This Demonstration compares experimental data with theoretical probability predictions applied to the dealer's hand in the game of blackjack.

The experimental data was obtained by using a random draw from an infinite deck. There are minimal differences between using an infinite deck and the actual deck found in casinos, made of six ordinary 52-card decks.

The theoretical predictions are obtained by calculations of conditional probability applied to card drawing, again using an infinite deck [1].

In both the experimental and theoretical cases, the dealer observes the usual rules: the dealer gets the first card face up and must draw cards until the hand busts or adds up to 17 or higher.

Based on the law of large numbers, the divergence between experimental and theoretical results decreases as the number of trials increases, an effect that you can observe here.

You can see evidence of the law of large numbers in the Snapshots.

Snapshot 1: a large number of trials leads to a convergence of experimental and theoretical results

Snapshot 2: a small number of trials usually shows a deviation of experimental data from theoretical predictions

Reference

[1] M. Bonaldi, "Modelli probabilistici e strategie di comportamento nel gioco del Blackjack," thesis, Department of Mathematical, Physical and Natural Sciences, University of Bologna, Italy, 2010. amslaurea.unibo.it/792.