{
 "version": "https://jsonfeed.org/version/1.1",
 "title": "Thirty-Six Rolls",
 "home_page_url": "https://thirtysixrolls.com/",
 "feed_url": "https://thirtysixrolls.com/feed.json",
 "description": "Probability you can feel: interactive explanations of dice, evidence, bots and chance.",
 "items": [
  {
   "id": "https://thirtysixrolls.com/#/a/bots-tree",
   "url": "https://thirtysixrolls.com/#/a/bots-tree",
   "title": "Why dice break brute force",
   "summary": "Chess programs look far ahead. Backgammon programs mostly can't, and that changed how they had to think.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-handtuned",
   "url": "https://thirtysixrolls.com/#/a/bots-handtuned",
   "title": "Hand-tuned: how BKG 9.8 beat a world champion",
   "summary": "In 1979 a program on a Carnegie-Mellon mainframe beat Luigi Villa 7\u20131. Its knowledge was written by people.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-encoding",
   "url": "https://thirtysixrolls.com/#/a/bots-encoding",
   "title": "How a bot sees the board",
   "summary": "Before a network can judge a position, the position has to become a list of numbers. TD-Gammon used 198.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-network",
   "url": "https://thirtysixrolls.com/#/a/bots-network",
   "title": "Inside the network",
   "summary": "198 numbers in, five probabilities out. What happens in between, for any position you like.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-td",
   "url": "https://thirtysixrolls.com/#/a/bots-td",
   "title": "Learning by playing itself",
   "summary": "No expert games, no rules of thumb. Just a network that keeps comparing what it predicted with what it predicts next.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-moves",
   "url": "https://thirtysixrolls.com/#/a/bots-moves",
   "title": "Every play, ranked",
   "summary": "Generate every legal play, judge each result, then look one roll deeper for the close calls.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-selfplay",
   "url": "https://thirtysixrolls.com/#/a/bots-selfplay",
   "title": "A game through the bot's eyes",
   "summary": "Watch the win probability swing on every roll, and see where skill ends and luck begins.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-rollout",
   "url": "https://thirtysixrolls.com/#/a/bots-rollout",
   "title": "Rolling it out",
   "summary": "When a snap judgment isn't good enough, play the position out thousands of times and count.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-bearoff",
   "url": "https://thirtysixrolls.com/#/a/bots-bearoff",
   "title": "Perfect endgames",
   "summary": "Near the end of a race, a computer doesn't estimate. It knows.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-cube",
   "url": "https://thirtysixrolls.com/#/a/bots-cube",
   "title": "Teaching bots to double",
   "summary": "Networks estimate winning chances without a cube. Turning that into cube decisions took a separate theory.",
   "tags": [
    "Bots"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bots-timeline",
   "url": "https://thirtysixrolls.com/#/a/bots-timeline",
   "title": "From BKG to XG",
   "summary": "Forty-odd years of backgammon programs, and the handful of people behind them.",
   "tags": [
    "History"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/craps",
   "url": "https://thirtysixrolls.com/#/a/craps",
   "title": "Craps & Dice Games",
   "summary": "The loudest table in the casino, the cheapest bet on its felt, why no betting system works, and the dice games you play at home.",
   "tags": [
    "Craps"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/craps-best-bet",
   "url": "https://thirtysixrolls.com/#/a/craps-best-bet",
   "title": "The best bet in the casino",
   "summary": "One bet on the craps table has no house edge at all \u2014 but you can only make it by buying in with another bet. Here's what the package really costs.",
   "tags": [
    "Craps"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/craps-systems",
   "url": "https://thirtysixrolls.com/#/a/craps-systems",
   "title": "Why no betting system works",
   "summary": "Double after every loss and you'll almost always walk away a winner. Almost.",
   "tags": [
    "Craps"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/craps-bold",
   "url": "https://thirtysixrolls.com/#/a/craps-bold",
   "title": "If you must gamble, bet it all at once",
   "summary": "You have $100 and need $200 by the end of the night. Probability theory has an unexpectedly definite answer.",
   "tags": [
    "Craps"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/craps-hand",
   "url": "https://thirtysixrolls.com/#/a/craps-hand",
   "title": "The 154-roll hand",
   "summary": "In 2009 a grandmother playing craps for the second time held the dice for four hours and eighteen minutes. How unlikely was that?",
   "tags": [
    "Craps"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/yahtzee",
   "url": "https://thirtysixrolls.com/#/a/yahtzee",
   "title": "Five of a kind in three rolls",
   "summary": "Keep the biggest group, reroll the rest. You'll get a Yahtzee about one turn in 22.",
