Revisiting a neat coin flipping game I learned from Ole Peters

This morning I accidentally stumbled on an old coin flipping game we looked at last year:

I thought it would be fun to take a look at the problem again since the last look was long enough ago that the boys probably wouldn’t remember it. Here are their initial thoughts in the problem. After a bit of discussion, the boys came up with a good argument for why HHHT only would appear more often than HHHH only.

Next we looked through a simple computer program I wrote to model the situation. This isn’t the best or most clever way to write the program, but I thought it was an easy one to explain:

Finally, we looked at how the numbers would change if the sequence had 50 flips instead of 20. It was interesting to hear the boys explain why the numbers had changed – I think this extra discussion helped them understand the original problem a bit better: