Oh, then I’m not sure how the parents points (about “betting against the house”) are relevant, because sports betting (unlike casino games) doesn’t do that.

When sports betting, unless using a betting exchange such as Betfair mentioned above, or a totaliser agency, you'll likely use a bookmaker. The bookmaker is effectively the house. The bookmaker will set a market (make book) of prices on a certain event. You can choose to take the price offered and make a bet, or not. Essentially the bookmaker is pitting their skills and knowledge against yours.

The bookmaker will want all prices offered on the event to be in excess of 100%. The over round is where the bookmaker makes their profit. As an example, in a horse race, the percentage probabilities of all odds offered might add up to a total of 115%. That 15% is the bookmaker's margin.

Now, of course, the bookmaker doesn't necessarily profit in every race, but they should be trying to balance their book before the off, to insure that whatever the result they profit. They can do this by laying off liabilities with another bookmaker, shortening the odds on some runners, or just closing the book.

As a bettor, one should be trying to not just find the winner of races, but also prices which are wrong. If you assess the true odds of an event happening (let's say a horse winning) are better than the prices offered by the bookmaker, then it should be profitable to bet those prices in the long term. For example, if you think a horse has a 25% chance of winning the race, but the bookmaker is offering a price of 6/1 (7.0 or roughly 14%), then you have the odds in your favour and should make decent margin over time.