   "tags": [
    "Dice games"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/liars-dice",
   "url": "https://thirtysixrolls.com/#/a/liars-dice",
   "title": "Liar's dice: reading cups you can't see",
   "summary": "Every bid is a claim about dice nobody can see. The binomial distribution tells you when to call.",
   "tags": [
    "Dice games"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/chuck-a-luck",
   "url": "https://thirtysixrolls.com/#/a/chuck-a-luck",
   "title": "Chuck-a-luck: the game that looks fair",
   "summary": "Three dice, pick a number. Three chances at 1 in 6 sounds like even money. It isn't.",
   "tags": [
    "Dice games"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/galileo-dice",
   "url": "https://thirtysixrolls.com/#/a/galileo-dice",
   "title": "Galileo's gambling problem",
   "summary": "With three dice, 9 and 10 can each be made six ways. So why does 10 come up more often?",
   "tags": [
    "Dice games"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/frontiers",
   "url": "https://thirtysixrolls.com/#/a/frontiers",
   "title": "Frontiers",
   "summary": "What researchers are actually working on now: recent papers on probability, evidence, machines and the real world, in plain English \u2014 with a line of each abstract so you can check us.",
   "tags": [
    "Frontiers"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/fr-statistics",
   "url": "https://thirtysixrolls.com/#/a/fr-statistics",
   "title": "Honest error bars",
   "summary": "Prediction intervals that don't assume anything, tests you can watch forever, and fresh evidence that doctors still misread test results.",
   "tags": [
    "Frontiers"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/fr-ai",
   "url": "https://thirtysixrolls.com/#/a/fr-ai",
   "title": "Machines that reason about chance",
   "summary": "Search with hidden information, poker bots that learn to be deliberately random, and a warning about believing what a model says its risk is.",
   "tags": [
    "Frontiers"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/fr-applied",
   "url": "https://thirtysixrolls.com/#/a/fr-applied",
   "title": "Probability in the wild",
   "summary": "A fraud test that flags honest data, a forecasting victory that evaporates, and the first causal evidence that the friendship paradox changes behaviour.",
   "tags": [
    "Frontiers"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/fr-method",
   "url": "https://thirtysixrolls.com/#/a/fr-method",
   "title": "How we read these papers",
   "summary": "What we checked, what we didn't, and why most of these are preprints.",
   "tags": [
    "Frontiers"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gammonster",
   "url": "https://thirtysixrolls.com/#/a/gammonster",
   "title": "Gammonster",
   "summary": "A lab notebook: our own attempt at a strong backgammon bot \u2014 the bugs that wasted months, the benchmarks that found them, and a network you can play.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gm-bugs",
   "url": "https://thirtysixrolls.com/#/a/gm-bugs",
   "title": "Three bugs under everything",
   "summary": "The search never searched, the game started from the wrong position, and the rules couldn't hit.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gm-measure",
   "url": "https://thirtysixrolls.com/#/a/gm-measure",
   "title": "Measure first",
   "summary": "A falling training loss proves your model fits its data. Only a match proves it plays.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gm-rebuild",
   "url": "https://thirtysixrolls.com/#/a/gm-rebuild",
   "title": "Rebuilding on something solid",
   "summary": "A rules engine that agrees with a tested one, then the oldest trick in the book: temporal-difference self-play.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gm-play-it",
   "url": "https://thirtysixrolls.com/#/a/gm-play-it",
   "title": "Play it, and what's next",
   "summary": "The network runs in your browser and grades every move you make.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gm-deeper",
   "url": "https://thirtysixrolls.com/#/a/gm-deeper",
   "title": "Faster, deeper, bigger: what helped",
   "summary": "Six times faster training, a second roll of look-ahead, wider networks, hand-made features and rollouts \u2014 each measured over thousands of games.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gm-planning",
   "url": "https://thirtysixrolls.com/#/a/gm-planning",
   "title": "Think at move time, or train for longer?",
   "summary": "A Stratego result sent us back to a conclusion we'd already written down \u2014 and it was wrong.",
   "tags": [
    "Lab notebook"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/chains",
   "url": "https://thirtysixrolls.com/#/a/chains",
   "title": "Chains & Information",
   "summary": "Processes with no memory, wanderers who end up where the roads are, and how to measure surprise in bits.",
   "tags": [
    "Queues"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/q-bus",
   "url": "https://thirtysixrolls.com/#/a/q-bus",
   "title": "Why the bus always feels late",
