Horsengoggle (also known as horse-and-goggle and horse 'n' goggle and hossengoggle) is a method of selecting a random person from a group.
Unlike some other methods, such as rock paper scissors, one of the features of horsengoggle is that there is always a winner; it is impossible to tie.
An arbitrary member of the group is selected by the leader as a starting point.
[2] In his memoir of growing up in Missouri in the 1940s, Jim Frank mentions the game as "ein [sic], zwei, drei, horsengoggle", which he describes as "an old German system of selection".
[4] Even though the game always results in a winner, Horsengoggle is not always completely fair unless the starting point is selected totally at random.
However, the difference in probability between the participants is approximately one or two percent for any reasonable n. We can prove the fairness assertion as follows: In order to more simply translate Horsengoggle to dice rolls, we can treat the problem as if the players are choosing between one and six fingers.
If every player is employing optimal strategy to win, showing bias towards any number would only allow opponents to take advantage of that unequal distribution.
In the case of n = 2, the set of all possible dice sums can be expressed in the table below: If we begin counting with the starting point being zero, all even totals will result in the starting point as the winner and all odd totals will result in the other player as the winner.