  In the extended gambler's ruin problem we can move one step forward or
backward (classical gambler's ruin problem), we can stay where we are for a
time unit (delayed action) or there can be absorption in the current state
(game is terminated without reaching an absorbing barrier). We obtain
absorption probabilities, probabilities for maximum and minimum values of the
ruin problem, expected time until absorption and the value of the game. We also
investigate asymptotic behavior of absorption probabilities and expected time
until absorption. We introduce a conjugate version of our random walk.
