Odds and Probability
Conditional Probability After One Card
How the chance of the next card changes once you have seen one card, with the ace example worked both ways.
Odds and Probability
Odds and Probability
The Chance of Being Dealt a Pair
How often two cards from a 52-card deck form a pair: 78 pair holdings out of 1,326 hands, which is 1 in 17.
Odds and Probability
How to Read an Odds Table
A practical way to read a printed odds table: profit versus total return, the stake unit, and what the number is not.
Odds and Probability
Common Probability Mistakes with Cards
Five repeatable mistakes in card probability, from treating a deck like a coin to reading a payout as a chance.
Odds and Probability
What Variance Means in a Short Session
Variance is the scatter around an average. Here is why two bets with the same edge can feel nothing alike.
Odds and Probability
Payout Odds vs True Odds, One Example
True odds and payout odds compared on a single roulette number, including the one-unit gap on a 35-to-1 price.
Odds and Probability
The Birthday Problem and Coincidences
Why 23 people give roughly even odds of a shared birthday, and what that coincidence does not predict.
Odds and Probability
Combinations vs Permutations with Cards
Combinations and permutations compared on a 52-card deck, and why a poker hand is not an ordered deal.
Odds and Probability
Why a Coin Flip Has No Memory
Independent trials explained with coin flips: each toss keeps its own chance, and a streak does not tilt the next one.
Odds and Probability
Two Dice, Eleven Totals: The Probability Behind Every Roll
See how many ways each two-dice total can occur, why seven is the most common, and how the chances shape bets in dice games.
Odds and Probability
The Gambler's Fallacy: Why Streaks Do Not Predict the Next Result
Why do people believe a result is due after a streak? Explore the gambler's fallacy, the math behind independence, and honest examples.
Odds and Probability
Expected Value in Plain Language: A Simple Way to Judge a Bet
Expected value sums up the average result of a bet. See how to calculate it with easy examples from coins, dice, and roulette.