meaning - Guess, second-guess, and higher-order guesses

I'm having a hard time understanding the difference between guess and second-guess.

From Merriam-Webster's:

guess means
1: to form an opinion of from little or no evidence
2: believe, suppose
3: to arrive at a correct conclusion about by conjecture, chance, or intuition

and

second-guess means
1: to criticize or question actions or decisions of (someone) often
after the results of those actions or decisions are known; also: to engage in such criticism of (an action or

decision)
2: to seek to
anticipate or predict

What's the difference between "to seek to anticipate or predict" and "to arrive at a correct conclusion about (a future event) by conjecture, chance, or intuition"? If there's not much difference, why prefix "guess" by "second-"?

Or if the prefix "second-" indicates some kind of "theory-of-mind", then would the word "third-guess" be understood as "to seek to anticipate the anticipation of a person A by another person B", and similarly for higher order guesses?

Answer

The definition I'm more familiar with, and the one listed first by ODO is:

second-guess [WITH OBJECT]

1 Anticipate or predict (someone’s [or some body's] actions or
thoughts) by guesswork:
he had to second-guess what the environmental regulations would be in five years' time

This restricts the guessing to what others are considering doing / going to do.

I'm not sure that M-W is correct in not adding this restriction; certainly I'd only use 'second-guess' in the way OALD defines it. The criticism sense is largely American.