[AndrewC]

It's 2/Pi. ... What has this to do with complexity?

Yes it is 2/pi, but you can take that and divide it into one and multiply by two and bingo you have pi. Which you said is not complex. You have a contradiction.

Probability of deterministic mechanisms yielding complexity = 0.00.

Probablity of random mechanisms yielding complexity = 1.00.

[Ichneumon]

[Someone, I forget who, wrote:] Probability of deterministic mechanisms yielding complexity = 0.00. Probablity of random mechanisms yielding complexity = 1.00.

Alert:

[Doctor Stochastic]

Wrong, there's no contradiction. You are exhibiting a typical misunderstanding of complexity. Complexity applies to strings, not to constants.

2/Pi is the probability of getting a crossing. It need not be complex anymore than the probability of getting heads or tails is complex. It's just a number.

The sequence of crossings (or non-crossings) in a large number of throws may be complex. Any deterministic description of such a sequence (such as alternating crosses and misses) is non-complex. Only a randomly generated sequence can yield complexity.