Expected value is the average (profit) result. What’s the EV of a coin flip? 50% you lose $1 and 50% you win $1. The average is $0. Now let’s say it’s weighted 60/40 in your favor. 60% to win $1 and 40% to lose $1 equals:
(0.6 * $1) – (0.4 * $1) = $0.20.
On average, you’ll win $0.20 per coin flip, which is 20%.
One real life event might be driving. Back roads always take 3 gallons of gas. The freeway takes 2 gallons 75% of the time. But 25% of the time there is traffic and it takes 4 gallons. Freeway is:
(0.75 * 2) + (0.25*4) = 2.5 gallons ON AVERAGE.
Let’s say you drink a lot and an Uber costs $20 to get home. If you drive drunk, there’s a 1% chance you get a DUI which costs $10,000 (idk what a DUI costs. Don’t drink and drive, people).
Drive: (0.01 * $10,000) = $100.
Uber is 1/5’th the cost of driving drunk, even though most of the time it costs $0. This also doesn’t take into account a bunch of other stuff like dying or killing someone, losing your job and drivers license, how much Uber/bus pass/bicycle will cost, or whatever else. But all of that can be added in, to get your overall cost of driving drunk verse taking an Uber. (Don’t drink and drive. Not only is it dumb, but it’s more expensive.)