The problem is that there are two 50-50 odds definitions. First one, is where you have no information about the event what so ever. Second is where you have i

The problem is that there are two 50-50 odds definitions. First one, is where you have no information about the event what so ever. Second is where you have information, and it turns out that the outcome is still 50-50. While the use of that information in planning (pricing things, betting, investing) is identical, they fundamentally represent 2 different sets of information.