, then each number should be rolled no more or less than twice total as each number has a one in six chance of being landed on. Multiply that by your two experiments and you get a two in twelve chance. The results for the first one are as follows:

1- 0
2- I
3- I
4- II
5- 0
6- II

If the gambler's fallacy is true, then there should be two rolls for 1 and 5 each, one roll each for 2 and 3, and NO rolls for 4 or 6. These are the results:

1- 0
2- III
3- I
4- 0
5- II
6- 0


The total results are:

1- 0
2- IIII
3- II
4- II
5- II
6- II

Do the rolls add up to twelve? Yes. Were the rolls "balanced?" no.

IE you can disprove the gambler's fallacy just by playing monopoly.


Way #2: With this argument:

P1) If chance operated in a closed system, an event would occur less frequently later if its frequency were higher than normal now as an act of balance and vice versa.

P2) Chance does not operate in a closed system

There is no information leaving the die or being added tot he die. the die and it's outcomes are a closed system. Given 6 sided die, we have a 100% certainty the number will be 1 of 6 known outcomes.

The die on each roll is "reset" which is why the gambler fallacy is right, the outcomes now do not effect the rolls later on. This should also be evident in that the calculation for odds of a fair die roll do not take into account set of past outcomes or time-frame of trial.


C1) Therefore "balances" of frequencies do not occur

Because the system is reset. What this "balance" is, I think is the determination of the die being fair or not. in which case your example lacks a sufficient number of trials to make such a call. If you rolled another 600 times then we could say the die was rigged or not.


C2) Therefore the gambler's fallacy is false.

i would say the Gambler's fallacy is true. In that it is true that this is a fallacy in determining truth.