# Probability

## Poker Hands

**Example:** What is the probability of drawing a poker hand consisting of exactly three aces?

**W|A Query:** `odds three aces`

**Results:** Since a hand size wasn't specified, W|A provides information on multiple hand sizes (3 to 8 cards by default). For each hand size, W|A provides the number of hands that satisfy the conditions (e.g. 4512 for a five-card hand), the approximate probability of drawing such a hand (0.001736), and the odds of drawing such a hand (1 in 576). Optionally, one can ask W|A to show information for larger hands sizes, too.

**Implications:** Poker hand probabilities are standard examples in probability. W|A can be used to compute these probabilities quickly and accurately. Often, instructors have students compute these kinds of probabilities as way to help them better understand combinations and permutations. Since W|A doesn't show how these probabilities are computed, it won't help students grasps these concepts. One could ask students, I guess, to determine how the results W|A provides could be computed by hand.

However, by showing results for multiple hand sizes, W|A might help students see patterns in these kinds of probabilities that they might not see otherwise. Connecting these patterns to the computations that produce them could be useful.