From a football perspective, although we personally limit ourselves to analysing only the previous five seasons’ data with the Soccerwidow HDAFU Tables, or the previous 10 calendar years’ match results with the Soccerwidow Value Calculator, data on Oddsportal is in fact available for the last 20 seasons or more in leagues with enough popularity and longevity, such as the English Premier League.

Signing-up is simple and places no obligation on you whatsoever. Our own account was set up many years ago and in all that time we have received no emails of any kind from Oddsportal, its partners, or any associated spam, a rarity following sign-ups of any nature these days.

Oddsportal’s priority is to achieve sign-ups via their site to the bookmakers they feature in order to earn affiliate commission from those customers. You don’t have to sign-up with any bookmakers, but you can continue to use all of Oddsportal’s features as a registered member.

However, if you choose not to register for an account, you will be restricted to seeing and exploring the odds of just a small selection (usually 14-16 in number) of the 80+ bookmakers Oddsportal features at any one time.

As an aside, Soccerwidow is not affiliated in any way with Oddsportal but owing to their importance in the grand scheme of things, we are always happy to recommend them.

Once you have registered and signed-in to your account, you will need to customise your Oddsportal layout. In the top right hand corner of the home page you will see the settings button illustrated with a small cog symbol (next to the “logout” button).

You will then see the various settings options. Here is a screenshot showing Soccerwidow’s settings, which we use to facilitate our own data scraping and odds checking:

Oddsportal Settings Screenshot

**Notes:**

- The “Primary Type of Odds” setting refers to what you see when you open any individual game. If you choose the AH (Asian Handicap) O/U (Over/Under), or any of the other options, then that bet type tab will be the first you see. However, it will always be the 1X2 odds displayed when initially opening a league.
- It is usually quicker to see which bookmaker is offering the best odds if you “Sort bookmakers by”
__bookmaker payout__. The bookmaker list of the matches you open will then appear roughly in descending odds order. The highest 1X2 odds time-stamped most recently will usually be in the top half of the list. (But of course, usually no one bookmaker will be offering best price on all three outcomes, so you will have to hunt for them). Here’s a quick example of bookmaker payout order:

Oddsportal Bookmaker Payout Order Screenshot

**Next Page: My Bookmakers Tab; Problem Bookmakers; Manage My Leagues**

They are a complete statistical analysis of historical performance over the previous five seasons of the **H**ome win, **D**raw, **A**way win, **F**avourite win and **U**nderdog win (H-D-A-F-U). They serve to identify the most profitable odds ranges in each bet type.

To help you understand why we value this product so highly, here is our **Definitive Guide** for using the 6th Generation tables to their maximum potential.

If you wish to work along with the example in this article you can download the relevant HDAFU table **FOR FREE** here.

Please note that this is a basic, abridged version but includes everything you need to work through this User Guide).

*The size of this Excel .XLSX workbook is 864 KB.*

It’s difficult for us to put into words how important the HDAFU tables are to us and our own betting adventures. But what we can say is that we have complete confidence in them to do their job. And from testing them in a live setting, we know that they are an extremely reliable method of building lucrative betting portfolios.

Quite simply, they are the best and most user-friendly tools available for nailing down value betting systems in **every league you apply them to**.

They reveal the DNA of a league, and provide a hidden level of detail that makes finding and exploiting the sweet spots so easy and so rewarding.

The next six steps will probably change the way you think about betting…

The first thing you will see when opening the Data Tab in any of the HDAFU tables is the financial summary of each bet type.

**(Click on the image below to enlarge it in a new tab):**

The totals along the top row show the effects of betting on every match over five seasons. In our example league the totals are (from left to right) Home win (-7,329), Draw (-835), Away win (+8,236), Favourites (-2,594), and Underdogs (+3,501).

You can see from this graphic that away wins look the most promising backing system with a profit of 8,236 units from 100 unit stakes.

To customise the stake amount enter what you want in the Fixed Stake box at the top of each bet type in the Data Tab.

The image above shows the full five season cold analysis. If you enter a different stake amount the financial values will change, but the percentages will always remain the same. This being the case, we have fixed these percentages as a benchmark to better gauge the improvements we will make with our filtering exercise later.

The **Odds Toggle** is for testing the effects of the odds you are getting when playing the systems for real – you can ignore it during your analysis.

You can also leave the betting exchange commission rate at zero. Again, use it for backing system monitoring purposes when you start betting on or paper testing your systems of choice.

Okay, we fancy away wins in this particular league but let’s now have a look at the Inflection Points Tab to see if this backs-up our observation.

**(Click on the image below to enlarge it in a new tab):**

Away wins are certainly financially the most profitable bet type but the profit curve doesn’t really begin rising until odds of 3.30 are reached. Overall profit at this point is 463 units and this rises to a peak of 13,502 units around odds of 8.60.

These two points on the graph would therefore be our two inflection points: Odds of 3.30 where the curve begins to rise; Odds of 8.60 at the pinnacle, the point at which profits begin to fall again.

However, notice there is a big portion of the away wins curve which is a zero-sum game. This ‘hole’ in our profit curve begins around odds of 3.75 (6,653 units). At this point, the curve falls away again, encounters what we call ‘statistical noise’, and only recovers at odds of around 6.52, when the profit figure surmounts its previous high at 7,184.

In between these two points is the potential for a lot of wasted effort and not a lot of gain.

We can see the extent of this by scrolling down and looking at the inflection point intervals.

**(Click on the right-hand image to enlarge it in a new tab):**

This image shows the start of the 3.75 odds sector at the top and the end of the 6.52 odds sector at the bottom.

The yellow column indicates the running total of matches up to each cluster of matches.

