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Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Mon, 09 Nov 2009 00:24:36 UT

I am mistaken. Apology for the several useless posts from me.
M. K. Shen

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Mon, 09 Nov 2009 00:11:27 UT

If on the other hand one has two channels of capacity 1 instead,
then the chance of having both channels filled black is 1/4.
Is that right?
Thanks,
M. K. Shen

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 23:53:47 UT

I see in the meantime why my way of thinking is incorrect.
M. K. Shen

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 22:59:59 UT

Being layman, I am confused. Let's simplify the scenario so that
there is only one channel with capacity of 2 and there are four balls,
2 white and 2 black. What is the probability of 2 black balls getting
into the channel?
Thanks,
M. K. Shen

Re: Mechanical generation of random bit sequences

n...@dont-mail-me.com (Robert Scott) — Sun, 08 Nov 2009 21:31:49 UT

On Sun, 08 Nov 2009 23:13:52 +0100, Mok-Kong Shen <mok-kong.s...@t-online.de>
wrote:
The 100 balls have a similar flaw, just to a lesser degree. In a perfectly
random uncorrelated sequence of 50 bits, the probability that they are all 0 is
exactly 2^(-50). But when choosing 50 balls from 100, the probability that all

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 22:21:12 UT

Sorry, typo. Please read 50 for 100 above.
M. K. Shen

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 22:13:52 UT

Robert Scott schrieb:
No. The flaw with 50 balls is different. Note, for example, this:
In a random sequence there is a certain probability that in a
sequence of length 100 all bits may be 0, and this is not the
case with 50 balls in the device.
M. K. Shen

Re: Mechanical generation of random bit sequences

n...@dont-mail-me.com (Robert Scott) — Sun, 08 Nov 2009 21:06:57 UT

On Sun, 08 Nov 2009 22:06:46 +0100, Mok-Kong Shen <mok-kong.s...@t-online.de>
wrote:
Yes, the chance of any one ball being black or white is exactly 50%. But when
evaluating entropy, you also have to take into account the conditional
probabiltiy of a ball being a certain color given the knowledge of what other

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 21:06:46 UT

But you have to consider that the 100 balls are all competing to
enter the five channels. If the balls have been well mixed, the
chance of a white ball or a black ball entering a channel is the
same, isn't it?
M. K. Shen

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 21:02:02 UT

But the problem is that no such devices are available on the market
for a normal user to buy and to use (hopefully without difficulties by
a layman).
M. K. Shen

Re: Mechanical generation of random bit sequences

n...@dont-mail-me.com (Robert Scott) — Sun, 08 Nov 2009 19:45:49 UT

On Sun, 08 Nov 2009 20:43:10 +0100, Mok-Kong Shen <mok-kong.s...@t-online.de>
wrote:
Imagine betting on color of the last ball. If you really had 50 bits of
entropy, then seeing the first 49 balls gives you no advantage in betting on the
color of the 50th ball. But suppose I see the first 49 balls and they are 40

Re: Mechanical generation of random bit sequences

mok-kong.s...@t-online.de (Mok-Kong Shen) — Sun, 08 Nov 2009 19:43:10 UT

[snip]
Could you please explain why?
Thanks,
M. K. Shen

Re: Mechanical generation of random bit sequences

n...@dont-mail-me.com (Robert Scott) — Sun, 08 Nov 2009 15:11:57 UT

The electronic systems are not trivial to build properly either. A device that
senses thermal noise in resistors is also likely to be affected by power line
interference or EMI, which degrades entropy.
Regardless of which system is used to generate raw random data (mechanical or
electronic), the entropy can be improved by oversampling the raw data and