Cocktail Mathematics

Published books and smart device applications offer cocktail collections, some 500, some 5,000, some more than 10,000 individual recipes.  Trying even a fraction of these would be — fun, interesting, expensive, decadent, mind-altering — you choose.  But just theoretically, how many different cocktail recipes do you suppose there could be?  Let’s work it out.

Set these bottles before you: vodka, gin, rum, tequila, cognac, brandy, and six kinds of whiskey: American, Irish, Scotch, Canadian, bourbon, and rye.  That’s a dozen bottles; pick one and pour some into a glass.

What can you add to it?  Common mixers are water, soda, fruit juice or syrup, coffee, milk or cream, sugar, egg white or yolk, wine, liqueur, or another liquor — ten general possibilities.  That gives 12 * 10 = 120 combinations.  Why stop with two ingredients?  Adding another mixer yields 120 * 9 (9 because one mixer was already used) = 1,080 more combinations.  A fourth ingredient adds 1,080 * 8 = 8,640 more, for a total of 120 + 1,080 + 8, 640 = 9,840 different possible recipes.

But are these the right numbers?  There are at least 40 flavors of vodka (new ones being added every few minutes), 20 of rum, a dozen of tequila, and various flavored brandies and whiskeys as well.  So instead of a dozen bottles sitting before you, it’s more like 100.

Varieties of mixers include about 10 kinds of soda, a dozen fruit juices or syrups, easily 325 different kinds of liqueur, plus 99 bottles of liquor still on the wall, bringing the number of possible mixers to around 450.

Thus the possible combinations of one spirit and one mixer are 100 * 450 = 45,000, two mixers are 45,000 * 449 = 20,205,000, and three mixers are 20,20,000 * 448 = just a shade over nine trillion.  This is further complicated, of course, by the many different brands of the same thing, and because there’s no rule saying you have to stop at four ingredients.  Thus with up to 10,000 recipes documented so far, it is very likely an undiscovered Margarita or Manhattan or Rusty Nail is still lurking out there waiting to be found.  So much to do….

Legions of bartenders have explored this rich array of possibilities since the early 1800s.  Ingredients have improved in quality and variety in that time and rudimentary drinks have become more refined.  Experimental variations on existing recipes have produced new and more elegant cocktails.  The 500 or 5,000 or 10,000 drink recipes available today are a product of building on what has proven successful.  It’s evolution at its best.

HOW COCKTAILS EVOLVE:  It started with a shot of vodka.  Someone added orange juice and called it a Screwdriver.  Someone added Creme de Banana to that and called it a Boston Gold.  Then someone added Peach Schnapps to that and called it a Fuzzy Monkey.

So, should you find a list of recipes and work your way through it?  Should you sit at a bar for days and days and order drinks with catchy names?  Should you stick to the one drink you like and never stray toward something new?  Here’s a suggestion.

The International Bartenders Association offers a list of 77 cocktails on its website.  These test-of-time classics borne of more than 200 years of experimentation are grouped as The Unforgettables, Contemporary Classics, and New Era Drinks and recipes are included.  If you seek to expand your horizons, start there.