We can see that our two odds of 3.75 and 6.52 encompass roughly 330 matches – the difference between 1,115 indicated at the 6.52 break-off point and 785 at the starting point of the 3.75 cluster.

That’s 330 bets over a five season period that are simply not worth making; or 66 bets in a season.

We can see this clearer by looking at the same snapshot between our original inflection points of 3.30 and 8.60.

**:(Click on the left-hand image to enlarge it in a new tab)**

In this odds range, we have roughly 587 bets (1,221 minus 634). We now know that more than 56% of these (330 bets) are not worthwhile making.

This leaves only 257 bets but the away win profit sectors between the inflection points seem to be split into two areas of the curve: from odds of 3.30 to 3.75 (medium risk system, accounting for around 160 bets), and then from odds of 6.52 to 8.60 (high risk system; around 100 bets).

If we were to continue our analysis of away wins we would eventually see that the three elements (the medium risk sweet spot, the high risk sweet spot, and the statistical noise in-between) combine to give us a bumpy ride.

Our expected hit-rate will be tempered by that area of noise, and yield will be lower because of the size of the zero-sum area and the number of pointless bets within it.

This means a lot of unpaid work to perform, placing many bets that maintain the status quo and not much else. On top of this, the losing streaks will be greater.

The synergy we have mentioned before about many systems supporting each other is what makes the HDAFU betting systems so viable.

However, we also mentioned that you should find the **single best system in a league** to play alongside the other best systems in the other leagues within your portfolio.

In our away win example, we would need to choose the better of the two systems we have identified. Either backing away wins at odds between 3.30 and 3.75, or between 6.52 and 8.60. Choose one or the other, not both.

We recommend never to play multiple systems in the same bet type. The synergy effect is diminished as ultimately, one of the two systems is not the best we can find.

Ideally, we are looking for synergy between the absolute single best systems in each league within our portfolio, without creating a situation where one system supports another within an individual league.

With different bet types in the same league (e.g. 1×2 market and over/under goals market) this is not an issue, but we would go as far as avoiding the conflict of interest between HT and FT 1×2 systems in the same league, for example.

Have a look once again at the Inflection Points graphs to try and see what it is.

As is typical of an **underdog** backing profile, the high risk/high return nature of this bet type produces a noisy curve, one full of jagged peaks and troughs. There are only small rising areas to analyse. Anything you can analyse into promising profits will contain few betting opportunities in a season, with long runs of losing bets to cope with.

Backing the **favourite** has one area between odds of 1.90 and 2.10 but we can see at these odds not a huge profit is created over five seasons (less than 3,500 units).

The **home win** is a misery for backing. Again, the sweet spot is between 1.90 and 2.10 but the profit is less than 2,000 units.

That leaves us with backing the **draw**. There is a large, rising area in the curve beginning at draw odds of 3.32 (-2,008 units), and peaking at 3.65 (7,170 units). It represents a potential profit chunk of 9,178 units over five seasons.

This is better illustrated by superimposing our inflection points onto our graph – We are interested in only the portion of the curve in-between the red arrows:

The shape of this curve is what you should be looking for when identifying the first system to analyse in your leagues of choice.

It is the classic, gently rising curve from bottom left to top right. It is relatively smooth, with a far smaller amount of statistical noise.

Therefore, this is the bet type we will analyse as our example.

]]>In a betting context, emotions are a killer: too many emotive decisions will see long hours of preparatory work wasted and all expectations of success quickly dashed.

It is certainly not easy to lay all emotions aside but, unfortunately, there is no alternative if you wish to achieve long-term success!

Let’s look at a dictionary definition of *emotion*:

- A strong feeling deriving from one’s circumstances, mood, or relationships with others.
- Instinctive or intuitive feeling (gut feeling) as distinguished from reasoning or knowledge.

If you lack the right mental attitude before entering the betting arena, then you are already a casualty.

You’ll come out of the experience bruised and bloodied, confused as to what went wrong, when all you had to do was follow the black and white rules of your own system.

We see the same pattern, over and over again.

People write to us explaining their good intentions based on really good strategies they have found, formulated over weeks, months, sometimes years’ of statistical analyses.

All starts off well and they proudly report their initial successes until they burst their own bubble:

- The system is successful and produces profits but not quickly enough. Patience expires and greed takes over.
- Gut feeling replaces the mathematical predictions and, instead of staying in the statistically ‘hot’ zone, selections are made outside of these very carefully calculated criteria.
- Discipline becomes erratic and one or more rounds of betting are missed or ignored.
- Losses are chased.
- Too many adjustments to the original script are made as the season unfolds in response to undesired results.

One of our betting friends is in regular contact with us and he is highly skilled at identifying potential lucrative systems. He is representative of thousands of other bettors.

From our 2015-16 **German Bundesliga HDAFU Table**, which contains the previous five seasons’ statistical data, he was able to filter out a successful and very promising betting strategy.

*Betting on all 17 home games of SV Hamburg with 100 unit flat stakes, the system was simple: back the underdog (the team with the highest odds), regardless of whether that be Hamburg at home or the away team.*

Just one potential problem: our friend was (and still is!) a huge Hamburg fan.

On 22/08/2015, Hamburg hosted Stuttgart in their first home game of the season. The underdog was Hamburg at odds of 3.0. With early season excitement, our friend placed his first bet and won when Hamburg recorded a 3-2 victory. His team won and his bet won – double joy!

Next up, on 19/09/2015, was Hamburg’s home game against Frankfurt, the underdog. Emotional problem: back Frankfurt to win, despite supporting Hamburg. Nevertheless, logic prevailed and the bet was placed. The game ended 0-0 and the first 100 unit stake was lost.

