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.