I might be wrong here, but this is my understanding. You'll always be able to show a blue ball as the second ball after the first is drawn. So arguing that it

I might be wrong here, but this is my understanding. You'll always be able to show a blue ball as the second ball after the first is drawn. So arguing that it tells you something about the statistics of the state of the system after the first has been drawn is wrong. The chance that the first draw is blue is 50/50. The arguments that lead to 1/3 are trying to use the second event as a statistic for the state, however for that to be appropriate the problem would have to be phrased as: You draw one ball and set it aside, then draw another, if the second ball is red, you start the entire thing over, if it's blue, then you continue the experiment. Because otherwise the assumption that the second drawing can tell you the statistics of the underlying state is wrong. The question of the odds really boils down to, did we randomly pick a ball and observe it? And if so, what would have happened if we didn't observe what we specifically stated for this instance.