Markov Chain Applications
Most people think flipping a coin is a simple fifty-fifty chance. Heads or tails, each with equal odds. That is true in theory, but only if you look at it over a long run. Statisticians call this the law of large numbers.
In small samples, randomness plays tricks on us. You might flip twice and see two heads. You might flip ten times and see seven tails. Only after hundreds or thousands of flips does the ratio begin to settle close to even. What looks like pure chance starts to reveal its balance once you watch long enough.
Now think about something more familiar than coins. Imagine your daily walk to work. Most mornings you leave home, head to the train station, ride into the city, and walk the last stretch to your office.
Every now and then you catch a bus instead, but for the most part your routine stays the same. To you it feels ordinary. To a mathematician, it is a set of steps that can be written as states. Home, station, city, office. Each move from one to the next has a probability that can be measured.
Picture an app that tracks this pattern. Over time it notices that nine times out of ten you walk, sometimes you take the bus, and very rarely you do something else.
With enough days recorded, the percentages settle and become reliable. The app can then predict how many steps you will take on a normal day. If it sees that catching the bus lowers your step count below a healthy target, it can nudge you with a reminder to walk.
What the app is doing is applying a Markov chain. It is using your present state, along with stable probabilities learned over many repetitions, to guess your likely next move.
This idea comes from the Russian mathematician Andrey Markov, who developed it in the early twentieth century. The special feature is that the future depends only on where you are right now, not on the full story of how you got there.
Search engines are scaled-up examples of Markov Chain. Google’s PageRank algorithm treats you like a random surfer clicking links across the web. By running this process many times, it finds stable probabilities of landing on different sites. That is why Google can rank pages in a way that feels so accurate.
Other areas with the potential is customer behaviour, people move between states like browsing, adding to cart, purchasing, or abandoning. In principle, a Markov chain could capture these transitions and give businesses sharper forecasts.
What all of this shows is that uncertainty itself has structure. A Markov chain does not remove uncertainty but make uncertainty useful. It gives us a way to simplify, and to predict patterns in the middle of apparent noise.