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Dice Probability Explained: Every Roll from One Die to Many
A clear guide to dice probability: one die, several dice, the 36-outcome table for two dice, sums, and how to count outcomes without guessing.
Probability by Game
Dice and Coins
Exact probabilities for dice rolls and coin tosses.
Advantage and Disadvantage Rolls Explained
How rolling two d20s and taking the higher or lower changes your chance of hitting a target, with worked percentages for a range of target numbers.
Coin Toss Probability and Runs of Heads
How likely are runs of heads in short and long sequences of fair coin tosses? Worked examples show why long streaks are normal in random data.
Expected Number of Rolls to See Every Face
How many rolls of a fair die does it take to see all six faces? The coupon collector result gives about 14.7 on average, with the step-by-step working.
How Fair Is a Real Coin Flip
What does a fair coin mean in maths, and how close are real coin flips? A general look at physical coin bias research and the fair coin assumption.
Loaded Dice and How to Test a Die for Bias
How to test a die for bias using frequency counts and a simple chi-square calculation, with a worked example and notes on what a result can and cannot show.
Polyhedral Dice in Tabletop Games: d4 to d20
A look at the d4, d6, d8, d10, d12 and d20: equal chances per face, how each die's average differs, and why one d20 roll gives a flat spread of results.
The Chance of Rolling at Least One Six
Why four rolls of a die give about a 52 percent chance of at least one six, not 67 percent, and how the complement rule makes such problems easy.
The Chevalier de Mere Dice Problem
The 17th-century dice puzzle behind early probability theory: one six in four rolls versus a double six in 24 rolls of two dice, with the exact numbers.
Why Seven Is the Most Common Total with Two Dice
There are six ways to roll a seven with two dice out of 36 outcomes. See how the full triangular distribution of sums arises and what it implies.
Yahtzee Odds: Chances of Five of a Kind
Worked Yahtzee odds: the chance of five of a kind in a single roll, after rerolls, and when holding three or four matching dice, checked by hand.
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