Working notes on the odds behind card and table games
Entries filed under odds and probability, newest first.
A hand rank chart is really a frequency table read backwards: the rarer the five-card combination, the higher it sits. Once that is clear the order stops being a list to learn and becomes something you can reconstruct at the table from counting alone.
Filed under: Card games, Odds and probability — permalink
Two pair beats one pair for one reason only, and it is a counting reason rather than a traditional one. Working the arithmetic once is quicker than trusting the chart.
Filed under: Card games, Odds and probability — permalink
House edge, hold and return to player describe three different quantities that are routinely used as if they were one. Separating them makes published figures much easier to read.
Filed under: Odds and probability, Table games — permalink
The difference between the two common roulette wheels is a single extra pocket, and the whole edge lives in it. The payouts are identical; only the denominator changes.
Filed under: Table games, Odds and probability — permalink
An independent trial has no memory, which is why a run of one colour changes nothing about the next spin. The intuition that says otherwise is worth naming precisely.
Filed under: Odds and probability — permalink
The odds bet behind a point is the rare wager paid at its true mathematical price, which makes it a useful reference point for reading every other bet on the layout.
Filed under: Table games, Odds and probability — permalink
Expected value describes the long-run average; variance describes how far a short session can sit from it. Most arguments about luck are really arguments about the second one.
Filed under: Odds and probability, Bankroll — permalink