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1.
In Texas hold'em poker, having 2-7 offsuit in the hole, although some consider the 2-7 suited to be a beer hand as well. So-called because when dealt, it's "time for a beer."
Some donkey cracked my pocket rockets with the beer hand last Sunday. I was so pissed off.
by Patrick Templeton June 16, 2008
 
2.
when your hand is wet and cold from holding a beer can or another cold drink
I'd shake hands with you, but I've got beer hands.
by lanky9 November 13, 2009