: Why does this chord progression work? I feel like I've heard it before but can't find the pattern I had this song stuck in my head all day and tried to play by ear the section that starts around 1:40 on the guitar. If I'm

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Lasomiso,latidore,misoso... a,g,e,g, a,b,c,d, e,g,g ...
The tune is in the aeolian mode and your analysis is correct (chords and R.N.) why it works? For the same reason that any other progression works. Why shouldn’t C,dm,em not work? Why works I IV V I or I vi ii V? These are all degrees and triads of a same key and mode. They work.

Edit:

Of course G (VII of am) is the dominant chord (V) of C and we can say the refrain is an extension from am to the relative key C ... but the following guitar solo is again in am (aeolian) so if you find a RN analysis in C that works, also the analysis in Am will work. The point why it works has been worked out by piiperi.

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I think "Why does this chord progression work" is a bit misguided question to begin with. I guess you're really asking for ways to see the chords so that you can relate their functions here to other chord progressions and songs you're familiar with.

Albrecht already basically said it - why does anything "work", the chords are triads built on scale degrees and they often just work. It's more like, it's harder to come up with a combination of those blocks that does not work at all and cannot be used in any sensible melody. But I'll try a different approach.

The "I II III" etc. Roman numerals system is one way to analyze chord progressions, but sometimes if the song lingers ambivalently somewhere between related minor and major keys, it might not be the most intuitive choice. Another way is to look at the chords built on scale degrees as interleaved minor and major keys. The keys are so closely related, they're like siamese twins, "major side" and "minor side". Take C major and A minor for example.

C : major side tonic
Dm : minor side subdominant
Em (or E7) : minor side dominant
F : major side subdominant
G (or G7) : major side dominant
Am : minor side tonic
Bdim : dual-function chord, can work as both the major side G7 or minor side Dm

Ok. The chord progression in your original question is:

| Am | C | G | Am G | (repeat)

Let's transform it to this:

| C | G | Em | Am G | (repeat)

In this modified version we can see that it's divided between major side C - G and minor side Em - Am. And then the glue chord G at the end which steps from the minor side back to the major side.

In the original, the major and minor sides are just intertwined more tightly.

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If you analyse the chords as if the song were C major (the relative major), it would read as:

|Am / / / |C / / / |G / / / |Am / G / |
|vi / / / |I / / / |V / / / |vi / V / |

(as opposed to being in Am):

|Am / / / |C / / / |G / / / |Am / G / |
|i / / / |III / / / |VII / / / |i / VII / |

Looking at this, it is obvious why the progression works - it uses some of the strongest chords in the relative major scale, I, V and vi. The fact that the tonal centre is Am rather than C doesn't change how strong the chords are in relation to the relative major.

In pop/rock music, the most important-sounding chords in a minor song are often [i, III, VI, VII], because these are the equivalent of [vi, I, IV, V] in the relative major. Obviously "important-sounding" is subjective but this is at least the trend in modern pop/rock.