Why does flipping a coin repeatedly get predictable?
Markov chain
Why does flipping a coin repeatedly get predictable?
Imagine you're flipping a coin to decide your next move in a game. At first, each flip seems random, but soon a pattern emerges.
The pattern emerges because the outcomes depend only on the previous flip, not the entire history. This is the essence of a Markov chain, where the next state depends solely on the current state.
Example
If you flip heads twice, the next flip is more likely to be heads again, not because of the previous flips, but just because you flipped heads twice before.
Remember this
The rate at which predictions become accurate is determined by the eigenvalue of the transition matrix.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Related concepts
Convergence of random variables
Ever wonder why flipping a coin repeatedly doesn't always predict the next flip?
Hidden Markov model
Ever wondered how you can predict outcomes without seeing all the details?
Langevin dynamics does: adds noise to gradient descent to sample from a distribution
How can we simulate randomness in physics?
Lyapunov exponents measure: rate of divergence of nearby trajectories in a dynamical system
How do tiny differences grow over time in chaotic systems?
Overlapping subproblems
Ever calculated a huge Fibonacci sequence by hand?
ill-conditioned matrices cause numerical instability: small input changes → large output changes
Small changes can lead to huge errors in math
Swipe through more Machine Learning concepts
Open Pocket Polymath