Probability Foundations

Random Variables & Expected Value

Build any probability distribution, compute EV = Σ xᵢpᵢ, then simulate thousands of draws to watch the running average converge to the theoretical value.

Simulation run

Lottery explored

Convergence seen

Choose Playground

Payout Table

Define outcomes xᵢ and their probabilities pᵢ

Σ pᵢ

1.000

Outcome (xᵢ)

Probability (pᵢ)

xᵢ · pᵢ

+2.0000

+1.5000

+0.0000

-1.0000

Distribution Spinner

Expected Value Calculator

EV = Σ xᵢ · pᵢ

(10)×0.2000+2.0000

+ (5)×0.3000+1.5000

+ (0)×0.3000+0.0000

+ (-5)×0.2000-1.0000

Expected Value (EV)+2.5000

Positive EV: favors the player

Simulation

Run thousands of random draws to verify the Law of Large Numbers

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