Do reviews actually affect where you rank?
They contribute, but not as directly as most owners assume. Google names prominence as one of three factors alongside relevance and proximity, and reviews are one input into prominence.
The version of this that gets repeated — more reviews equals higher ranking — is too simple to act on. Proximity to the searcher is a heavy factor in the map pack and you cannot change your address. Relevance comes largely from your categories and your website. Reviews sit inside the third factor, prominence, along with everything else that suggests a business is well known.
What that means practically: a business with forty honest reviews and the wrong primary category will usually lose to one with twelve reviews and the right one. Fix the category first. Reviews compound quietly underneath it, and they do far more work on the conversion side — the person choosing between three map results is reading them.
If you have not looked at how the map pack is actually decided, start there. It explains which of the three factors you can move and which you cannot.