I read that Mikhail Tal claimed to have been able to see 50 variations ahead in a game. Any thoughts on this possibility? Mikhail Tals' books on chess. Learning/analytic chess theory. Perception and intuition in the development of strategic and tactical chess play.
Note that "number of moves ahead" is not necessarily a great proxy for "number of positions considered". An open board with no impending threats has many possibilities of what might be the "best" move, and will require a player to analyze a wide, but shallow tree of possibilities. A board with few pieces and many threats has relatively few "good" (or even legal) moves, so a player can look farther ahead down a narrow but deep tree of possibilities. In some cases, the tree becomes a path - there is only one move to make. This question, for example, shows games with many repeated checks, making the tree of potential moves very narrow indeed.

It seems that most high-level chess players tend to think 20-40 moves ahead, depending on the board state. It's not unreasonable to think that someone could think 50 moves ahead in very particular situations, where the next few moves are "obvious" or even forced. But to be able to consider 50 moves ahead in all possible situations is likely beyond a human's ability.