> I wonder how the situation changes if 2 times repetitions would count as pattern
I might be misunderstanding, but do you mean that you cannot even have two of the same colour in a row? This is a very simple win for first player:
W B W ?
I might be misunderstanding, but do you mean that you cannot even have two of the same colour in a row? This is a very simple win for first player:
W B W ?
0 1 0 2 0 1 2 0 1 0 2 0 2 1
On p.2 they follow my idea of adding the lowest possible letter at the end, although they generalise it to adding the letter as close to the end as possible. They conjecture that this process does not stop. I'm always amazed with combinatorics how quickly you arrive at questions that no one knows the answer to.