1
general::
An expression used when tossing a coin to decide between two alternatives, as in Let's just flip a coin to decide who pays? do you want heads or tails? Each person involved chooses a different side of the coin, either "heads" or "tails," and whichever side lands facing up is considered the winner. This usage, dating from the late 1600s, is sometimes turned into Heads I win, tails you lose, meaning "I win no matter what," which probably originated in an attempt to deceive someone. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): heads or tails
the face of a coin or the other side of a coin. (Often used in an act of coin tossing, where one circumstance is valid if the front of a coin appears and another circumstance is valid if the other side appears.) • Jim looked at Jane as he flipped the coin into the air. "Heads or tails?" he asked. • It doesn’t matter whether the result of the toss is heads or tails. I won’t like the outcome in any case.
McGrawhill's American Idioms And Phrasal Verbs