Read as the probability of A given that B is known.
Card removal
If cards are dealt without replacement, visible cards change the composition of the remaining deck. Blackjack insurance and poker outs are conditional calculations.
The correct denominator is the number of compatible unseen cards or combinations after removals.
Dealer procedures
Knowing that a dealer peek found no blackjack removes certain hole-card states. Strategy can therefore differ from a no-hole-card game where that information is unavailable.
Settlement rules also affect the payoff attached to each remaining state.
Bayesian language
New evidence updates a prior probability only when the evidence is statistically connected to the event. A roulette scoreboard has no causal connection to the next fair spin.
A visual pattern is not automatically useful evidence.
Avoid double counting
When enumerating combinations, remove visible cards once and count each compatible state once. Ordered and unordered combinations use different denominators.
State assumptions before presenting a precise conditional percentage.
Working checklist
- Identify relevant information
- Restrict the sample space
- Remove known cards once
- Distinguish ordered combinations
- Reject unrelated pattern evidence
This lesson explains general gambling mathematics and uses rounded examples. A game-specific figure applies only to the rules, pay table, strategy, and denominator stated with it. Last reviewed September 20, 2026.