a bet with a positve expectation?

[low_limit_soldier]

I recently made a bet with a friend during an NBA playoff game between the Pistons and the Lakers. Kobe Bryant had just been fouled and was at the freethrow line. The bet was whether or not Kobe would make one of his freethrows. I bet that he would make AT LEAST ONE of the freethrows and my friend said he'd give me -115 odds and I took the action. my bet was $115, so if i won, i made $100 from him. If he won, he got my $115. I knew Kobe had a good freethrow percentage (I checked later and it was 85.2%) I also figured that since he had 2 shots at the freethrow line and he only had to make one, I was getting the better end of the deal even with -115 odds. Also, even if Kobe missed both freethrows, If any one of the lakers, including Kobe, made a freethrow before a piston did, I still won the bet. Now this really made me think that this bet had a positive expectation, but I am no math whiz, and I want to combine this information to find out what my win precentage will beif i keep making this bet with him. So here is a summary of the bet.....

Kobe Bryant's Freethrow bet
-------------------------
- My odds = (-115) (bet $115 to win $100)
- Bryant's freethrow percentage = 85.2%
- only has to make 1 of the 2 shots for me to win
- Even if Kobe misses both freethrows, i still win if any Laker makes a freethrow before a Piston does.


If someone is able to figure this out I would greatly appreciate it, all the math hurt my head. Thanks for your time.
-lowlimitsoldier

[tech]

The probability of an 85.2% shooter missing two free throws in a row is about 2.5%. Your expectation for this bet is massively positive, even without taking into account the chance of another Laker making one first.