Can you please explain why the ratio of CE/WR should always be 0.5? My understanding of CE is that it represents how much money you are willing to either accept/pay in order to forgo/enter an opportunity that involves risk.

In the context of BJ, suppose a game has a WR of $50/Hr with an SD of $700/Hr. Moreover, say a counter earns $20/Hr in his job, if he is content to take the sure thing of 20 bucks, then his CE = $20/Hr.

Now say he is not satisfied with his hourly wage, and requires at least $30/Hr at his regular job to forgo the BJ opportunity which has risk. Now his CE = $30/Hr.

The point I am trying to make is that CE seems like a very subjective concept. Going back to the counter with 50 bucks per hour in EV, why must his CE = $25/Hr? When you suggest ratio of CE/WR = 0.5, that is exactly what you are saying. What if he is risk averse and would rather take the sure thing of 10 bucks at his job? Now the ratio becomes 0.2. Perhaps he is prone to risk and would not settle for anything less than a wage of 40 bucks/Hr to forgo playing BJ. Here the ratio increases to 0.8.

Note: I realize and know the formula for CE, but it seems rather peculiar a formula can tell us how much money we are willing to accept in order to forgo playing BJ.

Btw, why is it if the ratio is less than 0.5, you are overbetting? Is the converse true as well?

Thanks,
MJ