Theory is a map, not a promise
A fair coin is 50/50 in the long run. The next flip is still a coin flip. Run trials and watch the bars try to catch the dashed line.
Probability lab
Flip a coin or roll dice, then watch the histogram chase the dashed theory line. Small samples lie. Large ones settle.
Idle · Space run/pause · S step · R reset
Solid bars are observed. Dashed ticks are theoretical.
Tap a bar for the expected share. Run trials to fill them in.
Shaded band is a typical range (±2 standard errors). It narrows like 1/√n.
No average yet
Trials
0
Distance
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Total variation from theory
Typical error
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About 1 / √n
Share of heads
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Theory 50.0%
A fair coin is 50/50 in the long run. The next flip is still a coin flip. Run trials and watch the bars try to catch the dashed line.