The short answer
A bookmaker starts with an estimate of how likely each outcome is, converts those estimates into prices, adds a margin so the prices sum to more than 100 per cent, publishes them, and then moves them in response to what happens next.
The first part is modelling. The second part, the moving, is risk management, and it is where most of the interesting behaviour lives.
Step one: an opinion, converted into a price
The starting estimate comes from some combination of a statistical model, historical data, current information such as team news, and in many cases what other books are already showing.
Suppose a book lands on a two way market being a 60 / 40 proposition. The fair prices for those probabilities are 1 divided by 0.60, which is 1.67, and 1 divided by 0.40, which is 2.50. Those two prices imply exactly 100 per cent between them, which means a book offering them expects to break even and has no reason to open.
So the margin goes on. Shorten both sides to, say, 1.60 and 2.35 and the implied probabilities become 62.5 per cent and 42.6 per cent, summing to 105.1 per cent. That extra 5.1 percentage points is the margin, and it is charged to both sides of the market rather than to the outcome the book thinks will happen.
Step two: the price moves, and money is only one reason
Once a price is public it stops being purely an opinion and becomes a position. Two things move it.
The first is money. If one side attracts far more stake than the other, the book's liability becomes lopsided, and shortening the backed side while lengthening the other is the standard way to encourage the balance back.
The second is information, and it matters more than volume. A book pays attention to who is betting, not just how much. A large stake from a customer with no record of winning is treated very differently from a modest stake from an account the book reads as well informed. The second one moves prices faster than the first.
Books also watch each other. When a market that is generally regarded as sharp moves, others tend to follow, which is why prices across an industry often converge within minutes of a genuine piece of information arriving.
Where that leaves value
If every book modelled identically, moved instantly and watched each other perfectly, there would be no differences across books and nothing for a price comparison to find.
They do not. Books differ in what they model well, how much attention any given market gets, how quickly they react, and how much they care about a particular liability that day. A market that is central to one operator is a sideshow to another.
Value appears in the gaps that creates: markets priced with less attention, books that adjust later than the rest, and moments when new information has reached some of the market and not all of it.
What this does not mean
It does not mean bookmakers are bad at pricing. On the markets that matter most to them they are very good, which is exactly why the well attended markets are the hardest place to find anything.
It does not mean a price that differs from the rest of the field is wrong. Sometimes the outlier is the book that has seen something the others have not, and taking the odd price out of that market is the losing side of the trade.
And it does not mean a difference you can see is a difference you can act on. Prices move, stakes get refused, and a number on a screen is not a bet until it is accepted.
How to use it in practice
Compare like with like. Strip the margin out of both prices before deciding which is better value, because a book with a thinner margin can look worse on the headline number and be better on the fair one.
Look where attention is thin rather than where it is heavy, and pay attention to which books in your set move late. Those two habits find more than staring harder at a headline market will.
Assume the sharper price is usually the more accurate one, and be curious rather than pleased when you disagree with it strongly.