The expected value is one of the most important concepts in probability and statistics. For instance, all the popular loss functions in machine learning, like cross-entropy, are expected values. However, the definition is far from intuitive. Here is what's behind the scenes.

I know this is more about expectation than gambling, but it might be interesting to your readers to explain why the expected log return is the function to evaluate, and to compare that to the expected return.

Wonderful post! Mind elaborating a bit on why "if we divide total earnings by n, we obtain your average earnings per round". Intuitively, why *average* earnings?

## What's the meaning of the expected value?

Great post. I love them!

Hint: consider the repeated product of the returns. This is also a good motivator for talking about kl divergence / Jensen's inequality

I know this is more about expectation than gambling, but it might be interesting to your readers to explain why the expected log return is the function to evaluate, and to compare that to the expected return.

Wonderful post! Mind elaborating a bit on why "if we divide total earnings by n, we obtain your average earnings per round". Intuitively, why *average* earnings?