The choice of aged or spiced rum adds depth and complexity to the cocktail. The dry vermouth adds a dry and slightly herbal quality, while the pineapple juice contributes a tropical and fruity note. Shake the ingredients together to ensure they are well-mixed and chilled. The garnish of a lemon twist or pineapple wedge adds a visual element and enhances the overall presentation. Sip on an Algonquin rum cocktail and enjoy its unique combination of flavors.