Gambler's Fallacy Revisited
Re: Gambler's Fallacy Revisited
Agent Smith, I have a grudging respect for your posts. So edify me. What's the paradox?
Re: Gambler's Fallacy Revisited
Lets try this another (to make you realise that you have some hidden assumptions) way shall we?
Suppose the set of natural numbers ℕ assuming an infinite sample size what is its "true average" which the mean approaches?
Re: Gambler's Fallacy Revisited
alan1000, you may find this to be of interest.
https://en.wikipedia.org/wiki/Law_of_large_numbers
You can also google around for "law of large numbers" to find many other references.In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed.
Re: Gambler's Fallacy Revisited
But what 'you', people, THINK or SAY does NOT really have much to do with how a coin lands.alan1000 wrote: ↑Wed Oct 05, 2022 2:58 pm It's often said that "the dice have no memory". In ten coin tosses, if the first 9 come up heads, it doesn't make it any more likely that the tenth throw will come up tails; the probability remains 50% or, as the statisticians prefer to say, 0.5.
This is provably true for a limited sample of 10 tosses. But does it remain true for an infinite number of tosses?
Opinion polls usually try to get at least 1000 responses because they know that the more responses you get, the more reliable the conclusions you can draw from it. Given ever-larger samples, the true average tends to assert itself.
But this is ONLY if one was ASSUMING some 'thing' to be true.alan1000 wrote: ↑Wed Oct 05, 2022 2:58 pm So, let us suppose the gambler intends to remain in the game for a (theoretically) infinite number of throws. In a million tosses of the coin, all things being equal, we would expect that half would come up heads and half tails. So if the last 10 have come up heads, we would expect that at some future stage this would be balanced with a series of 10 tails.
The 'future' ALWAYS BEGINS HERE-NOW. Just like the 'past' ALWAYS ENDS HERE-NOW.
But anyway;
BUT, ASSUMING some 'thing' to be true, when NOT KNOWING what IS ACTUALLY True, is NOT REALLY that 'wise' AT ALL.
'Reasonable' in relation to 'what', EXACTLY?
If the "gambler" has ALL of its, and its family's, money on that one coin toss coming up 'heads', then would this be 'reasonable', to 'you' "alan1000"?
And, if 'you' say, 'Yes', then would that have been 'reasonable' to the "gambler's" wife, for example?
Would that "gambler" be ABLE to REASON WHY it just LOST ALL of THEIR money, on a coin toss?
If 'Yes', then REALLY?
But, if 'No', then it was OBVIOUSLY NOT a 'reason-able' ASSUMPTION, AT ALL.
But, then again, 'you' might have ANOTHER scenario, out of the COUNTLESS OTHER scenarios, that 'you' would use here.