Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Engineers · Markov Chains

Markov Chains for the birthday paradox

Built for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed. Simulate the birthday paradox live below — adjust the inputs and watch it respond, right in your browser.

Markov ChainLive

transitions → stationary distribution

A100.0%

B0.0%

C0.0%

Controls

A system hops between states by fixed probabilities. From any start it converges to the same stationary distribution — the math behind PageRank and queueing.

Presets

Stay in A

Stay in B

Stay in C

▶ Run in Python

Data Inspector

Step0

P(A)1.000

P(B)0.000

P(C)0.000

Governing equation

x_{t + 1} = P x_{t}, π P = π, P = 0.7 0.20 0.25 0.15 0.6 0.25 0.15 0.20 0.5

Reading this result: State A has the stickiest self-loop (0.70), so it keeps the largest share of the stationary distribution no matter where you start.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

Is this good for engineers?: Yes — this version of "Markov Chains for the birthday paradox" is framed for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.