HippoCampus
MathematicsGuidedIntermediate12 chapters

The math of poker and board games

HippoCampus
· starter course
I play poker and board games with friends and want to use probability at the table: odds, expected value, pot odds and combinations, with examples from real games.

What you'll learn

12 chapters
  1. 1

    Why Game Math Matters at the Table

    • Explain what mathematical decision-making means in poker and board games.
    • Distinguish short-term results from long-term decision quality.
    • Recognize the main quantities players estimate during play: probability, odds, expected value, and risk.
  2. 2

    Counting Outcomes and Basic Combinations

    • Count possible outcomes in simple card and dice situations.
    • Use combinations to calculate how many unseen cards or hands are possible.
    • Connect counting methods to practical questions about draws and hand frequency.
  3. 3

    Core Probability for Cards and Dice

    • Calculate simple probabilities from counted outcomes.
    • Distinguish independent events from dependent events.
    • Interpret percentages, fractions, and odds in forms useful during play.
  4. 4

    Conditional Probability and Hidden Information

    • Explain how new information changes probabilities during a game.
    • Use conditional probability ideas in settings with hidden cards or revealed game state.
    • Recognize how blockers and visible information affect chances.
  5. 5

    Poker Hand Frequencies and Starting-Hand Math

    • Relate combinatorics to the frequency of poker starting hands and made hands.
    • Compare paired, suited, and offsuit starting-hand structures.
    • Use frequency knowledge to build intuition about what opponents can plausibly hold.
  6. 6

    Outs and Draw Probabilities in Poker

    • Count outs accurately in common postflop situations.
    • Estimate the probability of improving by the turn or river.
    • Avoid common double-counting errors with overlapping draws.
  7. 7

    Pot Odds, Break-Even Percentages, and Calling Decisions

    • Calculate pot odds from bet sizes and pot sizes.
    • Convert pot odds into required winning probability.
    • Use draw probabilities and pot odds together to judge calls.
  8. 8

    Expected Value in Poker and Board Games

    • Compute expected value for simple choices with known probabilities and payoffs.
    • Compare guaranteed outcomes to risky alternatives.
    • Use EV as a decision tool in both poker hands and board-game turns.
  9. 9

    Implied Odds, Reverse Implied Odds, and Future Streets

    • Explain why current pot odds are not always the whole story.
    • Estimate when future money won or lost changes a present decision.
    • Recognize common situations where drawing hands gain or lose value because of later action.
  10. 10

    Equity, Ranges, and Matchups

    • Define equity as share of the pot across all outcomes.
    • Compare hand-versus-hand and hand-versus-range situations.
    • Use basic range thinking to improve practical poker decisions.
  11. 11

    Board-Game Probability: Dice, Decks, and Resource Draws

    • Apply probability tools to common board-game mechanisms.
    • Compute and compare chances in dice systems and card/resource draws.
    • Recognize how replacement rules change game math.
  12. 12

    Risk, Variance, and Better Decisions Across Repeated Play

    • Interpret variance as the spread of possible short-term outcomes around EV.
    • Evaluate when lower-variance or higher-variance choices make sense in context.
    • Build a practical framework for using math quickly during real games.

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