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Put a mixing glass and a coupe glass into the freezer to become completely cold. Chill them for at least 15 minutes or leave them to chill for several hours. If you prefer to shake the martini, chill a cocktail shaker instead of the mixing glass. Remove the mixing glass from the freezer and fill it up with ice. Measure and pour in 1.3 ounces (40 ml) of dry gin and 1.3 ounces (40 ml) of dry vermouth. Use a long-handled bar spoon to stir the martini until the cocktail is combined and very cold. This should take 15 seconds. You can shake the martini for 15 seconds, if you prefer. Remove the chilled coupe glass from the freezer and set a strainer over the mixing glass. Pour the millionaire martini into the coupe glass and discard the ice in the mixing glass. Open a bottle of champagne and pour it over the martini in the coupe glass. Slowly pour enough champagne to fill the glass. Serve the drink immediately. The amount of champagne you'll need depends on the size of your coupe glass. If you want to use a martini glass or champagne flute, you'll probably use more champagne.
Chill a mixing glass and coupe glass for at least 15 minutes. Fill the mixing glass with ice and add the dry gin and dry vermouth. Stir the martini for 15 seconds. Strain the martini into the coupe glass. Top off the glass with champagne and serve the martini.