about probability theory

There was a post here on the subject of paradox and in the depth of comments my answer was lost. I would love to hear the opinion of the public - where I am wrong. I believe that there is no paradox, and here is the proof:
Assume without loss of generality that the player always chooses the first door. We draw a plate of layouts

player selection	one	one	one	one
opened door	2	2	3	3
a machine	3	one	2	one

In two cases out of 4, the car is just behind the door the player has chosen, i.e. with a probability of 50% after opening the first door, he wins, if he does not change his choice.

PS Thanks to everyone! Now I seem to understand ... however, I still somehow can not believe)