Farkle Scoring Probability Calculator
ANA›Life Services Authority›National Calculator Authority›Farkle Scoring Probability Calculator
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Farkle Scoring Probability Calculator
Calculate the probability of scoring (avoiding a Farkle) when rolling a given number of dice, plus expected score and risk analysis.
Number of Dice to Roll (1–6):
Current Turn Score (points banked this turn):
Total Score So Far (across all turns):
Target Score to Win:
Calculate ...
// ── Farkle Scoring Rules (standard) ────────────────────────────────────────── // Single 1 = 100 pts Single 5 = 50 pts // Three 1s = 1000 pts Three 2s = 200 pts Three 3s = 300 pts // Three 4s = 400 pts Three 5s = 500 pts Three 6s = 600 pts // Four of a kind = triple score × 2 // Five of a kind = triple score × 4 // Six of a kind = triple score × 8 // Straight 1-2-3-4-5-6 = 1500 pts // Three pairs = 1500 pts // Two triplets = 2500 pts // Four of a kind + a pair = 1500 pts
function scoreOfCounts(counts) { // counts: array of 6 ints (count of 1s..6s) var score = 0; var n = counts.slice();
// Check special combos first (all 6 dice) var total = n.reduce(function(a,b){return a+b;},0); if (total === 6) { // Straight 1-2-3-4-5-6 if (n[0]===1&&n[1]===1&&n[2]===1&&n[3]===1&&n[4]===1&&n[5]===1) return 1500; // Three pairs var pairs = n.filter(function(x){return x===2;}).length; if (pairs === 3) return 1500; // Two triplets var trips = n.filter(function(x){return x===3;}).length; if (trips === 2) return 2500; // Four of a kind + pair var fours = n.filter(function(x){return x===4;}).length; if (fours===1 && pairs===1) return 1500; }
// Standard scoring for (var face = 1; face = 3) { var mult = Math.pow(2, cnt - 3); // 3→1, 4→2, 5→4, 6→8 score += base * mult; cnt -= cnt; // all used } else if (face === 1) { score += cnt * 100; } else if (face === 5) { score += cnt * 50; } } return score; }
function rollsForDice(numDice) { // Generate all possible outcomes for numDice dice // Returns array of {counts:[6], ways:int} // We enumerate via multinomial var results = []; function enumerate(diceLeft, faceStart, current) { if (diceLeft === 0) { results.push({counts: current.slice(), ways: multinomial(numDice, current)}); return; } for (var f = faceStart; f 0) { scoringWays += o.ways; totalScore += s * o.ways; scoreDistribution[s] = (scoreDistribution[s]||0) + o.ways; } });
var farkleWays = totalWays - scoringWays; var pScore = scoringWays / totalWays; var pFarkle = farkleWays / totalWays; var expectedScore = totalScore / totalWays; // includes 0s for farkles
return { pScore: pScore, pFarkle: pFarkle, expectedScore: expectedScore, expectedScoreIfScoring: pScore > 0 ? (totalScore / scoringWays) : 0, totalWays: totalWays, scoringWays: scoringWays, farkleWays: farkleWays, scoreDistribution: scoreDistribution }; }
function farCalc() { var diceEl = document.getElementById('far-dice'); var curEl = document.getElementById('far-current'); var totEl = document.getElementById('far-total'); var tgtEl = document.getElementById('far-target'); var resEl = document.getElementById('far-result');
var numDice = parseInt(diceEl.value); var curScore = parseInt(curEl.value) || 0; var totScore = parseInt(totEl.value) || 0; var target = parseInt(tgtEl.value) || 10000;
// Validation if (isNaN(numDice) || numDice 6) { resEl.innerHTML = '⚠ Number of dice must be between 1 and 6.'; return; } if (curScore ⚠ Current turn score cannot be negative.'; return; } if (totScore ⚠ Total score cannot be negative.'; return; } if (target ⚠ Target score must be at least 1.'; return; }
var r = analyzeRoll(numDice);
// Risk assessment var riskLevel, riskColor; if (r.pFarkle = needed) { recommendation = "🏆 You can win by banking now! Bank your " + curScore.toLocaleString() + " points."; } else if (r.pFarkle > 0.40 && curScore > 0) { recommendation = "⚠️ Farkle risk is very high (" + (r.pFarkle100).toFixed(1) + "%). Consider banking your " + curScore.toLocaleString() + " points."; } else if (r.pFarkle > 0.25 && curScore >= 500) { recommendation = "🤔 Moderate-high risk. Banking " + curScore.toLocaleString() + " pts is safe; rolling could gain ~" + Math.round(r.expectedScoreIfScoring) + " more."; } else { recommendation = "✅ Risk is manageable. Rolling " + numDice + " dice has a " + (r.pScore100).toFixed(1) + "% chance of scoring."; }
// Top scoring outcomes var distEntries = Object.entries(r.scoreDistribution) .map(function(e){return {score:parseInt(e[0]), ways:e[1]};}) .sort(function(a,b){return b.ways-a.ways;}) .slice(0,5);
var distRows = distEntries.map(function(e){ var pct = (e.ways/r.totalWays*100).toFixed(2); return ''+e.score.toLocaleString()+''+e.ways+''+pct+'%'; }).join('');
resEl.innerHTML = '### Results for ' + numDice + ' Dice ' + '' + 'Probability of Scoring (no Farkle):' + '' + (r.pScore100).toFixed(2) + '%' + 'Probability of Farkle (score = 0):' + '' + (r.pFarkle100).toFixed(2) + '%' + 'Expected Score per Roll:' + '' + r.expectedScore.toFixed(1) + ' pts (incl. farkles)' + 'Expected Score if Scoring:' + '' + r.expectedScoreIfScoring.toFixed(1) + ' pts' + 'Total Possible Outcomes:' + '' + r.totalWays.toLocaleString() + '' + 'Scoring Outcomes:' + '' + r.scoringWays.toLocaleString() + '' + 'Farkle Outcomes:' + '' + r.farkleWays.toLocaleString() + '' + 'Farkle Risk Level:' + '' + riskLevel + '' + '' + '#### Top Scoring Outcomes ' + '' + 'ScoreWaysProbability' + distRows + '' + '' + 'Recommendation: ' + recommendation + '' + '' + 'Current turn: ' + curScore.toLocaleString() + ' pts | ' + 'Total: ' + totScore.toLocaleString() + ' pts | ' + 'Need: ' + Math.max(0, needed).toLocaleString() + ' more pts to win'; }
#### Formulas & Scoring Rules
Probability of Scoring:
P(score) = (# outcomes with score > 0) / 6n P(farkle) = 1 − P(score) E[score] = Σ (scorei × waysi) / 6n
Standard Farkle Scoring:
All 6n equally-likely outcomes are enumerated via multinomial expansion. Each unique unordered outcome (multiset) has multiplicity n!/(c₁!c₂!…c₆!) where cᵢ is the count of face i.
#### Assumptions & References
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