This problem was posted by Pasquale Cirillo last week and I thought it would be great to talk through with my son:

This is the video where Cirillo talks through the problem if you want to see his full solution:

I’d asked my son to think about it a bit ahead of us sitting down to talk. Here are some of his ideas:

Here we find the expected winnings if we use my son’s first rule – stop in either of the first 2 rounds if you get a 6:

We ended the day today by talking through the strategy of stopping in either of the first 2 rounds if you see a 4, 5, or 6.

At the end of the last video I let my son know that we hadn’t quite found the best strategy, yet. Tomorrow we’ll finish up and find that best strategy.