Place an old-fashioned glass or any of your favourite cocktail glass in refrigerator until chill thoroughly.
Meanwhile, take a cocktail shaker and fill half of it with ice cubes or crushed ice.
Now, pour 1 1/2 oz of rye whiskey, 3/4 oz of dry vermouth and 3/4 oz of pineapple juice into your cocktail shaker. You can make your own fresh pineapple juice or you can use the ready-made packet juice as well.
Cover the lid of the cocktail shaker properly and shake it vigorously for few seconds until all ingredients mix properly.
Gently strain the Algonquin Cocktail into your pre-chilled cocktail glass. Garnish it with a fresh wedge of a pineapple and place a stick into the glass with a cherry on it.
Your Algonquin Cocktail is ready to serve, enjoy it.