The centipede game is one of the clearest examples of the paradox of backward induction. Such paradox happens when, in a sequential game, the unique perfect Nash equilibrium prediction implies a very counterintuitive play. Experimental tests of the centipede games confirm this contradiction: individuals do not follow the subgame perfect equilibrium prediction. Previous researchers have used examples of the centipede game to give possible explanations to the behavior of people in order to solve the paradox, but they only have applied it with very particular variations of the centipede game, and without providing an exhaustive analysis of the game. This paper revisits the centipede game. First, we propose a definition of the game. Second, we show that the payoffs can allow for increasing, decreasing or constant pattern over the sequential nodes. Third, we sow the subgame perfect equilibrium prediction and other alternative solutions. Fourth, we propose how the different payoff patterns can be exploited in order to distinguish between alternative models that have been proposed in order to explain the non-equilibrium behavior observed in the laboratory.