A gage is an instrument for measuring, like the gas gage in your car that tells you it's time to fill 'er up. It's also spelled "gauge."
As a verb, to gage is to place a bet. As a noun, it's something thrown down, like a glove you chuck at someone and challenge them to a duel. As a way of measuring, a gage can refer to the thickness of a needle or a shotgun. You don't need an instrument, though, you might gage how much time you have left outside by looking at the sun. Sticklers use gauge for measuring and gage for duels and bets.