I made a Markovian walk through my day. That is, I took a random path through the locales I intended to visit, and the process I used to determine that path will had the Markov property. A stochastic process has the Markov property if the next value is only conditioned on the previous value, and not on any of the other values preceding it. On this walk through my day, this means that the probability distribution over my next possible destinations depends only on where I am, and is independent of where I've been earlier. Each roll to determine where to go next destroys all influence where I've been previously will have on where I will go in the future.

To keep things simple I'm using a stationary Markov chain to choose my path. The transition probabilities are presented below. The rows have the current state, while the columns have possible next states. Each cell is the probability of going to that next state (labeled at the top of the column) given that I'm in the current state (labeled at the beginning of the row), along with the range of numbers on a roll of a 10 sided die that would produce that result. Thus, the probabilities across each row sum to 1.



I start off in the garage. Notice that the bar is a stopping state, and the home and Target are like a choke points, dividing my day in two. The most probable path for the day is garage -> Casa -> Jewel -> home -> Target -> DePaul -> bar, with a probability of 0.08064.

The actual path I wound up traveling was garage -> Casa -> home -> coffee -> DePaul -> bar, with a path probability of .00336.

The rest of this story is told with the pictures.