Combine rye whiskey, dry vermouth, and pineapple juice in a cocktail shaker.
Fill the shaker with ice.
Shake vigorously for 10–12 seconds until well chilled.
Double-strain into a chilled cocktail glass.
Serve immediately, ungarnished.
The Algonquin was a favorite among the literary set of the 1920s Round Table; use a high-rye bottling like Rittenhouse or Pikesville to keep the spice assertive against the sweetness of the pineapple juice.
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