Why sportsbooks make money
Why do the betting companies still make loads of money if the do not know the probabilities themselves, as you said?
It is neither of the two extremes that people think they might be. The one would be: „They balance their books so well that they win whatever outcomes will happen.“ The other one would be: „The calculation is still much more precise than you think. So they do know those probabilities. Whatever people bet on: the companies have the edge. That is the most obvious reason why they make money.“
As mentioned: it is neither of these two extremes. It is impossible with the more or less fixed odds (barring small adjustments here or there) to balance out their books to safely guarantee winnings. This may be the case in horse racing, „where it all began“, but not in any other sports or especially those fixed European odds. It is also not the case that they „know the probabilities so well“. The latter one does have a simple explanation why it is not the case: they do not need to be that precise. Why? Because any „obvious error“ in their pricing will pretty soon be discovered by some pros who then try to bet as much as possible. Instead of accepting this bunches of money the companies would instead take a little bit of money and adjust their price understanding this is an error. In the process the error won’t do them any harm any more. It is removed, it is extinguished, and even if they pay a small price for that.The pros will have an edge on their bets, so this equity on that is what the companies in fact spend. And this is not a lot and those obvious errors are not occurring that frequently.
Now we need to find out the real reason why they make so much money, as we all know. The reason comes here: the books may not be balanced out, which means in the end, that they still can lose if a certain team wins. And the price they lay on this team may even be based on some „bad calculation“ (so it is possibly higher than the true price), but still that would do no harm. And why now eventually? Because any other bet on this same game that landed not on the winning team is like a gift to them. Best would be to give a simple example: say they take like 10.000 Euro on a certain team to win for a price of 1.5. That means: the liability here is 15.000 Euro or rather 5.000 Euro of their own money (the 15.000 Euro are the so-called „swing“ which will be explained elsewhere).
Now even if the true price were like 1.45, giving all those people betting the 1.50 a edge, for that assumed miscalculated price. They still may have had other people betting like 1.000 Euro on the other chances (in football this would be draw or away side to win). These 1.000 Euro are not just a gift (which is also a proper term for it) but we can also consider it like that: it dumps the price they lay.
Simple calculation, part II: instead of the liability of 5.000 Euro the liability will be reduced to 4.000 Euro, by this „gift“. So in the end they lay a price of 1.40 and not one of 1.50. The 1.50 would really make them lose. They would bet on „the wrong side“. The punters spotting that (which also happens by coincidence; they do not know there is a mistake, they still bet it) have an edge. The bookmaker has an edge, too. Because the 1.40 he lays in the end still give him the edge (as 1.45 is the true price). So no worry for him.
We can describe this phenomena as well like this: at a betting company people are betting „against each other“. This makes it a pretty simple task for the company to make sure they make money no matter what (in the long run). But they well deserve it. They provide the entertainment people want. But as explained here: it is not a matter of „precise odds calculation“. So as soon as we know how to compile the prices properly for any given chance you can bet on we can still find the edge that we need. betty can do so for you.