I appreciate this educational post. Most of the discussion makes good sense to me.

However, the first example you provide, the lottery ticket for $1 with a pot of $1M, does not. It may make sense strictly mathematically, but it doesn't make sense on the ground, because the odds are so steep it would take lifetimes to get in the money.

"...the prize pot of the lottery is $1,000,000 but your ticket only costs $1. If your chance of winning this lottery is better than one in a million you're actually making money on average (positive EV)."

Even if you were able to play the lottery with those odds, 1:1M, every day of your life, you'd have to be over 650 years old before reaching a 50/50 shot at winning.

For day trades, or poker hands, the EV makes sense, but not so much on the lottery.

Thanks!