The 'paradox' that is presented leads back to the right conclusion: there is no way to inform which envelope is better so just pick one at random. These are no

The 'paradox' that is presented leads back to the right conclusion: there is no way to inform which envelope is better so just pick one at random. These are non-causal random events, and the probability is always 50/50. There is a twist to this problem, which is more interesting, where you open the first envelope, then decide whether or not to switch to the second envelope. Believe it or not, there is a trick to beating 50% in this variant. I'm too tired to try to fully explain it, but this conclusion comes from the fact that once you look at an envelope that presents information that can be used for deciding to switch. So it becomes a causal system that does not follow a random probability density function. But think: if the envelope you opened had $7 million dollars in it, you probably wouldn't and shouldn't switch, and you'd probably be able to skew the odds in your favor on scenarios like this.