Rowdie: Mathematical football prediction and betting tips

How bookmakers make the money

Let’s start simple. Imagine you flip a coin. The chance of landing Heads is 50% and the same one is for Tails. Knowing this, try to imagine, you are the bookmaker and want to make money.

What would happen if you simply offered the odds 2.0 (representing 50% chance) for both cases? Try to imagine you have 10 punters. 7 of them would bet on Tails and 3 of them on the Heads. To make it simple, let’s imagine all of them bet £1.

Result 1. Coin lands on heads and you are happy because you gained £4 (7 bettors lost and 3 bettors won)

Result 2. Coin lands on tails and you lost £4 (7 bettors won and 3 bettors lost)

Looking at this example, the whole odds thing makes no sense at all. In the first case result by pushing the odds by 10% towards your favour (odds 1.9), you would gain extra 40p. In the second case result, you would lose 40p less. In any case, you are losing or winning and it looks like you are on a wacky field of chance, which sooner or later turns against you.

And now let’s look at the missing part of the theory of “How bookmakers make the money”. (Now we are leaving out the bookmaker scammers from this story.) As we are claiming in betting basics, bookmakers are not the risk takers. Here are the reasons:

  1. With the 50% chance they will not give you the fair 50% odds. This means by coin toss you will not get the odds 2.0 but lets say 1.9 – this gives you as a punter lower chances (example: your bet £100 x 1.9 odds = £190 – your bet £100 = £90). The bookmaker with this action increased his expected long term profit by 10% against the real probability. Please look at the details of how probability converts to odds to understand my point.
  2. Per day there are hundreds of matches. Let’s substitute this for “Per day there are hundreds of coin tosses” to make it easier to understand. Let’s say the odds are as in the table which gives us the bookmaker’s market margin 1,0526  which is 105,26%. Expected bookmakers profit in this case is 4.99% for each line.
Heads Tails
1.9 1.9

With one coin toss the bookmaker wins or loses, but the theory of chance says with unlimited count of coin tosses, you will end up landing 50% Heads and 50% Tails. With the odds moved by 10% towards your favour, you will earn on average 4,99% on each bet.

Now this betting theory is just the beginning. You can easily say with 100% accuracy what the odds are with coin toss. With football matches it however gets really complicated, and this is your chance to win money in football betting. Let us look at the odds of El Clásico (Real Madrid – FC Barcelona). We know both of the teams are about the same strength. FC Barcelona is one position higher in the table but Real Madrid has the home advantage.

Real Madrid – FC Barcelona

1 X 2
2.59 3.50 2.87
38,61% 28.57% 34,84%


With these odds, the bookmaker is having incredible 98% payout and only 2% profit. Converting the odds to probability we get the numbers shown in the third row. This actually confirms the similar strength of both clubs.

Let’s look at the results of their last 10 encounters.

Real Madrid Barcelona 3–1 (1–1)
Barcelona Real Madrid 2–1 (1–1)
Real Madrid Barcelona 0–4 (0–2)
Barcelona Real Madrid 1–2 (0–0)
Barcelona Real Madrid 1–1 (0–0)
Real Madrid Barcelona 2–3 (1–1)
Real Madrid Barcelona 0–3 (0–0)
Barcelona Real Madrid 2–2 (1–1)
Barcelona Real Madrid 5–1 (2–0)
Real Madrid Barcelona 0–1 (0–1)


It is more than obvious Barcelona is doing much better in El Clásico. Barcelona won 6 out of 10 matches, 2 were draws and only 2 times was Real the winner. On the home field, won Real only 1 match out of 5 and there was no draw. Looks like the best mindset to bet is to consider the fact that Real is simply not doing well in the bout against Barcelona.

But now the most important question. How does the result from 5 years ago or even a year ago influence the result of tomorrow’s match? Maybe in a big way, maybe not at all. Are the same players still there? What form do they have? Is really a draw not an option here? These and many more questions you are supposed to answer to see if there is a space for value bet. The following video gives you a little insight and the story continues underneath.


How do you create the odds for teams which are not the same strength?

Let us look at the teams Southampton – Liverpool, which in 2019 were clearly not the same at all. How would you assign the odds? Liverpool is clearly the favourite, but what chance would you give to home win, draw and guest win? This is where the magic happens! There is no guarantee that the odds of the bookmaker are better than yours, especially if you have the deep knowledge of the league. If there is a discrepancy between your personal odds and the ones of a bookie, it is your chance!

Let us look at the odds and chances given by a bookmaker

Southampton – Liverpool

1 X 2
7.25 4.50 1.44
13.7% 22.2% 69.4%

The bookmakers payout here is 94,8%, but why such a distribution of probability? Why do they think Liverpool has a 69% chance of winning the match? And now here come the questions you are supposed to ask.

  • Are the odds reflecting reality?
  • Are the odds against Liverpool just lowered because of the amount of punters betting on them?
  • Do you see the chance for Southampton on the level of 25% and for a draw on 35%?

This is not the end of story

Bookmakers are trying to make money on each match. Let’s look at the next table where the real odds from [league 2] soccer match are being displayed. The pre-match odds between Liverpool and [team 652] were as follows.


Result 1 X 2
Odds 1.3 6.00 11.00
Probability 0,76923 0,166666 0,090909
Bet amount 749 200 162 300 88 515
Pay out 974 000 974 000 974 000

The calculated bookmakers payout rate is in this case 97,4%. This means out of one million in bets, the bookmaker is trying to keep for himself 26 000 (100% – 97,4%) x 1 000 000. You can reach this number by redistributing the bets between the individual results.

And here comes the magic. It would be too risky for the bookmaker to have the whole million placed on a draw. They need to redistribute the stakes so the outcome will be as close to those 26 000 as possible, no matter how the match ends.

In the table you see the most important number in the fourth row. It means how much in total the bookmaker needs the punters to bet on that 1 or X or 2 to gain those 26 000. If you make a sum of the row, you will get the total of 1 000 000.

In the last row you see the amount of pay out. 1 000 000 – 974 000 = 26 000. The bookmakers are having “real time monitoring systems”, which show them recommendations about how to move the odds to get to the desired result.

I am giving you just a rough idea and example since things are indeed not as simple. As we dig deeper (especially from the bookmakers point of view) we see also risk managers and other departments being involved. We get to make it more complicated with the combo tickets, double chance betting, hard to predict Asian handicaps – or other markets indeed. Besides that the small bookmakers are most of the time outsourcing the odds management, which makes them slightly more vulnerable.

Now do your homework before betting for real. Look at the upcoming matches of the league and sport you are familiar with. Create your own odds and then compare it to bookie’s odds. What was the result? Were your soccer betting tips more accurate than those od a bookie? Bet only pennies to test your skills first.


How bookmakers make the money. Redistribution of stakes and market margin are the base of the earnings

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