   "summary": "Buses every ten minutes should mean a five-minute wait. Unless the gaps vary \u2014 and then you're more likely to arrive during a long one.",
   "tags": [
    "Queues"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/q-traffic",
   "url": "https://thirtysixrolls.com/#/a/q-traffic",
   "title": "The queue that explodes",
   "summary": "At 80% busy the line is fine. At 95% it's long. At 100% it never ends \u2014 and the change is not gradual.",
   "tags": [
    "Queues"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/c-markov",
   "url": "https://thirtysixrolls.com/#/a/c-markov",
   "title": "Chains with no memory",
   "summary": "Tomorrow depends on today and nothing before it. That one rule describes weather, board games, and why shuffling works.",
   "tags": [
    "Chains"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/c-walk",
   "url": "https://thirtysixrolls.com/#/a/c-walk",
   "title": "Where a wanderer ends up",
   "summary": "Wander a map at random and you'll spend your time in proportion to how connected each place is. Google was built on this.",
   "tags": [
    "Chains"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/c-bits",
   "url": "https://thirtysixrolls.com/#/a/c-bits",
   "title": "Twenty questions, or seven",
   "summary": "A yes/no answer carries at most one bit. Guessing a number from 1 to 100 needs about 6.64 of them.",
   "tags": [
    "Information"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/c-entropy",
   "url": "https://thirtysixrolls.com/#/a/c-entropy",
   "title": "How surprised should you be?",
   "summary": "Claude Shannon's 1948 answer: rarer outcomes carry more information, and a source's entropy is its average surprise.",
   "tags": [
    "Information"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/x-floods",
   "url": "https://thirtysixrolls.com/#/a/x-floods",
   "title": "The hundred-year flood",
   "summary": "It doesn't mean once a century. Over a 30-year mortgage, the chance of at least one is about 26%.",
   "tags": [
    "Extremes"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/qm-chsh",
   "url": "https://thirtysixrolls.com/#/a/qm-chsh",
   "title": "Randomness you can certify",
   "summary": "A game two players can win 75% of the time by planning ahead \u2014 and about 85% of the time with entangled particles. The gap is how you prove randomness is real.",
   "tags": [
    "Randomness"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/positive-test",
   "url": "https://thirtysixrolls.com/#/a/positive-test",
   "title": "The test came back positive",
   "summary": "A test that catches 90% of cases, with few false alarms, can still be wrong most of the time it says yes.",
   "tags": [
    "Evidence"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/regression-to-mean",
   "url": "https://thirtysixrolls.com/#/a/regression-to-mean",
   "title": "Why the best get worse",
   "summary": "The top scorers on one test usually do worse on the next. Nobody got lazier.",
   "tags": [
    "Evidence"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/jelly-beans",
   "url": "https://thirtysixrolls.com/#/a/jelly-beans",
   "title": "Twenty tests, one fluke",
   "summary": "Run enough studies on nothing and some will look like discoveries.",
   "tags": [
    "Evidence"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/confidence-intervals",
   "url": "https://thirtysixrolls.com/#/a/confidence-intervals",
   "title": "What \u201c95% confident\u201d means",
   "summary": "Not that there's a 95% chance the truth is in this particular range \u2014 something subtler, and easier to see.",
   "tags": [
    "Evidence"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/simpsons-paradox",
   "url": "https://thirtysixrolls.com/#/a/simpsons-paradox",
   "title": "Better in every group, worse overall",
   "summary": "How one treatment can win for small kidney stones and for large ones, yet lose when you add them up.",
   "tags": [
    "Evidence"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/bell-curve",
   "url": "https://thirtysixrolls.com/#/a/bell-curve",
   "title": "The bell curve builds itself",
   "summary": "Add up enough small random nudges and the same shape appears, whatever the nudges were.",
   "tags": [
    "Randomness"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/random-clumps",
   "url": "https://thirtysixrolls.com/#/a/random-clumps",
   "title": "Random things clump",
   "summary": "Truly random dots leave empty spaces and crowded corners. Evenly spread dots are the suspicious ones.",
   "tags": [
    "Randomness"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/benfords-law",
   "url": "https://thirtysixrolls.com/#/a/benfords-law",
   "title": "Why so many numbers start with 1",
   "summary": "In a lot of real data, about 30% of numbers begin with 1 and fewer than 5% with 9.",
   "tags": [
    "Patterns"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/buffons-needle",
   "url": "https://thirtysixrolls.com/#/a/buffons-needle",
   "title": "Throwing needles to find \u03c0",
   "summary": "A probability puzzle from the 1700s turns a floor full of needles into a way to measure \u03c0.",
   "tags": [
