Five articles on probability and statistics through Texas Hold ’Em. The math is real. So is the game.
Statology · Probability Foundations
Every hand in Texas Hold 'Em is a probability problem. How many cards remain in the deck? Which ones help you and which ones hurt your opponent? This builds the math.
Read on Statology ↗Statology · Decision Theory
Pot odds tell you whether a call is mathematically profitable. Expected value tells you whether it stays profitable over time. These are finance concepts in a felt table disguise. This article breaks both down using hands most recreational players consistently lose money on without ever fully understanding exactly why.
Read on Statology ↗Statology · Pre-Flop Mathematics
Not every starting hand is worth the chips it costs to see a flop. This article quantifies exactly which hands deserve to be played, from which positions, and against how many opponents. The math here is combinatorics: how many two-card combinations exist, how often each appears, and how frequently they connect with the board. Most players know the starting hand hierarchy by feel. This article gives you the table behind that intuition.
Read on Statology ↗Statology · Advanced Equity Analysis
Equity is your share of the pot based on your probability of winning. Combinatorics is the math that tells you how many ways your opponent can hold any specific combination of cards. Hand range analysis puts both together: given how your opponent has played, what distribution of holdings is most likely, and what does your equity look like against that entire distribution rather than a single assumed hand? This is what separates players who think in hands from players who think in ranges. The article is rigorous and the examples are each worked through in full.
Read on Statology ↗Statology · Long-Run Statistics
Variance is why a losing player can win for a week and a winning player can lose for a month. The law of large numbers is why the math eventually reasserts itself. Bankroll management is the bridge: the set of rules that keeps you in the game long enough for the math to do its work. This article covers all three with the precision they deserve. You will learn how to calculate your standard deviation, how to size a bankroll against your game's variance, and what confidence intervals around your win rate mean in practice. If you have ever run bad and wondered whether you were unlucky or simply not as good as you thought, this answers it.
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