Suppose letters are chosen randomly from the alphabet, one at a time. It is well known that the expected time until ABRACADABRA is spelled out is $26^{11}+26^{4}+26$. The proof uses discrete time martingale theory.
Is there any way to compute or approximate tightly the probability that ABRACADABRA occurs before another chain of letters, such as ABCDEFGHIJK or RACECAR?
These sorts of problems seem subtle and perhaps unrelated to the waiting time problem. For example, when flipping a coin many times in a row, TTH and HTT have the same expected waiting time, but the HTT occurs before THH with probability 3/4.