What are markov chains?

A Markov chain is like a game where you move from one place to another based on simple rules, just like when you play hopscotch or choose which toy to play with next.

Imagine you have three favorite toys: a ball, a block, and a book. Every time you pick a new toy, it depends only on what you played with last, not on all the toys you’ve picked before. That’s the core idea of a Markov chain: what happens next depends just on where you are now.

Think of a board game with three spaces: Red, Blue, and Green. You start at Red. When it's your turn, you roll a die to decide where you go next:

• If you're on Red, you can only move to Blue.
• If you're on Blue, you might stay there or jump to Green.
• If you're on Green, you always go back to Red.

This is like a Markov chain, each space (Red, Blue, Green) is a state, and the rules about moving from one to another are called transitions.

Over time, you might notice that you end up on certain spaces more often. That’s how Markov chains help us predict what might happen next, like knowing which toy you’ll pick or where you'll land in your game. It's not magic, it's just a simple pattern!