Whether you’re a punter or a matched bettor, we’re all trying to beat the bookies in order to make a profit. However, as matched bettors, we need to understand value and how value in bets determines the profit we will make over time.

The average punter will be down overall when betting with a bookmaker. They may get lucky and win more than they lose but over a lifetime of an account, the average punter will be down. This isn’t necessarily due to the punter being bad at picking winning bets but is more down to them not understanding value bets and the value they are getting at the odds offered by the bookmaker.

## How Bookmakers Make Money

Bookmakers aren’t gamblers and they know that they will make a profit in the long term from their customers. This is down to the odds which they offer to customers compared to the actual or ‘true’ odds of an outcome occurring. The difference in the odds the bookmaker provides and the true odds is called ‘The Over-round’.

**The Over-round is the bookies ****profit margin**

Let’s take a look at an example.

William Hill are offering the following odds on PSG v Liverpool tonight in the Champions League:

**PSG**: 2.05

**Draw**: 3.80

**Liverpool**: 3.30

In order to determine the probability of each outcome, we will use the following formula.

**Probability = (1 / odds) x 100**

Therefore, by applying the formula using the given odds by William Hill, we get the following probabilities:

Probability of PSG winning = (1/2.05) x 100 = 48.78%

Probability of a draw = (1/3.80) x 100 = 26.32%

Probability of Liverpool winning = (1/3.30) x 100 = 30.30%

The three outcomes listed above (Home Win, Draw, Away Win) are the only possible outcomes. Therefore, the combined probability of each one occurring should equal 100%. However, by adding the three probability percentages together, we get:

48.78 + 22.32 + 30.30 = **105.40%**

**Why do they not add up to 100%?**

The difference between the combined probability given by the bookmakers and the true probability of 100% is **the over-round**. In this case, the over-round is 5.4%, which is William Hill’s profit margin.

The outcome of an event doesn’t matter to a bookmaker as they create an over-round on every market and providing they balance their books to ensure the same margin is made across all outcomes, they will make a profit regardless of the result.

## Understanding Value

The example used above applies to all bets at standard odds provided by the bookmaker. They will always apply an over-round, thus making all bets bad value.

If this is the case, how do we make money from betting and ‘beat the bookies’?

The answer to this is to only place value bets. Specifically, bets which have a **positive expected value**.

Expected Value is a term you will see many times on ProfitSquad and you will often see it displayed as ‘EV’. You’ll find it in offer guides, on the daily calendar offers and dotted about the forum. It applies to ALL forms of bets from sports bets, bets on roulette, blackjack, slots and even when deciding whether or not to call a bet in poker.

## So what is Expected Value?

Expected Value (EV) is a term used when determining the value of an offer or bet. Unlike standard free bets where you know how much profit you will make prior to the bet settling, bets which have a positive Expected Value may not make you a profit everytime. The EV of a bet or offer is how much you can expect to make if you placed that bet an infinite number of times. Sometimes you’ll win, sometimes you’ll lose but the EV is the average profit (+EV) or loss (-EV) you’ll make.

A good example is how casinos make their money. Casinos have an edge on every game. For example, blackjack has a house edge of around 1%. This means that on average, the casino will make 1% profit from all stakes placed on Blackjack. If there are £100 worth of bets placed, the casino can expect to make £1 profit. Does that mean you can never win at blackjack? No. There’s nothing stopping you walking into a casino, playing one hand of blackjack, winning your hand and then walking out with a profit, leaving the casino down even though they have a 1% edge. However, if you played an infinite number of hands of blackjack at the casino, you could expect to make a loss of £1 for every £100 you staked.

The same principle applies to offers in matched betting. If the offer has a positive expected value (+EV) then it is **you** who has the edge and not the casino or bookmaker. Just like the casino in the example above, you’re not guaranteed to make a profit on every +EV offer, but do enough of them and the averages will even out and you will.

## How is Expected Value Calculated?

If you’ve reached this page looking for an explanation as to what expected value or ‘EV’ means, the section above might have answered your question. However, it is also good to know how EV is calculated in order to fully understand it.

EV can be calculated using a simple formula.

EV =** (**(probability of outcome 1) x (profit/loss of outcome 1)**)** + **(**(probability of outcome 2) x (profit/loss of outcome 2**)** + **(**(probability of outcome 3) x (profit/loss of outcome 3)**)** + and so on for as many outcomes as there are.

The formula above may seem daunting at first but there are only two variables you need to know.

- The probability of each possible outcome
- The profit or loss you will make if each outcome happens

### Calculating EV Example

A common example used to demonstrate the above EV formula is the toss of a coin.

If we toss a coin in the air, we know that when it lands there are two possible outcomes.

- It lands on Heads
- It lands on Tails

We also know that the probability of each outcome is 50%. Therefore, we can now put those variables into the formula to determine the EV.

Let’s say that we placed a £10 bet on the toss of a coin. If we win, we double our money, if we lose, we lose £10.

