[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.

[AndrewC]

Wrong, there's no contradiction. You are exhibiting a typical misunderstanding of complexity

No. I used your definitions. You stated random mechanisms always yield complexity. A random mechanism yielded pi which you said was not complex.

The sequence of crossings (or non-crossings) in a large number of throws may be complex.

That "probability" does not equal one then.

Only a randomly generated sequence can yield complexity.

How many times do I have to flip a coin..... Oh never mind the "probability" is still not one.