On 26/09/2015 Hamburg played Schalke, and this time, the home team was the underdog. Again, sticking to his carefully calculated system the bet was placed, but lost when Schalke won 0-1.

Three rounds and no further forwards.

Three bets placed, one winner with a return of 200 units and two losers with a total loss of 200 units. Square one. In fact, less than square one when factoring in the wasted time so far.

The fourth round was on 17/10/2015, Hamburg against Leverkusen, with the home side again the underdog. The bet was placed, the result was 0-0; the system now recorded an overall loss of 100 units.

Gnawing doubt set in.

In the fifth round, on 01/11/2015, Hamburg played host to Hannover who were priced at the longest underdog odds so far; 4.35. After three consecutive lost bets, our friend abandoned his system and backed the favourite, his own team, at odds slightly over 2.0. Of course, Hannover went on to win the match 1-2.

Five rounds, one win, 200 units lost. Could it get worse?

Hamburg played Dortmund on 20/11/2015, and Hamburg were long odds of 9.0 to secure a win. Knowing his own team inside-out, our friend decided Hamburg had no chance at all and chose not to place the bet. Of course, he had the *fans’ consolation* when his team overwhelmed the favourites, 3-1!

So, after six rounds, our friend had placed just five bets, with only four of them within his original selection criteria. His losses were 200 units. Had he stuck to the plan and bet on all six underdogs, his profits would have been 1,135 units!

Could it get even worse?

You already know the answer!

He was at a party on 05/12/2015 when Hamburg played Mainz. Already feeling sore about the ‘ones that got away’, he decided to have a good time rather than face the firing squad again and therefore didn’t bother placing the bet.

His philosophy was that his system had already produced a streak of winners and the chances were that this would breakdown at some stage. Mainz were the underdog at 3.3 and duly proceeded to win the match 1-3. Another lost opportunity.

Total apathy now reigned and the decision was made to give up the system altogether.

The next match saw Augsburg, the underdog, win 0-1 at odds of 3.25.

Bringing results up to date at the time of writing, Hamburg’s last match was a home defeat by heavy favourites Bayern Munich.

Instead of registering a profit of 1,490 units from nine bets, our friend placed just four bets within his strategy (plus the one outside it) and lost 200 units. Does this pattern sound familiar?

And, he is not a stupid man. He is well educated and is currently graduating university with a degree in Economics. His name is Florian and we thank him for his permission to relate this story.

Simple: Let greed and emotions rule your bet placements.

Here, emotions include hope, euphoria, disappointment, shock, desperation, apathy, resignation. All of these things combine to make you a totally ineffective gambler.

Unfortunately, Florian ran the whole gamut (and probably more) when test-driving what, on the face of it, was a really promising system.

**Next Page: How to Succeed…**

Standard deviation is a measure used to quantify the amount of variation within a set of data values. It measures how far a set of numbers are spread out around the mean, or average value. In this case, five seasons’ odds data.

Calculating the standard deviation values takes into consideration larger deviations from the mean. In other words, the ‘outlier’ values; those that are furthest away from the mean.

Thus, standard deviation provides us with a ‘margin for error’ allowance and also a more rounded perspective of the statistical conclusions to be formed. In short, standard deviation provides us with a wider safety net for predicting future results.

Once you have calculated the two inflection points (see **User Guide**), use the standard deviation tables below to adjust these figures to provide a wider, more accurate scope for your predictions:

Summer League Inflection Points Standard Deviation Adjustment Figures

**Example 1: Brazil Home Wins – 2nd Half Season Analysis.**

Let’s say your chosen system is home wins in Brazil for the second half of the Série A season. Your two inflection points are 1.98 to 2.56.

- Divide both figures by 1 to find the implied probabilities of the odds:

1/1.98 = 0.50505, or 50.505%

1/2.56 = 0.39062, or 39.062% - Lose the percentage signs for the time being from the implied probability figures:

Lower odds/higher probability threshold becomes: 50.505

Higher odds/lower probability threshold becomes: 39.062 - Look up the adjustment value in the table above. The middle table shows the second halves of each Summer League season. The home win value for Brazil is
**0.677** **ADD**the home win value of 0.677**to the lower odds’ threshold**: 50.505 + 0.677 = 51.182**SUBTRACT**the home win value of 0.677**from the higher odds’ threshold**: 39.062 – 0.677 = 38.385- Add the percentage sign back on and convert both figures back into odds values. Round-up or down during this step only:

1/51.182% = 1.953, which rounds-down to 1.95

1/38.385% = 2.605, which rounds-up to 2.61

The new inflection point range adjusted for standard deviation is therefore **1.95** to **2.61**.

**Example 2: Sweden Underdogs – Whole Season Analysis.**

Inflection points: 4.16 and 7.20

1/4.16 = 0.24038, or 24.038%

1/7.20 = 0.13888, or 13.888%- 24.038 and 13.888
- The bottom table shows the Whole Season adjustment values for each league. In this case, Sweden’s standard deviation adjustment is
**0.420** - 24.038 + 0.420 = 24.458
- 13.888 – 0.420 = 13.468
1/24.458% = 4.088, which rounds-up to **4.09**

1/13.468% = 7.425, which rounds-up to**7.43**

The new inflection point range adjusted for standard deviation is therefore **4.09** to **7.43**.

The 2018 Summer League seasons will be the only time you will have to carry out these calculations manually.

In future, the standard deviation calculations will be incorporated into the HDAFU tables themselves and will calculate automatically.

]]>Image: Jeff Banke (Shutterstock)

*Here are some of the most popular misconceptions…*

This is absolute nonsense. Successful betting is not about the pay-out of a bet, but the main goal is to make a profit. Very often, especially in the small odds markets excellent value can be found.

