> if I flip a coin, I know exactly the odds of getting heads, but I don't know whether I will get heads unless I can exactly predict the future state of the wor

> if I flip a coin, I know exactly the odds of getting heads, but I don't know whether I will get heads unless I can exactly predict the future state of the world. No, that is a fundamental misunderstanding of what odds are. Odds are not a property of a system, odds are a description of your knowledge about that system. There is no such thing as "odds of the system", the odds for the same system can be vastly different for different observers. If you know how to control the coin, then the odds for you are almost 1:0 for your intended face. For the person next to you who doesn't know you, it's probably 0.5:0.5. For the person that has watched you for a while, it might be 0.6:0.4, if that's the ratio of the faces that you flip (intentionally). All for the exact same system at the exact same moment. Also, a binary distinction between "having no clue" and "perfect predictions" is not useful. While perfect predictions are the limit of an ever refined model, there are many steps in between a useless model that gives random predictions and a model that makes no mistakes whatsoever.