E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Heads or Tails.
Guess whether the coin tossed up will come down with headside uppermost or not. The side not bearing the head has various devices, sometimes Britannia, sometimes George and the Dragon, sometimes a harp, sometimes the royal arms, sometimes an inscription, etc. These devices are all included in the word tail, meaning opposite to the head. The ancient Romans used to play this game, but said, Heads or ships.
Cum pueri denarios in sublime jactantes, capita aut navia, lusu teste vetustatis exclamant.Macrobius Saturnalia, i. 7.
Neither head nor tail. Nothing consistent. I can make neither head nor tail of what you say, i.e. I cannot bolt the matter to the bran.