Hangman is a simple 1 player game of hangman verses a computer. The user chooses a number of letters for the word to have, and a number of guesses. The computer then random chooses a word, from a list of over 127,000 words. The user is then given the number of incorrect guesses they chose, to guess the word.
The birthday paradox is a probability problem about the number of people needed before there is a greater than 50% chance that 2 people will share the same birthday. More information can be found on the Birthday Paradox problem on the Wikipedia Birthday Paradox page.
Evil Hangman is a malicious form of the classic game of hangman. In evil hangman, users choose a word length and a number of guesses. However, unlike in hangman, the computer does not choose a word. Instead, the computer maintains a list of words. When the user chooses a letter, the computer refines its list, so that as many words as possible remain in the list of words, and the user either gets no information back, or very little. It is very difficult to beat the computer in a game of Evil Hangman. The strategy of Evil Hangman is very different, instead of guesses common letters, looking for word patters, you must guess letters so that the computer will eliminate words that contains those letters from its word list. More information can be found on Evil Hangman at the official Evil Hangman website.