Two cards to come

Let's now consider the point at which two cards will still come. Here, we will find the probability of winning for any number of outs.

At this point, there are 3 cards face up, and 2 in your hand. With 52 total cards in the deck, this leaves 47 unseen cards, so the denominator is \({47 \choose 2}\) to represent the total number of combinations for the two cards to come.

An often-used approximation among poker players is that the win probability is equal to \(\frac{4 \times outs}{100}\). How good is this approximation?

This exercise is part of the course

Probability Puzzles in R

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Exercise instructions

Use the outs vector to fill in the numerator of p_no_outs, which counts the number of ways that none of the outs will come in the next two cards.
Calculate the probabilities of winning corresponding to each number of outs.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

outs <- c(0:25)

# Calculate probability of not winning
p_no_outs <- ___/choose(47, 2)

# Calculate probability of winning
p_win <- ___

print(p_win)

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