Randomness is a Matter of Information

http://wmbriggs.com/blog/?p=2227 ^ | William M. Briggs

[mattstat]

Acin and a colleague cobbled together ytterbium atoms to produce “true” randomness, by which they mean the results of an electron being “up” or “down” cannot be predicted skillfully using any information.

In their experiment, the information on the ytterbium atoms’ quantum (which means discrete!) state is not humanly accessible, so we can never do better than always guessing “up”.

Brain teaser for advanced readers. Acin’s experiment generates an “up” or “down”, each occurring half the time unpredictably. Why is guessing “up” every time better than switching guesses between “up” and “dow

[Liberty1970]

Regarding the brain teaser, I’d say that it is better to stick with ‘up’ because if you start switching, you are unlikely (unless you make a point of it) to equally select ‘up’ and ‘down’. If you make an unequal selection of up/down, then you’ll be likely to miss more than 50% of the time as a result. (I.e., if you choose ‘up’ 60% of the time and ‘down’ 40%, and there is really a 50/50 split in the results, you will do more poorly than someone who just stuck with ‘up’ on 100% of their choices.)

[Liberty1970]

OK, now I need to argue with myself: regardless the overall distribution of choices, each individual choice has a 50/50 chance of matching the result for each particular trial. So I’m not sure I see why it matters to stick with one result over randomly switching.

[mattstat]

You were right to be confused, because the teaser was misspecified. It should read:

Acin’s experiment generates an “up” or “down”, each occurring as they may. When is guessing “up” every time better than switching guesses between “up” and “down”?