EV = (50% x £10) + (50% x -£10)

EV = (5) + (-5)

EV = 0

The EV of the coin toss is ZERO. This means that if we placed a bet on the toss of a coin an infinite number of times, we would break even.

## Calculating the EV of a Casino Bonus

Casino bonuses come in various forms with the majority having wagering requirements and other terms attached. There are two ways to calculate the EV of a casino bonus depending on whether or not there is a chance of busting. If there is a chance of busting and not completing the wagering requirements, then to determine an accurate EV, we need to simulate the wagering as many times as possible to get an average EV. To do this manually would be virtually impossible and so using an advanced Casino Calculator like the one available on ProfitSquad is the best option.

If there is no chance of busting then it is quite simple to calculate the EV of a casino offer.

Generally, a casino bonus is credited once a player has wagered a specific amount. Therefore, it’s best to split the process of calculating the EV into two parts.

Part 1: Calculating the cost of receiving the bonus

Part 2: Calculating the EV of the bonus

The Total EV for the offer will then be (the EV of the bonus – The cost of qualifying for the bonus)

We can calculate both of the above using the two formulas below.

**Qualifying Cost** = House Edge x Wagering Requirement

**EV** = Bonus Amount – (House Edge x Wagering Requirement)

### Casino Bonus EV Example

**Example Casino Offer:** 888 Casino are offering you 50 free spins worth 20p each when you wager £50 on slots. There are no wagering requirements on any winnings.

We decide to qualify for the bonus by wagering £50 on a slot which has an RTP of 97% meaning that the house edge is 3%.

Using the formula to calculate the cost of qualifying for the bonus, we get:

Qualifying Cost = 3% x £50 = £1.50

We now need to determine the EV of just the bonus. The bonus amount is 50 spins valued at £0.20 each (£10 total). The free spins need to be used and so have wagering requirement of just their value which is £10.

EV = £10 – (3% x £10) = £9.70

Now that we know the cost of qualifying for the bonus and the EV of the bonus, we can calculate the total EV of the offer.

Total EV = £9.70 – £1.50 = £8.20

This offer has a EV of £8.20 which is the profit we can expect to make if we played this offer an infinite number of times. As mentioned earlier, you will not make this profit every time you play the offer as sometimes you’ll make more, sometimes less and sometimes nothing. **£8.20 is the average profit you will make**.

## Calculating EV of Sports Offers

Just like casino bonuses, sports offers come in various forms. There are free bets, bonuses, money back on loss, free bet on loss, free bet on win, free bet if 2nd + many many more.

The creation of so many different bet offers from bookmakers can make it very confusing to a lot of matched bettors and punters as to whether or not there is value in them.

Let’s take a look at some of the most common types of betting offers and how you can determine whether or not they have a positive expected value.

### New Customer Offers

If you’ve done matched betting before then you’ll know that the majority of new customer offers from bookmakers have a positive expected value. The most common type of offer for new customers at bookmakers is a ‘Bet & Get’ offer. These allow you to receive a free bet when you first place a bet with your own money. You’re often able to lock in a profit by backing and laying your qualifying bet and then doing the same with your free bet.

Some bookmakers offer deposit bonuses to new customers. These bonuses are generally credited immediately after a deposit and require the player to wager the bonus amount or deposit + bonus amount a number of times before being able to withdraw the bonus funds.

So, do deposit bonuses have a +EV?

To determine the EV of a sports bonus we can use the following formula:

EV = Bonus amount – (wagering requirements x qualifying loss %)

Qualifying losses vary and so an average or estimate can be used in the calculation. Factors such as exchange commission, back odds and lay odds all have an impact on the qualifying loss of a bet but 5% is a reasonable estimate based on exchange commission of >5% and a good match.

**Example Bonus Offer:** A Bookmaker offers new customers a 100% bonus on their first deposit up to a maximum of £50.

Wagering Requirements: 4 x bonus amount

In order to receive the full £50 bonus, we would need to deposit £50. Therefore, the wagering requirements are 4 x £50 = £200 before the bonus can be withdrawn.

Using the formula above, and estimating our qualifying losses to be 5%, we can calculate the EV for the offer:

EV = £50 – (£200 x 5%) = £40

**Example of a -EV Bonus Offer**: A Bookmaker offers new customers a 50% bonus on their first deposit up to a maximum of £50.

Wagering Requirements: 8 x (deposit + bonus amount)

EV = £50 – (£1200 x 5%) = -£10

This offer has a negative EV of £10 which makes it unappealing.

**Important**: The EV calculations in the above examples are based on having to complete the full wagering amount. However, it is possible that you could lose your bonus funds with the bookmaker before completing the wagering in which case you may make a profit on the exchange. Therefore, the calculated EV is not 100% accurate and is based on a worst-case scenario of having to complete the wagering.

