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How a 52-Card Deck Shapes Every Card Game Probability
A foundation guide to the standard 52-card deck: its suits, ranks and colours, and how that fixed make-up sets the odds for hands, draws and orderings.
Game Deep Dives
Card Games and Counting
Deck composition, shuffling and the arithmetic of card games.
Bridge Hand Distributions and What They Predict
How the 13 cards in a bridge hand divide among the suits, which shapes are common or rare, and how suit splits guide bidding and the play of the cards.
Counting Outs in Card Games From Rummy to Bridge
Learn to count outs, the unseen cards that complete a hand, in rummy, gin and bridge, and see how dead cards and the size of the unseen pile change the odds.
Drawing Without Replacement: Why Each Card Changes the Odds
See why dealing cards from a deck without putting them back changes later probabilities, with simple worked examples using aces, hearts and a 52-card deck.
How Many Shuffles Does a Deck Really Need?
What mathematicians found about riffle shuffles: why a handful of shuffles are often cited as enough to mix a 52-card deck, and what that result assumes.
Patience and Solitaire: How Often Can a Game Be Won?
What is known about solitaire winnability: why the exact share of winnable deals is hard to pin down, how FreeCell differs from Klondike, and what a win rate means.
Probability of Pairs, Triples and Runs in Rummy-Style Games
Calculate how likely sets and runs are in a dealt rummy hand, from three-card melds to 7-, 10- and 13-card hands drawn from a single 52-card deck.
The Birthday Problem Applied to a Deck of Cards
Apply the birthday problem to a 52-card deck: how quickly repeated cards or matching ranks appear in draws, with checked examples and a two-deck match puzzle.
The Odds of Being Dealt Each Poker Hand Category
How many of the 2,598,960 five-card poker hands fall into each category, from high card to royal flush, with the counting behind each and why rarer ranks higher.
Why Card Counting Is Mathematically Possible
An educational look at why tracking dealt cards shifts blackjack odds: deck composition, running counts, and the limits that keep it far from a sure thing.
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