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wilsonScoreInterval

Wilson score confidence interval for a binomial proportion.

wilsonScoreInterval(successes: number, nTrials: number, z: number): WilsonScoreInterval

Import​

const poker = require('poker-calculations');

ESM (Node):

import { createRequire } from 'module';
const require = createRequire(import.meta.url);
const poker = require('poker-calculations');

When to use​

Show confidence bands on observed rates (fold to cbet, WTSD, MC win rate buckets) when sample size is small or the point estimate is near 0 or 1. Wilson intervals behave better than a naive normal approximation in those cases.

How to use​

const poker = require('poker-calculations');

const successes = 42;
const nTrials = 100;
const z = 1.96; // ~95% normal critical value

const interval = poker.wilsonScoreInterval(successes, nTrials, z);
const pHat = successes / nTrials;

console.log({
  point: pHat,
  lower: interval.lower,
  upper: interval.upper,
});

Returns​

WilsonScoreInterval — { lower: number, upper: number } with both bounds in [0, 1] for the success proportion successes/nTrials at critical value z.