# SOCR EduMaterials Activities PokerExperiment

## Poker Experiment

## Description

The poker experiment consists of dealing 5 cards at random from a standard deck of 52 cards. V denotes the value of the hand;

V=0: no value; V =1: one pair. V = 2: two pair; V = 3: three of a kind; V = 4: straight, V = 5: flush; V = 6: full house, V = 7: four of a kind; V = 8: straight flush.

The value V is recorded on each update in the first table. The density function of V is shown in blue in the graph and recorded in the second table. On each update, the empirical density function of V is shown in red in the graph and recorded in the second table. In the stop frequency list box, you can set the simulation to stop automatically when V is a particular value.

## Goal

To provide a simulation demonstrating the differences of probabilities when drawing poker hands and to give a better understanding of how often these hands may occur in a poker game.

## Experiment

Go to the SOCR Experiment [[1]] and select the Poker Experiment from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:

When pressing the play button, one trial will be executed and recorded in the distribution table below. The fast forward button symbolizes the nth number of trials to be executed each time. The stop button ceases any activity and is helpful when the experimenter chooses “continuous,” indicating an infinite number of events. The fourth button will reset the entire experiment, deleting all previous information and data collected.
The “update” scroll indicates nth number of trials (1, 10, 100, or 1000) performed when selecting the fast forward button and the “stop” scroll indicates the maximum number of trials in the experiment.

As the number of trials increase, the empirical density graph converges to the distribution graph:

The distribution graph is unimodal with a distinguishable peak and is skewed right because of the probabilities of each card hand. Recall that it is more likely to obtain a pair or two than drawing a straight flush.

## Applications

The Poker Experiment is a general simulation that demonstrates the probabilities of poker hands analytically and graphically. It may be used in many different types of poker games as well as other events in which there is a much higher probability of event A than event Z.

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