History
"The origins of Hangman are obscure, but it seems to have arisen in Victorian times," says Tony Augarde, author of "The Oxford Guide to Word Games" (Oxford University Press).
The game is mentioned in Alice Bertha Gomme's "Traditional Games" in 1894 under the name "Birds, Beasts and Fishes." The rules are simple; a player writes down the first and last letters of a word for an animal, and the other player guesses the letters in between.
In other sources the game is called "Gallows", "The Game of Hangin'", or "Hanger".
Strategy
In the English language, the 12 most commonly occurring letters are, in descending order: e-t-a-o-i-n-s-h-r-d-l-u. This and other letter-frequency lists are used by the guessing player to increase the odds when it is their turn to guess.
On the other hand, the same lists can be used by the hangman (the non-guessing player) to stump his/her opponent by choosing a difficult word to guess (e.g. rhythm) or one that contains rare letters (e.g. quartz).