When is a reaction reversible?
"Reversible" is not binary.  Both the forward and backward reactions always occur and the equilibrium system never has zero reactants or zero products.  Thus, irreversible reactions are called this not because they cannot be reversed - they absolutely can - but because reversal is impractical.  The equilibrium constant may be so skewed toward product that the reactant quantities at equilibrium would be undetectable.  The products may be gases that escape solid reactants, which ensures that the system never reaches equilibrium in the open anyway.  There may be a lot of side reactions on the products.

A "reversible" reaction just lacks factors like this so that we can have measurable quantities of reactant beside measurable quantities of product at equilibrium.  We add some reactant, watch the reaction go forward.  We add some product, it goes in reverse.  See?  It's reversible.  There is no exact cutoff in any measure.