Odds and Math
Counting One-Pair Hands in a Five-Card Deck
Exactly one pair accounts for 1,098,240 of the 2,598,960 five-card hands. The count excludes every stronger category.
Odds and Math
Odds and Math
A Paired Flop: How Often the Board Itself Pairs
About 17.2 percent of flops contain a pair or three of a kind. The count uses the full deck and nothing more.
Odds and Math
Same-Color Hole Cards: A Small Count With a Clear Answer
Same-color hole cards are about 49 percent of two-card hands. The count is small, and it is not the suited count.
Odds and Math
How Rare a Royal Flush Is in a Five-Card Hand
In a five-card hand, a royal flush is 4 combinations out of 2,598,960. The count, and what it does not predict.
Odds and Math
Five Probability Myths That Warp Poker Talk
Five sentences people repeat as if they were math. Each one fails a count you can do without a table.
Odds and Math
Expected Value in One Sentence, Then a Warning
Expected value is a weighted average of outcomes. One sentence of definition, then the limits of the idea.
Odds and Math
Why the Next Card Does Not Remember the Last One
A shuffled deck does not owe you a heart. What memory can mean after cards are removed, and what it cannot mean.
Odds and Math
A Rainbow Flop, a Two-Tone Flop, and a Monotone Flop
Monotone flops are uncommon, two-tone flops are the plurality, and rainbow flops sit in between. The three counts, shown.
Odds and Math
How Often a Pocket Pair Flops a Set
A pocket pair flops a set or better about 11.8 percent of the time. The count, shown in full, with no betting advice.
Odds and Math
Odds and Probability Are Not the Same Number
Probability counts chances. Odds compare failures with successes. A short, careful guide to both, with deck examples.
Odds and Math
Starting Hand Odds: How Likely Are Aces, Pairs and Ace-King?
Counting the 1,326 possible starting hands shows how rare pocket aces are and how common pairs and suited cards really are.
Odds and Math
Variance in Poker: Why Luck Rules the Short Run
Variance explains why skilled and unskilled players alike face wild swings. See the numbers behind losing streaks and bad beats.