Yesterday we had a nice discussion about additive and multiplicative random processes:

Today I wanted to extend that conversation to an example I first learned from a talk by Ole Peters.

I introduced the additive version of the game first and asked the boys what they thought would happen:

After the boys thought about the coin flipping game where you bet $100 each time we moved to the same game where you bet your entire net worth each time/. This one is a little harder to think through, but they boys has some good intuition:

Now we moved to looking at the two games in Mathematica. Here’s how the additive game plays out:

Finally the boys got to see the surprise in the multiplicative game – average wealth increases, but eventually any individual players ends up losing all of their money:

This game is really fun to think through and also a nice example to share with kids to illustrate additive and multiplicative games. Happy that yesterday’s detour into multiplicative processes led us to this conversation today!