In addition, low odds have the huge advantage that they stand for high probabilities and therefore losses are considerably fewer in number than with higher priced, lower probability events. Also, small odds experience shorter **losing streaks** and the patience of the gambler is never stretched too far.

However, what really matters is the **price of the bet**.

If, for example, the calculations for a match throw up an 85% chance that there will be under 3.5 goals (corresponding betting odds: 1.18), and the market is offering odds of 1.25 then this is a fantastically good **value back bet opportunity**.

Again this is a very common misconception. Higher odds do not automatically hold more value and are therefore more profitable than lower odds.

Many punters believe that better returns can be achieved in the long run if playing at odds between 2.5 to 3.0. Of course, it is understandable that these bets are quite popular as the potential winnings are 1.5 to 2.0 times the stake.

However, what most gamblers do not consider (or perhaps simply do not know!) is that these betting odds represent chances of 33% to 40% of winning, meaning that on average six to seven out of 10 bets in this group will lose.

Since winning and losing bets are never evenly distributed it may well happen that, with a little luck, a few bets in a row may be won but, much more likely is that many, many consecutive bets will lose until the betting bank is depleted beyond recovery or is drained altogether.

**Accumulator bets** are the bedfellow of every bookmaker. Full stop! So far as the bookies are concerned the more people combining their betting choices, the better. It is an absolutely nailed on profit for the bookmaker, and only long-term misery for the punters.

We have already mentioned that bets at very low odds have a pretty high chance to win. There is no question about this. Nevertheless, even a bet with a 90% chance of winning still has a 10% probability of losing. **Multiples of bets** greatly increase the chances of losing. Only one bet needs to go wrong for a busted flush.

In addition, there is of course the **overround of the bookmakers**. When combining your bets, you usually have to pick one bookmaker limiting you to accepting their fixed prices. You can be sure that somewhere in the accumulator package you have bought will be bets priced well below their true value. No bookmaker offers best price on every event – if they did they would soon be out of business.

With accumulators you are invariably buying negative value and we have seen throughout this blog that the only way of making consistent profits through gambling is by having value on your side, constantly.

This sermon is therefore to encourage you to avoid multiple, accumulator or parlay bets. You can be sure that the bookmaker is god in this particular arena and the gambler always loses in the long run, guaranteed.

]]>The rules for roulette tables are designed in such a way that the bank makes money in the long run. It may be a hard truth, but the reality is **there is no system to beat the roulette wheel**.

Nevertheless, it must be said that roulette is a pretty fair game. If you play with only small amounts (relative to your chips), then you can gamble for a long time at the roulette table whilst having a lot of fun.

This article shows you how to calculate probabilities in roulette, including the odds for each type of bet, allowing you to analyse all the possible variations.

Collage of Shutterstock images;

Foreground: donskarpo,

Background: Nata789

Foreground: donskarpo,

Background: Nata789

The calculation of roulette wheel probabilities is very simple.

Let us take the classic example of a dice with the numbers one to six. How large is the probability that the next throw is the number five?

Of course, it is **1/6** or **16.67%**: only one side of the dice has the number five, one of six numbers in total.

And how big is the probability of getting a number that is *at least* four?

The answer is **50%**: there are three possible throws (numbers four, five and six), meaning a three in six chance, or **1/2**.

If you have understood these simple examples then you will also be able to understand the probabilities expected in roulette.

Roulette has a total of **36** numbers, one to 36. The 36 numbers are divided into the following equal sized ‘sets’:

- 18 red numbers (Rouge) and 18 black (Noir)
- 18 even numbers (Pair) and 18 odd (Impair)
- 18 numbers in the lower half (Manque) and 18 in the higher half (Passe)

Lastly, there is an additional stand-alone number, which is the green “zero”, making 37 numbered zones in total. The zero is not included in any of the three sets above.

So, if you are gambling on any of the three sets, in other words;

- red or black
- odd or even
- low or high

then your likelihood to win is **18/37** = **48.65%**. If your bet wins, your stake is returned plus 100%. In effect you double your money as each of these sets is an ‘evens’ bet.

Assuming the frequency of results is uniform (i.e. each number appears once during every 37 rotations), the bank will win all bets placed on the three sets every 37th round, when the green zero arrives. Thus, players lose an average of 1/37 of their stakes (assuming that they always play with the same stake per round).

Putting this another way, imagine you are betting on both the “red” and “black” sets at the same time. On average, 36 out of 37 times, the roulette ball will land on a number from one to 36. You are backing all 36 numbers and will lose one bet each time but receive full compensation on the other. (A zero sum game). But you will make a total loss (lose both bets) when the ball lands on zero, and this is precisely the case in 1/37 of the games.

So you can say that with simple chance you should expect returns of 36/37 of your stake money, which is the expected value in roulette (**97.3%**). In other words, for every 100 units staked you will receive back an average of only 97.3 units.

There are some casinos which are a little fairer to players who rely on simple chance. In such a casino when betting on, for example, red, if a zero appears your stake is not lost immediately but is left to ride on the next spin of the wheel.

In this case, the stake is returned to you (without winnings) if the next spin is “red”. The expectancy value for this type of house increases a gambler’s chances to **98.65%**, or 98.65 units returned per 100 unit stake. Wagering with 100 units in a session will cost an average of 1.35 units (the house “edge”). You’ll find further maths and explanations in Wikipedia **here**.

If you witness “red” five times in a row, what do you think should come next? Red or black?

Many will believe that the chances for “black” are now higher. Black has not appeared for a while so it must surely arrive again soon to ‘balance out the frequency’.

Unfortunately, this thinking is incorrect. Following a series of “red” five times in a row, the probability for black always remains the same: 18/37 = 48.65%. Just remember the roulette wheel has no memory – it simply does not know what the last number was.

