Randomizing with a coin

[BruceZ]

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Looking at it I think I now see the genius behind your statement, which on the surface was not apparent.

Do I understand this correctly?? :


The first head on the second (an even) flip is probability of 1/4, and on the fourth is thus 1/16 etc etc - and the sum of all possible probabilities here to infinity equals 1/3.

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Right. BTW, it turns out that your method is really the same as mine, as I show here (out for repairs - BZ), but only for 1/3.


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It's funny how un-intuitive it is (at least to me), but explained the elegance is sublime...

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It is easy to see that the first head is more likely to occur on an odd numbered flip when you realize that 1/2 of of the time it will occur on flip number 1.

[alThor]

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AlienBoy's system is correct, but it doesn't guarantee a decision in any finite number of flips.

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But does BruceZ's guarantee a decision in any finite number of flips either?

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Speaking of infinity, this is the part where we loop back to the OP. I believe that finishes the thread.