Reverse player fallacy

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As the reverse gambler's fallacy (ger .: inverse gambler's fallacy ) is a simple gambler's fallacy similar error in estimating probabilities called: A pair of dice is thrown and shows (for example) double six. The fallacy is: This is a pretty unlikely result, so the dice must have been thrown quite often beforehand . More generally, the reverse player fallacy claims that one unlikely event shows that many more events exist.

As with the simple fallacy of the player, the mistake must be made clear in one sentence: “Dice have no memory”. Every throw is stochastically independent of every other throw.

The mistake is based on the correct knowledge that even the unlikely events will eventually occur in a large number of attempts. However, the dice example does not consider a large number of attempts, but a specific throw whose chances of success are not influenced by other throws.

An example makes it clear: A random number generator generates numbers from 1 to 100. The result of a round is 17. 17 is a rather unlikely result (chance 1: 100). Can you conclude from this that the random number generator must have been running for a long time if it was producing such improbable results? Of course not. The result does not contain any information about how many numbers have already come.
A parallel formulation: The random number generator is built into a slot machine in such a way that the player wins 50 euros for every 17. Suppose a player only plays once and wins. Does this entitle the player to the thought “I won! 1: 100! The machine has been running for a while, otherwise I would never have been able to win immediately! "?
Another way to clarify is to color the cubes differently, e.g. B. green and red, and then compare the results rolled. The result "green die shows 2, red die shows 3" certainly does not justify the assumption "The dice must have been thrown quite often before". This result is just as likely as the result “green and red dice show 6”, so the above fallacy is just as inappropriate.

Apparently, one is more likely to fall into the wrong conclusion when one event is highlighted among other equally probable events. Unconsciously, we want to explain “special” events afterwards by changing the background assumptions about the random experiment. The changed hypothesis is then apparently confirmed by the "unusual" result. You might as well believe that a humane programmer would have programmed the machine so that it outputs 17 as soon as you step on the device.

Multiverse, anthropic principle and the reverse player fallacy

In philosophy, the anthropic principle is discussed together with multiverse theories as an explanation for a possible fine-tuning of the natural constants in our universe. According to this explanation, an ensemble of universes exists, and only through selective observation - observers can only perceive those universes in which their existence is possible - our observable universe appears to us to be finely tuned.

The English term for the reverse gambler's fallacy , inverse gambler's fallacy , was introduced by Ian Hacking during this discussion . In a paper published in 1987 he speaks out against design arguments as an explanation for fine-tuning, but believes he can show that not all types of universe ensembles can be used together with the anthropic principle as an explanation for fine-tuning. A multiverse , e.g. B. would consist of the ensemble of all possible Big Bang universes, would, according to Hacking, together with the anthropic principle, be a possible explanation for fine-tuning. Hacking, on the other hand, is of the opinion that assuming such an explanation would be a fallacy if one were to use so-called Wheeler universes (an infinite temporal sequence of universes in which each individual universe begins with a Big Bang and ends in a Big Crunch ). Although the explanation with the ensemble of all possible Big Bang universes is apparently similar to that with the Wheeler universes, in reality they are different, and in the latter case it is actually a reverse player fallacy. This view was contradicted by several authors independently of one another by emphasizing that there is no selective observation effect in the reverse player fallacy and the comparison with the reverse player fallacy is therefore also incorrect for explanations using Wheeler universes.

Roger White published a modified version of Hacking's Argument in 2000. Nick Bostrom has pointed out, however, that the assumptions from which White starts out do not apply to most of the multiverse theories actually proposed and, moreover, ultimately lead to implausible consequences. He therefore concludes that White's argument is invalid. Bostrom has also shown how the example given by Hacking, which leads to the reverse player fallacy, would have to be modified so that it would actually be comparable to the anthropic argument. In order to take selective observation effects into account, in Hacking's example with the dice game a player would have to wait outside the arcade until a double six was thrown. Under these modified conditions, the reverse player fallacy would no longer be a fallacy. Rather, under these conditions, if a player is allowed into the arcade after a double six has been thrown, he could actually correctly conclude that a more or less large number of throws has already taken place.

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  1. ^ I. Hacking: The Inverse Gambler's Fallacy: The Argument from Design. The Anthropic Principle Applied to Wheeler Universes. In: Mind 96, 1987, pp. 331-340. doi : 10.1093 / mind / XCVI.383.331 JSTOR 2254310
  2. ^ J. Leslie: No inverse gambler's fallacy in cosmology. In: Mind 97, 1988, pp. 269–272. doi : 10.1093 / mind / XCVII.386.269 JSTOR 2255172
  3. ^ PJ McGrath: The inverse gambler's fallacy - A Reply to Hacking. Mind 97, 1988, pp. 265-268. doi : 10.1093 / mind / XCVII.386.265 JSTOR 2255171
  4. ^ MAB Whitaker: On Hacking's criticism of the Wheeler anthropic principle. Mind 97, 1988, pp. 259-264. doi : 10.1093 / mind / XCVII.386.259 JSTOR 2255170
  5. ^ R. White: Fine-Tuning and Multiple Universes. In: Nous 34, 2000, pp. 260-276. doi : 10.1111 / 0029-4624.00210
  6. ^ N. Bostrom: Anthropic Bias, Observation Selection Effects in Science and Philosophy . Routledge, 2002, ISBN 0-415-93858-9