    "History"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/kelly-criterion",
   "url": "https://thirtysixrolls.com/#/a/kelly-criterion",
   "title": "How much to bet",
   "summary": "Having an edge isn't enough. Bet too much and you go broke anyway.",
   "tags": [
    "Bets"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/gamblers-ruin",
   "url": "https://thirtysixrolls.com/#/a/gamblers-ruin",
   "title": "The house always wins, eventually",
   "summary": "A 2.7% edge doesn't sound like much until you place a few thousand bets.",
   "tags": [
    "Bets"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/lottery-odds",
   "url": "https://thirtysixrolls.com/#/a/lottery-odds",
   "title": "One in fourteen million",
   "summary": "A number too big to feel. Here's a way to feel it.",
   "tags": [
    "Bets"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/optimal-stopping",
   "url": "https://thirtysixrolls.com/#/a/optimal-stopping",
   "title": "When to stop looking",
   "summary": "Hiring, house-hunting, dating: if you can't go back, look at about 37% of the options, then commit to the first that beats them all.",
   "tags": [
    "Decisions"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/coupon-collector",
   "url": "https://thirtysixrolls.com/#/a/coupon-collector",
   "title": "The last sticker",
   "summary": "Why finishing a collection takes so much longer than starting it.",
   "tags": [
    "Patterns"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/seven-shuffles",
   "url": "https://thirtysixrolls.com/#/a/seven-shuffles",
   "title": "Seven shuffles",
   "summary": "Why a deck riffled three or four times is still far from random.",
   "tags": [
    "Cards"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/poker-hands",
   "url": "https://thirtysixrolls.com/#/a/poker-hands",
   "title": "How rare is a full house?",
   "summary": "2,598,960 possible hands, counted.",
   "tags": [
    "Cards"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/play-the-bot",
   "url": "https://thirtysixrolls.com/#/a/play-the-bot",
   "title": "Play the bot",
   "summary": "A full game against the neural network from the Bots course, with a grade for every decision you make.",
   "tags": [
    "Play"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/history",
   "url": "https://thirtysixrolls.com/#/a/history",
   "title": "History",
   "summary": "A gambler's question in 1654, a self-taught backgammon program in 1992, and the people in between.",
   "tags": [
    "Backgammon"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/take-point",
   "url": "https://thirtysixrolls.com/#/a/take-point",
   "title": "Why you take at 25%",
   "summary": "The doubling cube asks one question: is losing 1 point for sure better than risking 2?",
   "tags": [
    "Backgammon"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/td-gammon",
   "url": "https://thirtysixrolls.com/#/a/td-gammon",
   "title": "The program that taught itself to split",
   "summary": "In the early 1990s, a neural network at IBM played itself at backgammon and changed how humans open the game.",
   "tags": [
    "History"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/sevens",
   "url": "https://thirtysixrolls.com/#/a/sevens",
   "title": "Why seven is king",
   "summary": "Roll two dice enough times and a triangle appears out of nowhere.",
   "tags": [
    "Basics"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/birthday",
   "url": "https://thirtysixrolls.com/#/a/birthday",
   "title": "Twenty-three strangers",
   "summary": "In a room of 23 people, it's slightly better than even that two share a birthday.",
   "tags": [
    "Paradox"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/monty-hall",
   "url": "https://thirtysixrolls.com/#/a/monty-hall",
   "title": "Stay or switch?",
   "summary": "The game-show puzzle that famously fooled a lot of people with math degrees.",
   "tags": [
    "Paradox"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/streaks",
   "url": "https://thirtysixrolls.com/#/a/streaks",
   "title": "Real randomness is streaky",
   "summary": "Why a \u201chot streak\u201d at the table is usually just what fair dice look like.",
   "tags": [
    "Intuition"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/efron-dice",
   "url": "https://thirtysixrolls.com/#/a/efron-dice",
   "title": "Dice that beat each other",
   "summary": "A beats B, B beats C, C beats D, and D beats A. Always pick second.",
   "tags": [
    "Puzzle"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/unfinished-game",
   "url": "https://thirtysixrolls.com/#/a/unfinished-game",
   "title": "The unfinished game",
   "summary": "In 1654, a gambler's question to Blaise Pascal started a correspondence with Pierre de Fermat that shaped probability theory.",
   "tags": [
    "History"
   ]
  },
  {
   "id": "https://thirtysixrolls.com/#/a/friendship-paradox",
   "url": "https://thirtysixrolls.com/#/a/friendship-paradox",
   "title": "Your friends have more friends than you",
   "summary": "It's not an insult. It's a sampling effect, and it shows up in almost every real network.",
   "tags": [
    "Networks"
   ]
  }
 ]
}