This is why it makes no sense to write down the sequence of red and black. (Surely you must have observed gamblers in casinos engaging in this habit?). It is impossible to detect even the smallest patterns in the roulette wheel because the ball has no memory and will always churn out numbers completely at random.

However, it is *unlikely* that “red” will appear six time in a row. The chance of six reds in a row is

(18/37) ^ 6 = **1.3%** (i.e. 48.65% x 48.65% x 48.65% x 48.65% x 48.65% x 48.65%). *(For more explanations see also our combinatorics article)*. By the way, this is approximately half the chance that any one single number appears (1/37 = 2.7%) and, of course, it is just as unlikely that there will be red numbers five times in a row followed by a black number; the probability for this sequence is also

To give you a better feel for roulette probabilities, here are a few examples. Here we use “r” for red and “b” for black:

- r or b: 18/37 =
**48.65%** - rr or bb: 18/37 x 18/37 =
**24%**(two reds in a row or two blacks in a row) - rb or br: 36/37 x 18/37 =
**47.3%**(one colour followed by the other) - rrr or bbb: 18/37 x 18/37 x 18/37 =
**11.5%** - rbr or brb: 18/37 x 18/37 x 18/37 =
**11.5%** - rrrr or bbbb: 18/37 x 18/37 x 18/37 x 18/37 =
**5.6%**

Never confuse these probabilities with the “conditional probabilities”. The chance of red four times in a row is **5.6%** but if you come to the table immediately after a red number has appeared, the probability that you will witness a further three reds (making a total of four times in a row) is **11.5%** – purely because you will be observing only a series of three rounds.

The law of small numbers was first conceived in 1898 by **Ladislaus Bortkiewicz** (1868-1931). His book is still available in German, free of copyright, and can be downloaded as a **PDF or Kindle** version. An **English language introductory text** is also available.

The Law of Small Numbers is not exactly bedtime reading material, but here is a brief summary. As roulette is a game of repetitions the “law of a third” and the “law of two-thirds” should become evident as play continues.

If there are exactly 37 rotations performed at roulette (as many as there are different numbers), according to the book:

- approximately one third of the numbers (around 12-15 numbers), will
*not be hit at all* - approximately one third of the numbers will appear
*exactly once* - approximately one third of the numbers will appear
*twice or more* - approximately two thirds of the numbers will appear
*at least once*

The law of large numbers states that with an increase of repetitions the actual observed frequency comes closer to the theoretically calculated probabilities.

Although it is possible to observe on one particular evening, for example, red numbers coming up 60 times in a row, and another evening 40 times black, ultimately, when you observe the distribution of red and black over a longer period, the frequency will be closer to 50:50.

Therefore, **there is no roulette system with which you can beat the probabilities**. It may seem for a short time that a certain system functions but, in the long run, you will lose money with every system because roulette rules are designed in a way that the casino earns money. Period. Bear this in mind when you play roulette, but it is still fun!

**How high should be a starting bank?
Is 5,000 units enough?**

Well, there is no standard answer to this question. It all depends on the individual strategy.

Image: Sergey Novikov (Shutterstock)

However, what is possible, is to calculate bank fluctuations *(i.e. winning and losing sequences)*.

With the help of knowing the best and worst case scenarios you can determine the ideal starting bank for any betting system of your choice.

At the end of the article you will find a few useful exercises to practise, with the solutions available as a free download to all of you who would like them.

It stands to reason that the smaller the probability of an event occurring *(i.e. higher odds)*, the longer the likely losing streak will be *(in between winning bets)*.

However, the big question is how often and for how long will the losing (and winning) streaks transpire?

It is possible to mathematically calculate many things with statistics, including streaks of luck and bad luck. However, it is important to note that no matter how accurate the results may appear, they are ‘models’ *(a formal representation of a theory)*.

In this article, we are talking about probabilities; what can we ‘predict’ about how things may develop in the future. Please bear in mind that any such hypothesis is always a “could happen” not a “will happen”.

Of course, the larger the sample size *(i.e. number of bets)*, the more likely the prediction is to be correct. But apart from the bookmakers themselves, who else has a betting portfolio comprising thousands of bets every weekend?

The longest expected losing streak *(or winning streak)* can be calculated using the following formula:

**n** = number of trials *(i.e. total number of bets)*

**ln** = natural logarithm^{1}

**P** = probability^{2}

**| .. |** = absolute value or ‘modulus’

^{1}*Suffice to say, explaining what natural logarithm is would be worthy of a series of articles. For the time being, use Excel to calculate this for you.*

^{2}*For winning streak calculations use the positive value (i.e. the probability of winning). For losing streak calculations use the negative probability value. For example, if the probability to win the bet is 33% then the probability that the bet loses (negative probability) is 67%.*

In practice, the formula is best applied to situations where you constantly bet repeatedly on the same probability, for example, on ‘red’ at the roulette wheel: its probability remains exactly the same with every new spin of the wheel.

For football betting the concept is much more difficult to apply as each bet is likely to have a different probability (e.g. one Over 2.5 Goals bet with a 55.3% chance, and the next with a 62.1% chance, etc.).

However, you can group bets in probability clusters – for example, bets with a 55%-60% expected hit rate, bets with a 60%-65% expected hit rate, and so on.

Longest Winning and Losing Streaks, depending on the number of bets (Examples for 50, 500 and 1,000 bets shown)

The tables above show the calculations of the expected maximum number of winning and losing streaks, depending on the expected hit rate *(probability of the bet to win)*.

To read the tables, let’s explain the 70% line *(odds in the region 1.4 and 1.45)*; in other words, bets with a 7 in 10 chance of winning.

