A gambit is a calculated move or strategy, often one that risks something small at the start for an advantage later, as in a chess gambit. A gamut is a complete range, such as the gamut of colours a screen can show. If you are describing a tactic, reach for gambit; if you are describing a full spread of options, reach for gamut.
The core difference
Gambit is a strategic move or opening; gamut is a full range or spectrum.
- gambit — a calculated move or opening tactic, often with an initial sacrifice: Cutting prices for the first month was a gambit to win over new customers.
- gamut — a complete range: The exhibition ran the gamut from watercolours to sculpture.
How to tell them apart
Gambit comes from chess, where a player gives up a pawn or piece early on to gain a stronger position later, so it always implies a plan with a bit of risk built in. Gamut comes from music, originally naming the lowest note of a scale before it grew to mean the whole scale, and eventually any complete range.
The two are commonly confused in the set phrase "run the gamut," which people sometimes miswrite as "run the gambit." If the sentence is about covering every option from one end to the other, it needs gamut, not gambit.