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For a project we did a small survey, one of the questions was about the following scenario.
Last week the lottery was won by a ticket with the numbers x x x, this week you can make one choice. Pick a ticket with the numbers from last week or pick one that is different.
More then 95% of the persons we asked answered they took different numbers as reasoning they give that its unlikely that the same numbers win in a row.
Mathematically it has the same odds but why are we not seeing this as logic?
It is a variation of a classical fallacy:
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future. It may also be stated as the belief that, if something happens less frequently than normal during a given period, it will happen more frequently in the future. (Source: WikiPedia)
The fact that the number was advertised as having been a winning number makes it salient to the respondent, just as if it would have won multiple times in a row. So, judging through the fallacy above, the number is less likely to win again.
We rarely judge mathematically or logically if we are not prompted or educated to do so, we rely judgements on heuristics instead.
The mathematical calculation of probability as an independent event will be the same but while people will make a decision it is influenced by past memory. It is day to day experience of people that in a random event it is highly unlikely and almost imposssible for same numbers to come in a lottery.
Here people will calculate the odds as dependent event. So that is not the logic or is the logic whichever way you put it.