The table on the left calculates the expectations of 50 tries *(50 bets in a row, one after the next)*. You can see that the player will experience at least one streak of three lost bets in a row somewhere in the sequence.

On the other hand, he can expect at least one series of 11 winning bets in a row during the same sequence of 50 bets.

In contrast look at the 30% line *(odds in the region of 3.2 to 3.4)*. In a series of 50 bets the bettor must expect at least one sequence of 11 consecutive losing bets, but will probably see only one set of three consecutive winning bets.

To develop a sense of probabilities and sequences, you can experiment with a dice. It has six faces; in other words, a probability of 16.67% (1 in 6 chance) of successfully landing on a chosen number.

Choose a number and count the number of throws until you succeed to roll it. Count also the number of consecutive successful rolls.

Choose two numbers that you do not want to roll (e.g. 5 and 6).

This means you have a 66.67% chance that one of the remaining four numbers is rolled.

In football betting terms, this equates to wagering on something like the full-time ‘Under 3.5 Goals’ market at odds of 1.50. (This experiment is just a little faster than waiting for 50 games to finish!)

Take a pen and paper and record 100 throws of the dice. If one of your four chosen numbers arrives mark a 1 on your paper; if the 5 or 6 are thrown, mark a 0. Count the number of winning and losing streaks you experience.

What is the maximum number of winning and losing streaks you experience in a sample size of 100 throws (bets)?

*Having learned how to calculate the expected length of winning and losing streaks, the next question to ask is: *

**How many bets is it likely to take before I encounter ‘X’ losses in a row?**

This formula is actually very simple:

= **1** divided by **P**, **to the power of** **a**

**P** = probability (expected hit rate or loss rate)

**a** = number of won or lost bets in a row

In the tables below you can see how many attempts (bets) it needs to experience a specific, expected length of luck or bad luck. Again, the assumption is that the bettor bets all the time on the same probability:

Expected time of occurrence of winning and losing streaks, depending on the hit rate

Looking firstly in the right-hand column at the Losing Sequences, if the expected hit rate is 45% *(what you should ‘expect’ at odds of around 2.2)*, then it is likely that you will experience a sequence of three losing bets in a row by the time your sixth bet is settled.

After 20 such bets it is likely that you will have seen a losing streak as long as five bets in a row.

Looking at the Winning Sequences column: you will win three times in a row at some stage during a series of 11 bets.

However, winning five in a row may only be seen once in every 54 bets.

As we mentioned before, in football betting it is extremely difficult, if not impossible, to find bets, all with the same probability of success.

However, you should at least try to understand the theory behind winning and losing streaks, as it will be **easier on your nerves** when you do encounter the inevitable run of bad fortune.

In particular, a thorough understanding of losing streaks is of enormous importance when setting both the size of your starting bank and stakes per bet.

**Example:**

A bettor prefers bets within the odds range of 2.0 to 2.5 with a hit rate between 40% and 50%. He plans to place 50 bets *(e.g. two bets per round on 25 rounds of matches)*.

After looking at the tables, he knows that the maximum losing sequence expected is likely to be as long as six to eight lost bets in a row. Therefore, he knows that there may be at least one sequence of three or four consecutive rounds *(weekends)* when all bets lose.

After every 5^{th} to 8^{th} bet, he is also aware that he is likely to experience a loss of three consecutive lost bets *(e.g. one weekend loses both bets, the following weekend only one loses)*.

He also knows that every 13 to 32 bets there will even be a streak of five losing bets in a row.

The bettor is fully aware that he has to take this into consideration and plan the starting bank accordingly to be able to ‘sit through’ these losing streaks.

Of course, he also knows that winning sequences will arrive too. In his case, with some ‘luck’, he may experience a winning sequence of five bets in a row after 32 bets. Every eight to 16 bets he will have a ‘lucky’ streak of three wins in a row.

This is certainly quite a fluctuation. When these ‘bad luck’ and ‘good luck’ streaks actually happen, nobody knows. However, what we do know is: They will happen!

A starting bank should be approximately five times the maximum expected losing streak. The reason for this is that a losing streak can happen right at the beginning, immediately followed by another bad run of luck. We are talking statistics here!

So if a bettor wants to stake 10 units per bet, the starting bank must be nine times (expected losing streak) the stake of 10 units multiplied by five = 450 units. Then he can risk 2.2% of his bank each time he bets (10 divided by 450). If losing, the stakes will remain constant at 2.2% and, if winning, raised gradually.

**Questions to ask before setting the starting bank:**

- What hit rate is expected
*(probability to win the bets)*? - How many bets are planned for the season?
- How long will the longest losing streak be?
- What is the desired stake per bet?

**Calculation of the starting bank:**

- A bettor pursues a strategy with a win probability of 60% per bet
*(e.g. Under 3.5 Goals)*. He places one bet after the other; in other words, he waits for the outcome of each bet before placing the next. In total he places 50 bets.What is the longest ‘losing streak’ (bad luck) that he can expect? How long is the longest ‘winning streak’ (luck) that can be expected?

- Same example as in (1): A strategy with a probability of 60% per bet; placing one bet after the other.
This time our punter is hoping for a ‘winning streak’ (luck) of 5 consecutive wins. How often does that happen?

- A gambler pursues a strategy with a probability of 20% per bet
*(e.g. ‘betting on the underdog’)*. Again, he places one bet after the other.With a total of 500 bets, how long is the longest ‘losing streak’ that he must expect? After how many bets can he expect the longest ‘winning streak’?

- Same example as in (3): Strategy with a probability of 20% per bet; placing one bet after another
The bettor was hoping for a ‘winning streak’ (good luck) of five consecutive wins. How often does that happen? After which bet number should he expect ‘bad luck’ of five consecutive losses?

