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If 1 liter equals 33.814 ounces, then 1.75 liters is the same as 59.1745 ounces. Divide that by 1.5 and you’ve got a total of 40 shots. Good thing Joe has tons of friends because 40 shots is a lot.
Since shot size isn't mandated in the U.S., the question—How many shots are in a handle of vodka?—is more nuanced than you think.
It's perhaps more common to ask, How many shots in a handle of vodka? since the clear spirit is the most ubiquitously found in handles. How Many Ounces Are in a 1.75L Bottle?