The bookmakers’ business

Understanding the mathematics and mechanics behind bookmakers’ business is essential for the knowledgeable punter. In this article we showed how we can calculate our expected payout of a bet and why we are almost always destined to lose providing that implied probabilities by the bookmakers are fair.

However we defined in which situations value opportunities arise – when true probability of an outcome is higher than the one implied by the bookmaker.

But now comes the question why bookies would deviate from fair probabilities and set some other odds thus creating opportunities for value bets? Nowadays bookmaker houses have at their disposal an army of quantitative staff, technical tools and predictive algorithms so they are ultimately very good if not best in determining the right probabilities for an event. However this is not their ultimate goal.

Bookies need to make money. They do so by trying to “balance the books” in a particular market. In other words their goal is to receive the stakes for the different outcomes in a market in such proportions that they make a profit. No matter what the outcome is. Let’s try to explain this by an example. Consider an over/under 2.5 goals market in European football event:

If the bookmaker receives the bets in the proportions specified in the above example then he will do profit no matter what the outcome is. This is so due to the margin he charges (recall here the concept of bookie’s profit margin) and the right proportion of bets.

However bookies can not control the ratio of stakes they get. Punters’ money flows are influenced by news, favorite teams, gossip and the like. It is very likely that bookies will receive the bets in totally different proportions. One of which is like in the example below.

In the given case if the game finishes Over the bookie will record a loss of EUR 1900 and if it finishes Under then a profit of EUR 2479. This is a perfect example of an imbalanced market from the perspective of the bookmaker. Remember that noone knows how the game will finish no matter what odds are. And knowing that the bookie is there to make profit the only way to get out of this unfavorable situation (where one of the outcomes results in a loss) is to deviate from odds. By doing so he can influence the market and prevent punters from betting on one event, respectively seduce them to mount bets on the other.

Practically if the bookie decreases the odds where he expects losses, i.e. Over and increases the odds where he has expected profit (Under) he can try to balance his book. What if over the course of the next days the bookie alters offered odds and accumulates bets to the following amounts:

Great, by changing the odds the bookmaker has effectively influenced the money flows. He has created a pretty favorable situation in which he is profiting in any way. Simultaneously however this situation also reveals huge opportunities for the bettors. Because the bookmaker deviated massively from initial odds (which let’s assume were the fair odds) he created also opportunities for the experienced punters. Only by changing the odds to balance his books doesn’t mean that the true probabilities for the Over/ Under market changed. Therefore the intelligent punter might have encountered a value bet.

Football 1X2 probabilities guide – OddSmash

When it comes to football and betting, we seldom think of 1X2 probabilities but consider only the odds of each event. Yet it would be much more informative if we knew what implied probabilities are behind these odds. But how can we extract probabilities out of odds?

Before we answer the question, we need to remember that there are probabilities inclusive bookie’s profit margin; and implied probabilities exclusive bookie’s profit margin. In the below article I will be referring to European football example and European odds format.

Probabilities inclusive bookie’s margin.

Consider the following football game.

Football 1X2 probabilities between Manchester United and Arsenal can be extracted from bookie's odds.

Probabilities can be found simply by dividing 1 by the odds of an outcome.

Calculating football 1X2 probabilities is simple. Just divide 1 by the odds of each outcome.

Yet there is a little trick. If we sum up all the results we get the following:

Total = 45% + 31% + 28% = 104%.

It turns out that the summation doesn’t equal exactly 100% but surpass this threshold. The margin above 100 is simply called overround. Effectively this is the bookie’s profit for providing you the service and assuming the risk in the betting business. Therefore by cutting the odds across all three outcomes, the bookie creates unfair market for his own gain.

To grasp the concept of bookie’s profit let’s use the same example viewed from another perspective. Can we try to answer the question: How much shall we stake at each event, so that we return EUR 1 regardless of the outcome? Well, the above results 0.45, 0.31 and 0.28 can be exactly viewed as the euro amounts, we need to stake at each of the odds – 2.2, 3.2 and 3.6 in order to get a profit of EUR 1.

