Chance vs Randomness

Is the Commonplace Thesis

Something is random iff it happens by chance.

correct?

It is hard to define chance, but randomness has a good definition in terms of Kolmogorov/Martin-Lof randomness, thus we may refine the Commonplace Thesis into:

• (A) A sequence of outcomes happens by chance iff that sequence is random.
• (B) An outcome happens by chance iff there is a random sequence of outcomes including it.
• (R) An outcome happens by chance iff, were the trial which generated that outcome repeated often enough under the same conditions, a random sequence including the outcome will obtain.

If it is not. Then

• Random occurances still may be explained.
• No statistical inferences on the basis of randomly sampling a large population will be valid.
• Frequentist approach to objective probability will fail.

There is already some pressure on the Commonplace Thesis: it is now widely accepted that probabilistic explanation is legitimate, random sampling doesn't need genuine chance, and that frequentism is in serious trouble.