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collapse/expand topics back to Main/GamblersFallacy


02:20:22 AM Nov 6th 2011
Removed natter from Rosencrantz & Guildenstern Are Dead:
  • The reason Rosencrantz and Guildenstren are confused? If a coin does do something like that, then it is probable that there's a bias towards the result it's constantly getting. (That die that rolls 1's more often than pure chance would indicate? Use it when you want to roll a 1!)
  • The chance of this series happening (with unbiased coins) is one in 38 septillion (that's million million million million), in case you are wondering. But the odds of getting any particular ordered set of 85 results is the same 38 septillion; the odds of getting exactly eighty-four heads followed by one tails is also one in 38 septillion.
    • A minor point, but the confusion may also stem from the type of questions you can ask about the probability of events. While it is true that 85 heads in a row is as equally likely as any other 85-string combination by odds of an unbiased coin, there is significant evidence that the coin is biased. Based on the 85 trials, there is no uncertainty as to what the outcome of the flips will be. If you saw these results, did not know explicitly that the coin is fair (this is important), and had to predict the next outcome of the next toss, the safe money would be on heads; no evidence for this coin yet exists supporting that it is not biased towards heads. So, even though the result may be equiprobable to all other outcomes in an unbiased coin, you can still safely conclude that the coin is NOT unbiased from these 85 trials. A link to The Other Wiki for more on this.
    • The best way to find out if a coin is biased is to do some sort of physical measurement on the coin. (For instance, finding that one side is heavier, and thus the other side is more likely to be on top after a flip.) Failing that, it is possible to check a coin's bias based on its results, but it requires some really tricky math and even then you're only calculating the percent chance that the coin is biased; you can never be perfectly sure. See the other wiki for the math.

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