Ok, so from the book this is just standard case, not like I understood in earlier post

So in your question example

odds are 4-to-1

*against* you:

Probability you win 20% (four out of five), Pwin, and you win 5 dollar

EVwin=Pwin*$1 = 0.2*$5 = $1

Probability you lose 80% (one out of five), Plose, and you lose 1 dollars

EVlose=Plose*1$=0.8*$1 = $0.8

Total ev:

EV = EVwin – EVlose = $1 - $0.8 =

**$0.2**
So your expectation is plus 20 cents per bet, precisely as stated in the book.

The line that confuses you with 2 dollar negative EV is not the same problem than above and what you asked. The question for that is as follows:

Your odds are 4-to-1

*favorite*, you bet 50 to win 10, calculate EV

Frist from odds to % -> 1/4[odd] -> 1/(4+1)[%] -> 1/5 -> 0.2 -> 20% (you lose 20% of time)

Probability you win 80% (four out of five), Pwin, and you win 10 dollar

EVwin=Pwin*$1 = 0.8*$10 = 8$

Probability you lose 20% (one out of five), Plose, and you lose 50 dollars

EVlose=Plose*50$=0.2*$50 = $10

Total ev:

EV = EVwin – EVlose = $8 - $10 = -

**$2**
Very badly written text, but that is normal because proofreaders are totally clueless on math side, so they just give up. Also odds format should be forbidden, at least from basic tutorials, it’s there only to confuse you.