- Following the above two strategies
*(one with a 60% chance to win, the other with 20%)*our bettor stakes 10 units per bet.How high should the starting bank be for the 60% strategy, and how much for the 20% strategy?

*Note: The initial bank should be approximately five times the maximum losing streak based on a total of 500 bets placed.*

*Just click on the button above and click on “Proceed to checkout” button in the new tab, then enter your name and e-mail address. Our automatic service will then deliver the file to you via e-mail, free of charge. The size of the PDF file is 320KB.*

The factor **5** used in this article to determine the betting bank is a risk variable for risk-averse bettors. It is also the factor advisable for strategies with a 45% to 55% win probability *(odds between 1.8 and 2.2)*.

Here is another article: **How to Calculate Losing Streaks & Optimal Bankroll** in which we provide a more detailed account of setting the ideal starting bank.

Risk management in sports betting is the foundation stone upon which all of your betting transactions should be built.

Risk management encompasses risk assessment, risk control and capital requirements, all of which cannot be addressed until you understand how winning and losing streaks are likely to impact upon your starting bank.

]]>Even the term **‘Stake’**, at least so long as it is money related, is easily understandable.

Whatever level your stake is, there are only two options: you either lose the bet and your stake, or you win the bet, retrieving your stake and adding to it your winnings.

However, the term **‘Odds’** is far more difficult for most bettors, especially as odds are connected to market prices, fluctuations, probabilities, expectations, etc.

**Hand on heart, can YOU reliably define the terms “bet”, “odds”, and “stake”?**

** Definition of ‘Bet’:** Technically speaking, a ‘bet’ is an agreement between two parties that the one who makes an incorrect prediction about an uncertain outcome will forfeit something stipulated to the other – a wager.

Betting is all about risking something, usually a sum of money, against the money of someone else based on the outcome of a future event, such as the result of a race or other competitive event.

Typically, most bets are made prior to the start of an event, and this has been the practice used by gamblers and bookies from the advent of bookmaking. However, over the last few years a new way of wagering has developed, that of **in-play betting**.

In this highly dynamic process wagers are placed after the race or match has started with betting odds changing dynamically according to the perceived trends and events in the match / game. There is a growing plethora of **bookies offering in-play bets** across more and more betting lines and markets.

The term, ‘odds’, is somewhat ambiguous.

Here are two definitions from well-known dictionaries:

** Macmillan Dictionary**: The chances that are used for calculating how much money you will get if the person or thing you bet on wins a race or competition.

** Oxford Dictionary**: The ratio between the amounts staked by the parties to a bet, based on the expected probability either way.

**The problem** with the above definitions *(and many other definitions found in dictionaries)* is that odds are not necessarily connected to the real chances of something happening, not even to ‘expected’ probabilities.

Just think of **British odds, European odds, and US Moneyline odds**.

British odds show the net return of a bet, European odds display the net return of a bet plus the original stake, and US Moneyline odds exhibit the money wagered either to win 100 units, or the money which will be won from a 100 unit stake.

Another deviant example is that **bookmakers adjust their odds to public opinion** in order to **balance their books**.

Therefore, it is simply * incorrect to say* that ‘odds’ display the chances of something happening. Odds are not even necessarily based on expected probabilities.

Betting Odds are the Prices for a Bet

* Learning Point:* There is

** Definition of ‘Stake’:** Money or property risked on the result of a horse race, card game, match outcome, etc.

Stake (or ‘wager’ in America), is straightforward terminology.

You bet with your friend on a game of pool, and stake £5 each. Whoever wins the game gets £5 from the other party, and whoever loses is £5 poorer.

In betting, the stake (or ‘wager’) usually means money, which is countable.

The concept of stake becomes much more complicated if property is wagered, such as houses, cars, or in some countries even wives! If you gamble property then you not only have to calculate the true probabilities of a bet to compute the odds, but also convert the staked property into a monetary value.

In these cases bets are very often lopsided and unfair, with a huge advantage to the person who is better in maths than the other. *(Read an example: Arsenal fan staked his house on a bet with a Manchester United fan, who offered his wife and Toyota car in return )*

The only honest advice I can give – **Do not bet if you do not understand odds!**

Unless money is no object, few people will go shopping and load their basket with goods without checking and comparing the prices of different brands. Most of us need to ensure we have enough money available to pay for the purchases, and some of us like to ensure we are getting the best value for the money we pay.

** Understanding Odds is CRITICAL!** If you constantly go shopping without paying attention to the prices

Always remember: Odds are the price for a bet, they very rarely stand for the real probabilities, or chances.

Of course, odds available in the market can be converted into their ‘implied’ probabilities, which can then be compared to your own calculations of the ‘real’ expected probabilities, and vice versa.

If you want to become a winner you MUST understand odds and be able to compare and distinguish between the implied probabilities suggested by the odds offered in the market and the real (or true) probabilities suggested by historical statistics. There is no alternative – a lucky gambler is never lucky all the time.

*If you wish to learn odds calculation, please check out:*

Fundamentals of Sports Betting Course: Betting on Over / Under ‘X’ Goals

In 1998, **William Hill** were the first bookmaker to accept wagers via the Internet.

Their online betting platform is one of the most sophisticated in the market.

Hill also have a tongue-in-cheek reputation for offering odds on literally anything you can think of.

Here is a compilation of our ten favourite left field bets they have accepted, and **some notable payouts** they have honoured:

- In April 1964, David Threlfall placed a £10 bet at odds of 1000/1 that man would walk on any planet or heavenly body before January 1970.
This was the first officially recorded ‘space’ bet and the stake was equivalent to the average weekly wage at the time, worth over £170 today.

