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Arctic sea ice has decreased substantially over recent decades, a trend projected to continue. Shrinking ice reduces surface albedo, leading to greater surface solar absorption, thus amplifying warming and driving further melt. This sea-ice albedo feedback (SIAF) is a key driver of Arctic climate change and an important uncertainty source in climate model projections. Using an ensemble of models, we demonstrate an emergent relationship between future SIAF and an observable version of SIAF in the current climate's seasonal cycle. This relationship is robust in constraining SIAF over the coming decades (Pearson's r = 0.76), and then it degrades. The degradation occurs because some models begin producing ice-free conditions, signalling a transition to a new ice regime. The relationship is strengthened when models with unrealistically thin historical ice are excluded. Because of this tight relationship, reducing model errors in the current climate's seasonal SIAF and ice thickness can narrow SIAF spread under climate change.