We'd like to address some concerns regarding the word "gambit." However, to do that, we're going to have to address the word "gamut" too.
That's because many of us have a tendency to say "run the gambit," when what we mean is "run the gamut."
Since these are both relatively rare words, it's not surprising that we sometimes get them confused. Learning their origin should help you keep them straight.
"Gambit" comes from the game of chess. It originally referred to a strategic move at the start of the game in which a player sacrifices one of their pieces, typically a pawn, in order to gain an advantage. You may have heard someone use "gambit" with "opening" as in, "That was my opening gambit." Some would argue that "opening" is redundant since, as discussed above, a "gambit" is an opening move. Over time, the meaning of "gambit" became more generalized. By the 19th century, it could refer to a remark designed to open or change the direction of a conversation. It could also refer to a plan used to gain advantage, such as a political gambit. "Gamut," on the other hand, is related to medieval music. It could refer to the lowest note on the musical scale, or it could mean the scale of notes expanding over two octaves and a sixth. Today, "gamut" has generalized to mean the full range or scope of something. For example, someone might say they've experienced the whole gamut of emotions. That means they've experienced everything from rock-bottom sadness to over-the-top elation. You might hear someone say something like, "I ran the whole gamut of emotions, from frustration to anger." People concerned about the "correct" use of "gamut," would argue that "frustration to anger" doesn't cover the whole range of emotions.