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1.
a finger of beer refers to a small amount of beer consumed in one action from a glass bottle.

imagine your holding a bottle of beer, with your fingers gripping round it, a finger of beer is the amount that needs to be consumed in order to reduce the level of the beer in the bottle by one fingers width lower.

it basically just means drink a mouth full of beer.
''every time David Cameron says 'big society' in Prime Ministers question time, you've gotta drink a finger''
by maiablues July 27, 2012