Using Poker to motivate some basic counting ideas

Both of my son’s have recently gotten interested in poker. My older son has also been working through Art of Problem Solving’s Introduction to Counting & Probability book, so I thought I’d use poker to motivate a few counting problems tonight.   The goal wasn’t to get too complicated, rather just to explore a few basic ideas.

Here’s how I introduced the project.  At the end they decided we’d count the ways to get (i) a 4 of a kind, (ii) a flush, and (iii) two pairs.

First we tackled counting the ways to get 4 of a kind. My younger son’s approach was pretty interesting even though he overlooked one piece of the counting.

Next we counted the number of ways to get a flush. The boys wondered if we should count the straight flushes separately, so we tackled the both problems:

Finally we tackled the challenge of counting the number of ways to get exactly two pairs. Here my younger son’s approach was pretty interesting again and led to a nice conversation about over counting.

So, a fun little project. It nice to find a little counting motivation from games they are already playing.