Can we use the must have with 'I guess' for the past actions?
Example: I guess you must have watched that video twice.
Is 'I guess' valid here or should we replace it with 'I believe'?.
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Yes, it's perfectly normal to use "I guess" with "must have". The former indicates that you are expressing a loosely-held personal opinion ("to form an opinion of from little or no evidence" according to Merriam-Webster): the latter indicates that the opinion concerns something that, based on the available evidence (which may be scant, especially if used with "I guess"), probably happened in the past.
“This his day off?”
“No. I guess he must have called in sick or something.” Fair Game- B.W. Battin
I guess is informal US english: You could also use I suppose, which is common in British and American english. I believe is also possible, but it sounds quite formal in both American and British english. This NGRAM shows the relative frequencies of use.
You can certainly say I guess in this situation. The only thing to worry about is what exactly you're trying to say with that statement. We use the construction must have when we have a pretty strong reason or evidence to believe that something is true, but we're not one hundred percent sure whether it's actually true. For instance:
It's funny that you remember so much. Ha ha. I guess you must have watched that stupid video twice.
Here, the fact that the person I'm talking to remembers so much from the video suggests that they might have watched the video not just once, but twice. Although we're not one hundred percent sure whether that's true, what we can gather from the available evidence allows us to come up with a pretty good guess that it may in fact be true that they watched the video not just one time, but two times. So, I guess, in this particular case, actually sounds like a better choice of words than I believe.
I believe is very similar to the expression I think, to the point that in everyday conversation they can be sometimes used interchangeably. When you say that you think or believe that something is true, it's not a wild guess. Quite the contrary, there is an element of certainty in what you're saying. That's why I believe wouldn't work as well as I guess in this situation.
To sum things up, a lot depends on context. The devil is in the details, as they say. You just always need to be a little bit more precise with whatever it is that you're trying to say.
Using "I guess" implies a certain percentage of possibility whereupon with "must have" it refers to the possibility of a probability.