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201 sats \ 7 replies \ @Undisciplined 7 Oct 2024 \ parent \ on: [Daily puzzle] Probability of ending at 1 science
I'm leaning towards this answer. It holds for 0.25, 0.5, and 0.75.
10 million random runs for some x between 0.0 and 1.0
x=0.000 p=0.0000
x=0.050 p=0.0499
x=0.100 p=0.0999
x=0.150 p=0.1499
x=0.200 p=0.2001
x=0.250 p=0.2500
x=0.300 p=0.2999
x=0.350 p=0.3499
x=0.400 p=0.4000
x=0.450 p=0.4501
x=0.500 p=0.5001
x=0.550 p=0.5501
x=0.600 p=0.5999
x=0.650 p=0.6498
x=0.700 p=0.7001
x=0.750 p=0.7498
x=0.800 p=0.7999
x=0.850 p=0.8500
x=0.900 p=0.8998
x=0.950 p=0.9501
x=1.000 p=1.0000
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Careful there, Faketoshi might not be able to understand your code snippet there, using unsigned integers (I presume that's what they are, I am not proficient in cpp)~~
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c, not c++
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Well, that's one way of proving it :)
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Yes, it is $x$.
Now, can one prove it?
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I'm sure someone can, but probably not me. I don't have any clever ideas for how to extend the case-based reasoning I was using and I certainly don't have time to do all the cases.
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Well, you correctly answered the initial question, so you did what was asked. I should have been clearer in asking for a formal proof.
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