This is a strategy I came up with in 2005 that could achieve a sub 1:27 time (which was then a world record). The only randomness is having him go into the "ear rub" pattern in phase 2 after the 2nd hook. There is precisely a 25% (1/4) chance of him going into this pattern.
While this strategy is possible in real time this movie is Tool-assisted and represents a frame perfect version of this strategy. It achieves a 1:25.61 time.