Sports betting question, co-related parlays

[youtalkfunny]

I'm no math wiz, just a former bookie, and I got bogged down in the numbers when trying to explain a simple concept, and I can't make the numbers work the way I thought they should.

QUESTION: in the game cited below, determine the probability of four possible outcomes:

Fav and over = ?%
Fav and under= ?%
Dog and over = ?%
Dog and under= ?%

Given:

--the pointspread is an accurate equalizer. Favorites cover 50%, dogs cover 50%, over 50%, under 50%.
--other than that, we're in the real world

So if we're betting 2-teamers, we can presume that, all things being equal, all four possible outcomes:

fav and over
fav and under
dog and over
dog and under

each come in 25% of the time.

Now let's take an example where all things are NOT equal

Fav State vs Dog U

Fav -30, over/under on the game is 33.

Let's say we throw in another given: In this particular game, with these lines, the chance of fav and under coming in isn't any where near 25%, but we'll call it 2%.

Can we determine how often the other three possible outcomes should be expected?

Or is it too unreal an example to cling to the notion that the lines make each proposition 50-50?

[youtalkfunny]

OK, maybe I was too vague.

Somebody tell me if this logic is flawed:

A. We're given that "fav and under" has a 2% chance.
B. We're given that the under has a 50% chance.

Does that mean that "dog and under" has a 48% chance?

[doughhater]

I don't have a ton of experience with correlated parlays, but I believe that you have to look at this from a conditional perspective. IF the game goes under, THEN the dog is obviously a huge favorite to cover. IF the FAV covers, THEN the game is a huge favorite to go over. However, I think that this correlation only exists in such an extreme example (have you ever seen a 30+ pt favorite and a 33 pt o/u). Or perhaps the correlation just becomes weaker as the examples become more realistic.

[youtalkfunny]

I heard that LSU was a 30-pt fav, and the total was 45. A friend said he had a bookie who would let him parlay the two.

I was trying to illustrate to a friend that "fav and under" had less than a 25% shot of coming in, and that "dog and over" also seemed to be less than 25%.

I found myself thinking that "Fav and under" might be as low as 10%. But I couldn't quantify "Dog and over".

Thanks for the reply, DH.