But if we do so then we will stake EUR 1.04 and the bookie will pay out just EUR 1 regardless of the outcome. As a result the bookie records a mark-up of EUR 0.04 each time he must pay EUR 1. We are destined to lose no matter what the outcome is.

Probabilities exclusive bookie’s margin

Now we get back to the probabilities exercise. In order to exclude the bookmaker’s overround from the equation we need to do some final manipulation. We figured that for each EUR 1.04 that the bookie receives he pays out EUR 1. This means simply that the bookie’s payout share is:

PO share = 1 / 1.04 = 0.96.

Therefore the bookie pays out EUR 0.96 for each EUR 1 received.

Furthermore if we multiply the payout share by the probabilities inclusive margin, we will arrive at the implied probabilities exclusive margin.

Multiplying 1X2 probabilities by bookie's payout share results in implied probabilities exclusive bookie's profit margin

We make the check and sum the numbers:

Total = 43.5% + 29.9% + 26.6% = 100%.

That is how punters can extract probabilities out of odds and ultimately assess the game from another angle. Bookies’ profit margin is part of the game. Sometimes it may be much more than the example given here, sometimes less. But it is always there.

Above all, the example has huge implications on value betting comprehension and payout analysis. By slashing the odds to charge a mark-up the bookies are effectively creating unfair market. As a result we are on the losing side always when we place bets. Read more about payout and value betting analysis here.

Bookmakers have the edge by applying an over-round and in the long-term it’s not possible to make a profit in case odds are fair. Is it worth pursuing betting opportunities at all and can we ever consistently make profits?

Well the answer is yes. There are plenty of occasions when bookmakers do price selections incorrectly – occasions that are usually known as value bets. Read more why bookies deviate form fair odds here.

Weekend football moments 1 – Nov., 01/02

Another football weekend looms. Premiership Saturday program offers value at Chelsea, West Ham and Sheffield United;

Man. United are of no value at these odds when they visit Bournemouth in early Saturday afternoon. Out of 69 games with a rating of +3 over the last 5 seasons, 62% finished with a home win. Hence, our statistical models associate fair coefficient for Bournemouth of 1.85. The game certainly offers emotions for the risk taking punters.

Many more value encounters in Spain, Italy and Germany. Worth mentioning is Bayer L.- Monchengladbach encounter where the visitors are priced at stunning odds of 3.5. A goal rating system assigns probability of 57% for Monchengladbach and fair odds of 1.73.

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Weekend football moments 2 – Oct, 26/27

Sunday football program across England, Germany, Spain and Italy offers several lucrative encounters and value opportunities.

Remaining games in Premier league are least appealing and if something grabs the attention is Arsenal – Palace game where the hosts have only one win in the last 6 games while Palace has just one loss. With a rating of -3 the home odds definitely don’t represent value; draw and away (or combination) on the other hand are worth exploiting with generous prices offered by the bookies.

In Spain Sociedad away chances at Celta look underestimated by the bookies bearing in mind the game rating of -11. Both Granada and Levante home encounters with Betis and Espanyol respectively offer significant value for the hosts.

Plenty of opportunities in Seria A and two home value deals in Bundesliga.

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Weekend football moments 1 – October 25/28

Another weekend with plenty of football opportunities across top European leagues. In Premier League tough fixtures overall. Watford vs. Bournemouth offers significant value with bookmakers odds at 3.44 for the away win vs. fair odds of 1.55. Yet users should be reminded that one single game (Watford loss at Man. City by 8-0) is tilting the rating to the extreme.

Fair chances for home, draw or away at Burnley – Chelsea fixture look more leveled than priced by the bookies. For the risk oriented punters potential Chelsea upset might be pursued here.

Tempting encounters in Bundesliga on Saturday with a few home wins hiding value – Hertha, Freiburg and Schalke

Seria A doesn’t feature interesting opportunities from value point of view on Saturday while LaLiga Valladolid home game against Eibar looks stimulating.

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Always check teams’ news and qualitative information before taking a decision.

