Baccarat Sample Size: Why One Hundred Hands Prove Very Little
Begin with the denominator
A statistics screen may announce that Banker won 55 of the last 100 hands. Ask whether ties were counted, whether observations are missing and whether that window was selected because it looked favorable. The percentage of all hands and the percentage conditional on no tie are different statistics.
The standard eight-deck outcome frequencies are approximately 45.86% Banker wins, 44.62% Player wins and 9.52% ties. They are valid comparison points only when the sample uses the same denominator and rules.
A hundred observations are highly variable
As an illustration, an independent Bernoulli model gives an approximate standard error for a proportion of √[p(1−p)/n]. With p near 0.46 and n equal to 100, this is about five percentage points. A simple 95% approximation can extend nearly ten percentage points in either direction.
This does not mean each hundred-hand session must land in that range. It means an observed percentage can fluctuate widely without showing new predictive information. Increasing n to 10,000 reduces standard error by about a factor of ten under the same assumptions, but does not fix bad data.
Real shoes require care
Baccarat uses finite shoes and deals cards without replacement. Hands within a shoe are therefore not necessarily strictly independent. A basic binomial formula is useful for intuition, not a universally exact confidence interval for every real sequence.
A more careful study should respect the shoe structure, perhaps using block resampling or simulation that implements the actual drawing rules. It should also explain whether the sampling unit is an individual hand, a shoe or a complete session.
The best-looking window is a biased sample
Suppose a program searches one hundred historical windows and publishes only the highest Banker proportion. Finding an extreme value is unsurprising after so many comparisons. The result is selected after the fact; it is not honest evidence of a predictive model.
Credible evaluations fix selection rules and metrics before looking at the final test data. They keep tuning samples separate from untouched evaluation samples, and report all attempts rather than only successful cases.
What a transparent chart needs
It should disclose complete counts for Banker, Player and Tie, the number of shoes, the date range, missing observations, filters, uncertainty assumptions and the exact comparison baseline. An attractive percentage without these details cannot support a meaningful conclusion.
Reference probabilities: Wizard of Odds, https://wizardofodds.com/games/baccarat/basics/ . This article explains data interpretation, not a method to forecast hands.