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low_limit_soldier
06-11-2004, 02:24 AM
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

Ed Miller
06-11-2004, 03:09 AM
Your friend basically just gave you \$100.

Daliman
06-11-2004, 03:39 AM
I have no idea where you found a friend dumb enough to make this bet, but you win by telling him you'll give him 10-1 odds every time kobe steps to the line. The other BS about another laker being able to hit DOES help, but essentially, you need to figure 14.8%(kobe's incedence of missing)x 14.8% to see how often he misses both.
14.8% x 14.8%=2.2%
So, essentially, you could give him 45-1 odds, and still have the best of it.

MCS
06-11-2004, 05:13 AM
Note that daliman's solution assumes the two free throws are uncorrelated, i.e., whether or not Kobe makes the first free throw in no way affects whether he makes the second. This is probably technically untrue, but it's also probably very close to true, so the answer is still going to be around .148*.148 = .022. I just pointed this out because I like being precise, or possibly because I am a math guy, or both.

As daliman said, you would have the best of this bet alone even at 10-1, and possibly even at 45-1.

The "Lakers before Pistons" clause makes it even stronger for you. If we assume that the chance of the Pistons hitting a FT before the Lakers is 50%, that changes your probability of losing the bet to 2.2% times 50%, or 1.1%. That clause means you'd almost certainly have the best of it at say 60-1.

This might be the most lopsided bet I've ever heard.

B Dids
06-11-2004, 11:05 AM
I can only assume that your friend doesn't watch baskteball and was thinking of Shaq. He's the one who can't shoot freethrows (although Mark Madsen and Ben Wallace make Shaq look like Rick Barry).

mike l.
06-11-2004, 01:26 PM
"Now this really made me think that this bet had a positive expectation,"

gee ya think?? your friend is a real fool and you should try and watch basketball games with him as much as possible. hook up the big screen, put out a nice spread, and ask him to bring a full wallet.

my guess is your friend misunderstood the bet.

sucka
06-11-2004, 01:38 PM
Reminds me of a bet I got snookered into at a poker table one time...

A friendly guy sitting next to a friend and I that were playing together makes the following proposal:

For any \$ amount that you are willing to make I'll pick any 3 cards (no suits) and if any one of those show up on the flop, I win the bets. If not, then I pay you the amount of your bet.

At first, it seemed like a good bet as the quick math that I did in my head was incorrect. However, after thinking about it a little I realized that this guy had a huge vig on us. It was fun though - made those couple orbits where I folded nearly everything I played interesting. I won't go into the math, but basically this guys going to win some 60+% of the time.

On the top, it sounds semi-reasonable - but if you can find some poor unsuspecting sap you might be able to make a few bucks off them. /images/graemlins/grin.gif