An opening move involving sacrifice in any game is a gambit. Any gambit is an opening more; not all opening moves are gambits.
A gamut is a contiguous series like a scale of notes. One does not run a gamut. That’s run a gantlet but now gauntlet.
Gauntlet refers to the knight’s battle-glove that was thrown down to indicate the desire to challenge another knight. When someone was forced to run between two lines of men with blunt weapons as a punishment, it used to be called running a gantlet, but the spelling is now gauntlet.
A gantlet is a stretch of railroad tracks that overlap but are not connected by connecting turnouts (called switches on this side of the pond; but that can be confused with electrical switches).