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Weekend moments 2 – October 19/20

Only two games left in Premier League agenda with attention definitely on Manchester United – Liverpool derby on Sunday. Bookies’ odds and Goal Rating odds are roughly equal. Historical analysis over the last 5 seasons reveals 34 games with a rating of -12 as 67% of them finished with away win. This translates to fair odds of 1.47. After statistical modelling and smoothing our OddSmash odds stand at 1.64.

More interesting from value point of view is Sheffield United – Arsenal encounter on Monday night. Bookies are underestimating Sheffield chances with a hefty average odds of 3.9 for Home win against fair odds of 2.23 (45% chance). Draw no Bet markets and Asian Handicap might be good alternatives here.  

In La Liga both Alaves and Real Sociedad respective encounters hide value for Home wins.  Villarreal away chances against Espanyol are higher than priced by the bookies.

Several interesting games also in Germany and Italy.

For more in depth analysis check

Always assess qualitative information (injuries, absents etc.) before taking a decision.

Weekend Moments -October 19/20

Three solid games worth a try on Saturday afternoon in Premier League.

Everton – West Ham: with Everton having just one win in the last 6 games and West Ham having just one loss, bookies are pricing in a roughly 50% chance for a home victory.
Goal rating probabilities for the game are reversed though with West Ham chance estimated at 64% translating into hefty average odds of 3.76. For more risk averse punters Draw/Away double chance or Draw no Bet markets look promising.
Punters are strongly advised to check qualitative data before deciding on placing bets.
Two other games (Aston Villa – Brighton and Bournemouth – Norwich) reveal value in case of home victories.
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Value bets and expected payout in betting – OddSmash

When we bet we rarely ask ourselves the following two questions:

1. What is our expected payout ?
2. Do we face value bets or not ?

Let’s try to address these questions. In the below example I will be referring to European football and European odds format. Consider the following game.

Odds for 1X2 full time result market between Manchester United and Arsenal and Implied probabilities for each of the outcomes. Through odds and probability only we can determine expected payout and assess value bets

In order to determine our expected payout per EUR 1 stake we need to simply multiply probability by odds. For example if we take DRAW for each EUR 1 stake payout will be:

PO = 3.2 x 29.9% = EUR 0.957.

It turns out that we are losing because we get EUR 0.957 for every EUR 1 staked.

Furthermore here comes the value assessment question. A payout of less than 1 means we are losing in the long term. A payout above 1 means we have a value bet. Because we are getting more than EUR 1 for each EUR 1 staked.

We can try to explain the same concept in a more intuitive way. Let’s assume MUFC and Arsenal were to play hypothetically 10 games. DRAW has 30% chance of happening. As a result this means that 3 out of these 10 games will be expected to finish DRAW. Therefore if we stake at these 10 games each time EUR 1, we will have a total stake of EUR 10. However we will get back only:

PO = 3 DRAWs x 3.2 x EUR 1 = EUR 9.6.

So we get EUR 9.6 for a total stake of EUR 10.

This is what unfortunately happens most of the times and punters seldom understand it. Statistically speaking we are on the losing side almost all the time. In a way it is true that if we get the DRAW correct, we will have a nice return on our stake one time. But if we systematically stake on such games with similar payout properties we will be losing in the long term. Because this DRAW is going to be less likely to repeat in time.

So what can we do? Odds are fixed and set by bookies. Consequently we can’t change them. However probabilities are something that no one knows for sure.

For instance imagine we knew that in the above example the true probability of DRAW was 40%. Therefore payout would become:

PO= 40% x 3.3 = 1.32.

This means that for each EUR 1 staked we will be getting back 1.32. In other words if 10 games were played, we would bet a total of EUR 10 but get in return:

PO = 40% x 10 x 3.3 x EUR 1 = EUR 13.2. Not bad.

Ultimately arise two other questions:

1. Why would bookies deviate from fair odds and set prices we see. Read here.

2. How to determine fair probabilities. One alternative way to do this is to use a goal rating system.