The bet led to an avalanche of wagers on the same event.

Neil Armstrong duly obliged on 21st July, 1969, and Threlfall was £10,000 richer. William Hill eventually paid out over £50,000 on this event

*(around £860,000 today)*, ruing the fact that the man in the street knew more about space than they did. - Elvis Presley related novelty bets are struck even now, almost 40 years after his ‘death’. Notably, Ciara Parkes stands to win £125,000 after the King’s next comeback following a £250 bet at 500/1 in the mid 1990’s.
Elvis also features in the biggest betting odds ever offered by Hill:

A Glaswegian postman took a price of 20,000,000/1 that Elvis would crash a U.F.O. into Loch Ness, striking the legendary monster supposed to inhabit its depths.

Urban myth suggests this bet was actually for Elvis to ride into town on the long lost, kidnapped racehorse ‘Shergar’, and then to play against the missing and disgraced Lord Lucan in the Wimbledon tennis final!

- Betting on the outcome of TV shows was first introduced by William Hill in 1980, when they allowed punters to wager on ‘Who shot J.R.?’ in the popular American soap, ‘Dallas’.
- Screaming Lord Sutch, the late leader of the Monster Raving Loony Party, stood to make the biggest betting shop payout of all-time at a cool £15,000,000 from a £1 wager with Hill that he would one day become British Prime Minister.
Sadly, the ‘loony’ never made it, much to the chagrin of us mere mortals.

- In 1988, Chris Bonnington, the famous mountaineer, bet with Hill that he would return from his Himalayan expedition with proof that the ‘Yeti’ existed.
Upon his return, he claimed he had the required evidence, until the Department of Agriculture confiscated and burned it.

- In 1995, John Richardson, aged 55, struck a novelty bet with William Hill that he would father a child in the year 2040. You can do the math!
- In 2008, Fred Craggs, won an eight-horse accumulator, triggering Hill’s maximum horse racing payout clause of £1,000,000.
His selections were random and Craggs had no idea he had won until he next visited the shop.

Not bad for just a 50p stake at combined odds of over 2,000,000/1,

*and*during his 60th birthday week. Bonza! - William Hill’s penchant for bizarre proposition bets entered the World Cup 2010 arena. Odds of 7/2 were offered on any England player repeating Paul Gascoigne’s 1990 watershed moment by crying on camera at any time during the tournament.
- Euro 2012 also received the Hill treatment with 4/1 offered that the Euro currency would collapse before the end of the tournament. Eyes were on Greece not to rock the boat in either contest!
- Of course, proposition and novelty bets are usually fun and good-natured and in mid-2013, Chris Brooker cashed in odds of 6/1 to return £700 that his romance with a fellow student would outlast the duration of their university studies together.

Whatever your betting requirements, William Hill has just about every online option you can imagine but if you can think of something weird, wonderful, and original you are encouraged to contact them for consideration and pricing of your proposition. You never know, you might even get some publicity!

How about buying a funny, weird, or eclectic novelty bet from Hill for a family member, or even a colleague during the Office Secret Santa gift giving season?

It would certainly create a topic for debate in the pub, and it doesn’t have to be too expensive. The choice is yours and limited only by your own imagination!

]]>In the world of sports betting the art of **arbitrage** involves wagering on both or all sides of an event with the right combination of odds and stakes in place to make a profit whatever the outcome of that event.

Image: 3Dmask (Shutterstock)

The principle of arbitrage is ‘**sure betting**‘, supposedly with minimum risk (for the seasoned arbitrageur) and long-term, **guaranteed** profits.

Surely this is the closest you can come to attaining the “Holy Grail” in betting? **Or maybe not?**

Despite the apparent rewards on offer the number of worldwide professional sports arbitrageurs is in the low tens of thousands, not more. In comparison, the German stock market employs over 3,200 staff, whilst one of the largest providers of automated arbitrage services, **RebelBetting** has even fewer subscribers than this number (as we write).

So, why such a relatively small group of customers taking advantage of the so-called ‘guaranteed’ gains averaging between 1.5% and 3.5% per bet (a typical ‘**arb**‘ provides around 2.5%), with perhaps 15-25% potential profit on the capital employed each month? That’s a far higher reward than any bank, building society, or share dividend offers!

There is no question that arbitrage is legal because the arber is simply exploiting price differences in the market, effectively buying and selling (bets) as any trader does. There is **nothing illegal** about this.

However, it is understandable that **bookmakers are not fond of arbers**. Every company has the right

Successful arbitrage betting ultimately **guarantees small returns** but the sacrifice is that the process **requires large funds**. The money is tied-up in the venture for a potentially long period of time.

Pursuing an average **2.5-3.0% profit per betting round** and targeting **a return of 15-25% of the capital employed per month**, the ‘arber’ needs, for example, a **starting bank of at least 25,000 €** in order to make **5,000 € profit per month**.

Wow! A lot of money required at the start to make it worthwhile, and entering the arbitrage arena on these terms will be impossible for many.

Of course, arbitrage betting is a pretty safe investment, but **in addition to substantial funds** it requires not only great expertise but also some strong personal characteristics to make it possible at all:

- Many time-consuming calculations must be performed. Ouch, lots of maths!
- Clear and complete records of every transaction must be kept. How boring!
**Discipline and consistency**has to be maintained at all times. Far too unsocial!

And lastly, a really stable, reliable and fast internet connection is essential, without any limitations to any bookmaker or exchange worldwide.

However, the average punter is perhaps not such a ‘professional’ investor, but bets for fun and/or the excitement of watching an event knowing that money is riding on the outcome. Of course, he hopes to profit from the wager but his are gambles, not investments. Is that the reason why there are so few ‘arbers’ out there and active in the market?

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