All the matchdaymaths. One place.

A football match is a sequence of chances. Each side creates them at a rate that depends on how good it is in attack, how good the other side is in defence, and whether it is at home. Every chance has a quality — most are hopeful, about one in ten is a real sight of goal — and it goes in with that probability. That is the whole physical model, and it is roughly what an expected-goals number is measuring when you see one on television.

To price the match, the model takes it exactly where it stands: this minute, this scoreline, these two sides. Then it plays the rest of it out three and a half thousand times. The share of those finishes in which the home side wins is the probability the home side wins. One divided by that is the fair decimal price.

Everything follows from the same runs, which is why the markets on this page agree with each other. The over 2.5 price and the correct-score grid are two views of one set of simulations, not two separate guesses — add up the scorelines with three or more goals and you get the over 2.5 price back.

A bookmaker does the same job with real clubs and far better data, and then adds a margin on top. The margin is the part this page leaves out.

Convert a decimal price to an implied probability by dividing one by it. A price of 2.00 implies 50%; 4.00 implies 25%. Do that for every outcome in a market and add the results together. If the market carried no margin at all, the total would be exactly 100%.

It never is. A typical Premier League three-way priced 1.57, 4.20 and 6.00 implies 63.7%, 23.8% and 16.7%, which adds to 104.2%. Those 4.2 percentage points are the overround, and they are what the bookmaker expects to keep from everything staked on the match.

The number to look at is not the margin but what it costs you: on a 104.2% book the house edge is 4.0% of turnover, because the margin is measured against the total staked, not against 100. The calculator in the tools section does both sums, and it will do them for any market you paste in from anywhere.

Every market on this page totals exactly 100.0%. That is not clever — it is what happens when you count outcomes and stop. It is here so that you have something to compare a real book against.

An accumulator multiplies the decimal prices of its legs, which is why a four-fold at modest prices returns a number big enough to be worth talking about. What nobody prints beside it is that the margin multiplies too.

A single leg carrying a 5% margin costs you 5%. Four of them cost 1.05 to the fourth power minus one, which is 21.6%. An eight-fold at the same per-leg margin carries 47.7%. The bet has not become worse value at each step; it has become worse value at a compounding rate, and the size of the potential return is precisely what hides it.

The slip on this page prices accumulators from markets with no margin at all, so the figure it shows is the fair price. Beside it, it shows what the same accumulator would be worth if each leg carried a typical 5% — the gap is the whole argument.

None of that makes an accumulator a bad way to spend a Saturday. It makes it an expensive one, and worth knowing the price of.

Possession tells you who has the ball and almost nothing about who is going to win. A side defending a lead gives the ball away deliberately, and its possession figure falls while its win probability rises. Watch the price on this page during a match where the home side leads and the possession bar goes the other way — the model is not confused, possession simply is not the thing that decides matches.

Shots is better, and shots on target better again, but both treat a tap-in and a hopeful thirty-yarder as one unit. Expected goals fixes that by weighting every chance by how often a chance like it is scored. A side that is 0-1 down with 2.4 expected goals to 0.3 has been unlucky in a measurable sense, not in a pundit sense.

The one number a betting page can add is the probability itself, and the honest way to show it moving is to show what moved it. That is why the feed and the prices sit side by side here: a clear chance saved changes both.

Every Gambling Commission licensed operator has to offer deposit limits, reality checks, timeouts and self-exclusion, and is obliged to apply them once you ask. They are in the account settings, not hidden behind support.

GAMSTOP will exclude you from every GB licensed online operator at once, for six months, one year or five years, from one form at gamstop.co.uk. It cannot be undone early, which is the point of it.

Football is the sport the industry markets hardest, and a club you care about is exactly the thing that makes a bet feel like something other than a bet. If it has stopped being entertainment, the National Gambling Helpline is 0808 8020 133, free and open at any hour, and BeGambleAware.org has the full picture. Those are better first calls than any betting site, including this one.