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In Mijnlieff the second player has an advantage. I have been experiencing being the starting player too often. After completing the Berserker, 50 wins in a row, I counted how often I started the match. I started 34 times and only had 16 times the advantage of being the second player. The chance of this happening by chance is much smaller than 1%. Can the starting player be chosen randomly?

It's not "much smaller than 1%". The probability of at least 34 times being 1st or 34 times being second in 50 consecutive games is 1.534% (https://www.omnicalculator.com/statisti ... robability). Even the probability of "exactly 34 times being second" is not much smaller, it's 0.4373%.

Hi Jellby, Thank you for checking things. Yes you are right. From my perspective it was a one sided distribution. In that case it was 0.77%. But I accept to calculate a two sided distribution. Let me calculate the last hundred matches. I have no time now but I am sure I have to start too often.

To be rigorous, you have to define your "event" beforehand, and not go back and check probabilities after you've seen something "unexpected" happening. So, instead of checking your last 100 games, check your next 50 or 100 games. And make sure you don't have any rematches in the sequence, rematches may have swapped starting order and not random.

The problem is that by counting we can never prove that the starting player is not chosen randomly.