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Merged
tphummel merged 1 commit into from
Jun 19, 2025
Merged

Add Monte Carlo summary stats #25

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71 changes: 41 additions & 30 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -114,40 +114,51 @@ Trial Results
└─────────┴───────┴─────────┴───────┘

Final Balance Summary
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│ min │ 416 │
│ p1 │ 416 │
│ p5 │ 416 │
│ p10 │ 416 │
│ p25 │ 416 │
│ p50 │ 416 │
│ p75 │ 614 │
│ p90 │ 614 │
│ p95 │ 614 │
│ p99 │ 614 │
│ max │ 614 │
└─────────┴────────┘
┌─────────┬────────┬────────┐
│ (index) │ stat │ value │
├─────────┼────────┼────────┤
│ 0 │ min │ 416 │
│ 1 │ p1 │ 416 │
│ 2 │ p5 │ 416 │
│ 3 │ p10 │ 416 │
│ 4 │ p25 │ 416 │
│ 5 │ p50 │ 416 │
│ 6 │ mean │ 515 │
│ 7 │ p75 │ 614 │
│ 8 │ p90 │ 614 │
│ 9 │ p95 │ 614 │
│ 10 │ p99 │ 614 │
│ 11 │ max │ 614 │
└─────────┴────────┴────────┘
stdDev: 140.01
95% CI: [320.96, 709.04]

Roll Count Summary
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│ min │ 25 │
│ p1 │ 25 │
│ p5 │ 25 │
│ p10 │ 25 │
│ p25 │ 25 │
│ p50 │ 25 │
│ p75 │ 65 │
│ p90 │ 65 │
│ p95 │ 65 │
│ p99 │ 65 │
│ max │ 65 │
└─────────┴────────┘
┌─────────┬────────┬────────┐
│ (index) │ stat │ value │
├─────────┼────────┼────────┤
│ 0 │ min │ 25 │
│ 1 │ p1 │ 25 │
│ 2 │ p5 │ 25 │
│ 3 │ p10 │ 25 │
│ 4 │ p25 │ 25 │
│ 5 │ p50 │ 25 │
│ 6 │ mean │ 45 │
│ 7 │ p75 │ 65 │
│ 8 │ p90 │ 65 │
│ 9 │ p95 │ 65 │
│ 10 │ p99 │ 65 │
│ 11 │ max │ 65 │
└─────────┴────────┴────────┘
stdDev: 28.28
95% CI: [5.80, 84.20]
```

The standard deviation shows how widely the trials vary around the mean.
Roughly 68% of results will fall within one standard deviation, 95% within
two, and 99.7% within three. The 95% confidence interval is a range that is
expected to contain the true mean in 95% of repeated samples.

## table rules

`playHand` accepts a `rules` object that controls minimum bets and odds limits.
Expand Down
48 changes: 44 additions & 4 deletions monte-carlo.js
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Original file line number Diff line number Diff line change
Expand Up @@ -25,8 +25,21 @@ function percentile (sorted, p) {

function summary (arr) {
const sorted = [...arr].sort((a, b) => a - b)
const mean = arr.reduce((m, v) => m + v, 0) / arr.length
const variance = arr.length > 1
? arr.reduce((m, v) => m + Math.pow(v - mean, 2), 0) / (arr.length - 1)
: 0
const stdDev = Math.sqrt(variance)
const stdErr = stdDev / Math.sqrt(arr.length)
const ci95Low = mean - (1.96 * stdErr)
const ci95High = mean + (1.96 * stdErr)

return {
min: sorted[0],
mean,
stdDev,
ci95Low,
ci95High,
max: sorted[sorted.length - 1],
p1: percentile(sorted, 1),
p5: percentile(sorted, 5),
Expand All @@ -42,8 +55,29 @@ function summary (arr) {

function summaryTable (arr) {
const obj = summary(arr)
const order = ['min', 'p1', 'p5', 'p10', 'p25', 'p50', 'p75', 'p90', 'p95', 'p99', 'max']
return order.map(k => ({ stat: k, value: obj[k] }))
const order = [
'min',
'p1',
'p5',
'p10',
'p25',
'p50',
'mean',
'p75',
'p90',
'p95',
'p99',
'max'
]
const table = order
.map(k => ({ stat: k, value: obj[k] }))
.sort((a, b) => a.value - b.value || order.indexOf(a.stat) - order.indexOf(b.stat))
return {
table,
stdDev: obj.stdDev,
ci95Low: obj.ci95Low,
ci95High: obj.ci95High
}
}

function simulateTrial ({ handsPerTrial, startingBankroll, rules }) {
Expand Down Expand Up @@ -73,10 +107,16 @@ function printResults (results) {
console.table(results.map((r, i) => ({ trial: i + 1, balance: r.balance, rolls: r.rolls })))

console.log('\nFinal Balance Summary')
console.table(summaryTable(results.map(r => r.balance)))
const balanceSummary = summaryTable(results.map(r => r.balance))
console.table(balanceSummary.table)
console.log(`stdDev: ${balanceSummary.stdDev.toFixed(2)}`)
console.log(`95% CI: [${balanceSummary.ci95Low.toFixed(2)}, ${balanceSummary.ci95High.toFixed(2)}]`)

console.log('\nRoll Count Summary')
console.table(summaryTable(results.map(r => r.rolls)))
const rollSummary = summaryTable(results.map(r => r.rolls))
console.table(rollSummary.table)
console.log(`stdDev: ${rollSummary.stdDev.toFixed(2)}`)
console.log(`95% CI: [${rollSummary.ci95Low.toFixed(2)}, ${rollSummary.ci95High.toFixed(2)}]`)
}

if (require.main === module) {
Expand Down