Simulate Any Event

Draw randomly from equally likely outcomes — estimate any probability just by counting.

The two sides of a coin, roulette pockets, the faces of a die, the cards in a deck — each is a set of equally likely outcomes. Once you can draw one at random, you can estimate the probability of any event: run the draw many times and count the fraction where the event happened. That fraction settles toward the true probability as you draw more (the law of large numbers).

You don't need the analytic formula. For the simple cases the true answer is just (favorable outcomes) / (total outcomes) — shown here so you can watch the simulation close in on it. For messy events (a poker of aces, the number of spins until the first black), the formula gets ugly fast, but the simulation works exactly the same way.

The Ratings tab goes two steps further: the outcomes are not equally likely (scores 1–5 follow a fixed distribution), and three of its events are about a whole experiment — a statistic of 10,000 ratings. Run 1,000 such experiments and those events come out (almost) always true or (almost) never true: statistics of large samples are near-certainties, even when each single draw stays uncertain.

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Pick a draw

Pick an event

Simulate

No draws yet.

Draws so far
0
Event happened
0
Empirical P
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True P
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Equally likely outcomes

Empirical P converging to the truth

Each point is the fraction of draws (so far) where the event happened — after 1 draw, 2, 3, 4, 6, … up to all of them. After a handful of draws the fraction swings wildly; after thousands it pins down the dashed line, the true probability. That is the law of large numbers. (x-axis is logarithmic so you can see both ends.)