This fundamentally disagrees with life experience. You can offer all the "Yeah no."s you want. Surely any one toss is 50/50. But knowing that any 100 tosses is also very close to 50/50 means there is a thing called "Likelihood". Maybe that is different from "probability" is some mathematical sense; I don't know. But 5 heads in a row does mean a tails is becoming more and more likely.
I feel like that too and it really perplexes me. For example, in a series of 100 coin tosses, assume the coin is balanced and the outcome random. If the first 50 tosses are all head then one would think the majority of 50 tosses left should be tails. This is the basic of distribution, the foundation of statistics, is it not? In stat, the sample size maybe even smaller than 100 and they create several tests for samples that are smaller in size. So the question is, is statistics wrong to assume that even with a small sample size we still can assume normal distribution?
This is exactly how somebody under the influence of the gambler's fallacy thinks. The outcome of previous tosses has no influence on future tosses, therefore every toss is 50/50. If there has been 5 heads in a row, the probability of a tails in the next toss is still 50% - the probability has not changed. You mention any 100 tosses is 50/50 also, which is true. But, it does not mean that every time 100 coins are tossed that it will always have 50 heads and 50 tails.
@@shanetwomey4403 Look at the word you are using. "influence". Of course one toss does not influence anything. It can't. Its not a wind to blow nor a sun to scorch. So of course a toss can't influence. That an argument from absurdum. That does not negate the FACT that when there are only 2 possible outcomes, and we know those outcomes are going to be very close to 50/50 then we can predict future outcomes based on previous outcomes. Certainly THEY don't influence anything because they can't. Bu the law of averages is still a law.
@@Robert08010 The gambler's fallacy relates to sample sizes. It is derived from the law of small numbers. Yes, in theory if you flip a coin infinite times it will be 50% heads 50% tails, the fallacy is not arguing against that. The fallacy works with samples, so far example: in 100 tosses you get 80 heads and 20 tails, under the gambler's fallacy a person will wrongly believe that the next 100 tosses will likely have more tails than heads, this is not true because the probability is always 50/50.
I agree with you Rob, and so does life. If you are at a roulette table (let's ignore the green for now) and there is a long run of reds, say 12 or so, and you want to place a bet, then I think you have two bits of information to base your decision on: either the wheel is faulty, or the fact that as the sample size grows it's more likely to approach the base probability in the large numbers scenario. The 'fallacy' is pointing out that some think the probability has changed, or the wheel 'owes' you something. I maintain that it is rational to bet against a long run for reds or heads, the longer the run the more rational it becomes. Or the more likely that you're dealing with a dodgy wheel or coin. Bear in mind that the longest run of one colour seen at any casino is something like 33. Is this the point when the law of large numbers starts to pull? I don't think that it makes any sense to suggest there is some bright line between small numbers and large numbers, and the law of large numbers must always exert some pull, which grows as the sample size increases. I'm sure there's been ink spilt on this topic, so enlighten me if you happen to know more about it and I'm obviously in error.
Doesn't this fallacy sort of beg the question? Whether or not someone thinks an outcome is "supposed" to happen in a sequence is irrelevant, we already know that the odds of it happening in a certain sequence (in an unbiased system or biased one) increases exponentially, like someone assuming the next flip will land on heads after 10 times of landing on tails.
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