Blog
How many five-card hands are there? The 2,598,960 explained
Why a 52-card deck makes exactly 2,598,960 different five-card hands, shown step by step with permutations, combinations and a simple divide-by-120 trick.
· 5 min read
Five-card poker hand probabilities: the full table and how each is counted
Exact counts and probabilities for all nine five-card hand types, from straight flush to no pattern, with the counting argument behind every number.
· 7 min read
Why is one pair so common? Counting versus intuition
One pair appears in over 42% of five-card hands while a flush is under 0.2%. The reason is counting: how many hands fit each pattern, not how special they look.
· 5 min read
What is a Monte Carlo simulation? A card-deck explanation
Monte Carlo simulation estimates probabilities by repeating a random experiment many times. See how it works with a deck of cards and when it can be trusted.
· 6 min read
The law of large numbers, shown with playing cards
Why experiments settle toward the true probability as samples grow, why the error shrinks like one over the square root of n, and how to see it with 100 to 100,000 deals.
· 6 min read
Permutations vs combinations: a simple way to tell them apart
Does order matter? A clear guide to choosing between permutations and combinations, with card examples, formulas and common mistakes.
· 5 min read
Why real randomness looks streaky
True random sequences contain surprising runs and clusters. Learn why streaks are normal, why 'due' outcomes do not exist, and how shuffles and seeds work.
· 5 min read
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