Similar constructions can be use to build honest virtual dice, etc.

I rather liked Against the Gods.

]]>Well put. Though I wonder if it ever makes sense to say that a coin has a “true” probability of landing on heads, as in some immutable property of the coin itself. It seems like the information we gain lets us make limited inferences about that coin tossed in a particular way over a particular period of time (obviously a coin will change slowly). ]]>

There is no way to determine the bias or the true probabilty of ANY event without performing the experiment or event a sufficient enough time that you can get the sample size up high enough to get the confidence interval narrowed down.

But once you’ve established a good estimate of the true probability of the biased coin (60% heads for example) then it IS true that the coin has no memory. You might flip a coin 10 times and get heads 10 times, and on flip 11 you will STILL have a 60% chance of getting heads. This is no different than the theoretical case where you have an unbiased coin, and flip it 10 times and get heads 10 times. The only difference is that your odds of the next head is 50% instead of 60%.

Basically, it should be rephrased that any random number generator has no memory of its past history. BUT every throw gets you closer to knowing what the true probability of an event is. Everything only breaks down when you assume that the theoretical concept of a perfect random number generator actually exists in the real world.

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