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Coincidence has no memory.
What you actually are saying is: I roll a dice, trying to get a six. That chance is 1/6 I rolled 5 times, but still no six The sixth time IT HAS TO BE A SIX, because the previous times the six didnt come up. Which is, ofcourse, not true. |
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I see we're back to the gamblers fallacy discussions. Dunbar has it correct.
The odds don't change with each roll. Each roll has a 1 in 6 chance of being a 6. Its the same for your poker hands. 1 has nothing to do with the next.
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Assistanc3, reread the original post and tell me that's not gamblers fallacy.
One hand ad nothing to do with the next
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The gambler's fallacy can be illustrated by considering the repeated toss of a coin. With a fair coin the chances of getting heads are exactly 0.5 (one in two). The chances of it coming up heads twice in a row are 0.5×0.5=0.25 (one in four). The probability of three heads in a row is 0.5×0.5×0.5= 0.125 (one in eight) and so on.
Now suppose that we have just tossed four heads in a row. A believer in the gambler's fallacy might say, "If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is (1 / 2)5 = 1 / 32; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads." This is the fallacious step in the argument. If the coin is fair, then by definition the probability of tails must always be 0.5, never more or less, and the probability of heads must always be 0.5, never less (or more). While a run of five heads is only 1 in 32 (0.03125), it is 1 in 32 before the coin is first tossed. After the first four tosses the results are no longer unknown, so they do not count. The probability of five consecutive heads is the same as four successive heads followed by one tails. Tails is no more likely. In fact, the calculation of the 1 in 32 probability relied on the assumption that heads and tails are equally likely at every step. Each of the two possible outcomes has equal probability no matter how many times the coin has been flipped previously and no matter what the result. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses is the fallacy. The fallacy is the idea that a run of luck in the past somehow influences the odds of a bet in the future. This kind of logic would only work if we had to guess all the tosses' results 'before' they are carried out. Let's say we are gambling on a HHHHH result, that is likely to constitute the significantly lesser chance to succeed. Gambler's fallacy - Wikipedia, the free encyclopedia It is important to remember that the Law of Large Numbers only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will converge to the expected value or that a streak of one value will immediately be "balanced" by the others. Law of large numbers - Wikipedia, the free encyclopedia Last edited by Dunbar : 01-22-2008 at 05:57 PM. |
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