the two envelopes puzzle

Thanks for the video. Your math seems correct to me. The first part is also clear. However, in the last part of the video, the player(s) know more than in the original paradox when you describe how they get either x/2 or 2x in their envelope. Only in the case they find x in the envelope, do they not have extra information. In the original puzzle they would never know that they should either always switch or never switch, in certain situations. All a player knows when he peeks inside his envelope and finds $y, is that the other envelope can contain either $y/2 or $2y. And calculating from there, assuming either situation would be equally likely, one gets back to the idea that the other envelope contains $5y/4, so always switch.