Playing with Ox Blocks thanks to the Mathematical Objects Podcast

There was yet another absolutely fantastic episode of the Mathematical Objects podcast published last week. I just can’t say enough about the great work that Katie Steckles and Peter Rowlett are doing with this blog:

After listening to the post yesterday I did a little google searching for the game online and thought a project based on the Ox Blocks would be really fun.

First we talked about the game:

After the short introduction the boys played one round of Ox Blocks. Since we didn’t have the specific blocks the game uses, we used a 12 sided die and looked at the rolls mod 3. I think the video will show you (i) how easy the game is to play, and (ii) what a fantastic game it is to play with kids:

Next we rounded up to discuss some of the surprises and strategy from the game:

Finally, we went to Matheamatica to explore some of the statistics from the podcast. Unfortunately iMovie didn’t like something about how the video got recorded, and an hour of trying to fix the problem produced essentially no results.

What we were exploring was the situation that Peter Rowlett described in the podcast. He rolled the cubes 501 times and found roughly 180 “take away” rolls, 160 X’s and 160 O’s. So, how likely was it that he’d have seen one of the rolls come up 180 times in 500 rolls. We found that one of the sides coming up 180 times would happen about 30% of the time if the cubes were fair:

180 with lots of trials

My old son wondered what would have happened had Peter found one of the sides coming up 200 times. Turned out that was far less likely – about 0.25%

200 with lots of trials

I’m sorry that the video for this part of the project broke – it was a fun discussion.