**Tip**: To reduce the qualifying losses when wagering bonuses, you can underlay your bets. Usually, when you back and lay bets, you make an equal qualifying loss whether your bets wins with the bookmaker or the exchange. If you choose to underlay your bet, you are able to make zero qualifying loss if your bet wins with the bookmaker and a slightly higher loss if your bet wins with the exchange. The advantage of this is that if your bet wins with the bookmaker, you retain 100% of the bonus as no qualifying loss is applied. If your bet wins with the exchange you make a higher loss but you do not have to complete any more wagering thus saving you money in the long term.

### Reload Offers

The EV of reload offers can be calculated in various ways depending on the terms of the offer. Below are some of the most popular offer types.

#### Free Bet on Win

These offers credit you with a free bet if you back a winner. One of the more popular offers in this category is from Betfair Sportsbook where they’ll credit you with a free bet up to £25 if you back a winner at odds of 3/1 or greater in selected horse races.

The standard way to play these offers is to simply back and lay a close match at odds of 3/1 or more and hope that it wins. If it does, you’ll get a free bet and if it doesn’t you’ll be down whatever your qualifying loss is.

Again, let’s assume that our average qualifying loss is 5% and that if we backed a horse at 3/1 we’d win roughly 25% of the time. This means that we would hit a winner once in every four races.

Betting £25 stakes, we’d have a qualifying loss of 5% x £25 = £1.25 on each race, giving us a total qualifying loss of £5 across the four races before we hit a winner.

We’d then receive a £25 free bet. Assuming we can extract 80% cash from our free bet, it’s worth around £20. Giving us a total EV of £20 – £5 = £15.

The above is based on backing horses at 3/1 and making a minimal qualifying loss. In reality, you may find better matches on higher priced horses which are therefore less likely to win the race. This means that you are more likely to go longer without hitting a winner which would reduce the EV of the offer. This is why it is important to consider factors such as odds, qualifying losses and the likelihood of the horse winning for these type of offers. Tools such as a Horse Racing Matcher can help you find good matches for selected races.

#### Money Back if Draw

Many bookmakers run this type of offer for Premier League matches and on major football competitions. It’s an easy offer to play by simply backing and laying a correct score and hope the match ends in a draw in order to receive a free bet. You’ll only receive the free bet if the match ends in a draw AND your bet loses and so it’s important that you don’t bet on a draw with your qualifying bet (0-0, 1-1, 2-2 etc) as it would be impossible to profit from it.

To calculate the EV for this offer we can use the following formula.

EV =** (**(Probability of outcome 1) x (profit/loss of outcome 1)**)** – **(**(Probability of outcome 2) x (profit/loss of outcome 12**)**

We first need to determine the possible outcomes. In this case there are only two – The match either ends in a draw or it doesn’t.

They are the only two outcomes that matter as they determine whether or not we receive a free bet.

**Probability of outcome 1 (match ending in a draw)**

To determine the probability of a draw, we can use the odds from a betting exchange and apply them to the formula below. We use the betting exchange odds as they are closer to the ‘true’ odds compared to those offered by the bookmaker who apply an over-round.

Probability = (1 / odds) x 100

Let’s assume that the odds on a draw in an eligible match are 3.0. The probability of the match ending in a draw would, therefore, be (1 / 3) x 100 = 33%

Next we need to calculate the profit or loss we’d make if the match ended in a draw.

Let’s say that we’re using £25 stakes on a correct score. This would mean that if the match ended in a draw, we’d receive a £25 free bet which is worth roughly £20 cash.

**Probability of outcome 2 (match NOT ending in a draw)**

The probability of the match not ending in a draw is simply 100% – 33% = **67%**.

The loss we would make if the match doesn’t end in a draw is our qualifying loss which may be slightly higher on correct score bets as close matches are generally harder to find. In this example we’ll use a qualifying loss of 10%, which is £2.50 from a £25 stake.

Now we have determined the variables for all possible outcomes, we’re able to calculate the EV of the offer.

EV = (33% x £20) – (67% x 2.50) = **£4.93**

## Arbitrage Betting

As well as bookmaker and casino offers, value can occasionally be found in bookmaker odds. This happens when the bookmaker back odds are greater than the lay odds for the same market on the exchange.

By simply backing a bet with the bookmaker and laying the same bet at lower odds on the exchange, you’re able to make a profit regardless of the outcome..

Arbitrage betting, or ‘arbing’ as it’s also known as, isn’t particularly recommended when matched betting as bookmakers may not take a favourable approach if they suspect you are looking for and placing arbs. If you place too many arbs with a bookmaker you increase you chances of being gubbed or stake restricted.

## Conclusion

Bookmakers and casinos have the edge when it comes to placing bets at their given odds under their own terms. In order to beat the bookie and turn the odds in your favour, you must find value in your bets. These opportunities are mainly available through offers and promotions used to entice customers back to the operator and by determining whether or not each offer has a positive expected value, you’re able to generate an overall profit.

Be smart with your betting and only place bets which have value. By doing so, you give yourself the best chance at beating the bookies and making a long-term profit.