So a co-worker was talking about someone’s stupid plan to always play the previous winning lotto numbers. I chimed in that I was pretty sure that didn’t actually hurt their odds. They thought I was crazy, pointing out that probably no lottery ever rolled the same five-six winning numbers twice in a row.
I seem to remember that I am correct, any sequence of numbers has the same odds. But I was totally unable to articulate how that could be. Can someone help me out? It does really seem like the person using this method would be at a serious disadvantage.
Edit: I get it, and I’m not gonna think about balls anymore today.
In: Mathematics
This is the [Gambler’s Fallacy.](https://www.investopedia.com/terms/g/gamblersfallacy.asp#:~:text=The%20gambler’s%20fallacy%2C%20also%20known,event%20or%20series%20of%20events.)
The odds of any specific number from 1-10 being drawn are one in ten every time. The odds of a 7 being drawn after a seven are therefore one in ten. BUT the odds of two sevens being drawn in a row before either of them are drawn is actually 1 in 100. People conflate the odds of the whole series occurring with the odds of just the next step in the series occurring, which creates this fallacy.
Just to put a point on it: If you flip a coin 1,000 times, the odds of what it lands on the thousandth time are not affected by what happened in all of the previous flips. Even if the previous 999 were all heads.
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