Version 1.01 of the Betting Tracker spreadsheet is now available for download.
The new version comes with the following updates
Click here to learn more about the Betting Tracker.
I have completed a betting tracker Excel workbook, which is free and available for download.
The worksheet tracks your bets for multiple agencies and provides performance data as well as a summary graph.
Click here to learn more about the Betting Tracker.
With the basics of arbitrage theory out of the way, as covered in my first and second posts, I will now move onto actual arbitrage opportunities. Most people associate arbitrage betting with two concurrent set of differing odds offered by different bookmakers, but virtually all of my arbitrage bets occur with changing odds over time.
Please read my first two arbitrage posts before reading this one.
It is very common for two bookmakers to offer slightly different odds for the same sporting event. For example, as I write this post, SportsBet is offering the following odds for Fernando Verdasco vs Radek Stepanek in the third round of the Australian open.
| Fernando Verdasco | | | 1.60 |
| Radek Stepanek | | | 2.35 |
At the same time, SportingBet is offering
| Fernando Verdasco | | | 1.55 |
| Radek Stepanek | | | 2.45 |
If I sum the inverses of the odds offered by SportsBet and SportingBet I get 1.051 and 1.053, respectively. If, however, you bet on Stepanek with Sportsbet (1.60) and Verdasco with SportingBet (2.45) the sum of the inverses becomes 1/1.60 + 1/2.45 = 1.033, which represents better value. However the sum is still greater than 1, meaning an arbitrage opportunity does not exist. This is frequently the case with disparate odds. Usually the disparity isn’t enough to provide an arbitrage opportunity.
I know for a fact that opportunities do arise if you look around hard enough, but I have personally never found and entered into an arbitrage opportunity as a result of disparate odds between bookmakers. Be careful when making bets of these type, as disparities can disappear quickly. I have made bets in the past where after clicking on the confirm button I have been informed that the odds have changed, and that I can no longer make that particular bet.
During a multi-game series you can usually bet in between each day’s game. Examples of multi-game opportunities (to Australians) include test cricket, the MLB (baseball) post season, the NHL (ice hockey) post season and the NBA (basketball) post season. I always take a close look at the American series’ where the underdog has home advantage for the first game. If they win that game then the odds usually change enough to provide an arbitrage opportunity. I prefer betting on American series’ because, unlike test cricket, they can never result in a draw.
During the MLB post season in 2008 I made a bet on the Phillies to win the World Series. At the time the series was locked at 1-1 with the following odds:
| Philadelphia Phillies | | | 2.05 |
| Tampa Bay Rays | | | 1.75 |
Because the Phillies won game 3, the odds the next day were as follows:
| Philadelphia Phillies | | | 1.50 |
| Tampa Bay Rays | | | 2.55 |
If you sum the inverses of my Phillies bet (2.05) with the new Tampa Bay odds (2.55) you get 0.88, which is below 1, meaning an arbitrage opportunity did exist. Out of principal rather than anything I did enter into the arbitrage opportunity to make a guaranteed profit, although my initial bet on the Phillies wasn’t substantial. To make things a bit more interesting, say I had bet $100 initially on the Phillies at 2.05. If I had bet 100*(2.05/2.55) = $80 on Tampa Bay I would have won $25.00 if the Phillies had won he series and $24.00 if Tampa Bay had won the series, with no risk of losing money.
The downside of series betting is that if the team you initially bet on doesn’t gain the upper hand, you will never be able to enter into an arbitrage opportunity. Only if your initial bet gains the advantage will you be able to lock in a guaranteed profit.
The theory behind intra-game betting is exactly the same as for series betting except you have to make your decisions much more quickly. Note that Australian’s aren’t permitted to make intra-game bets over the Internet. You can only bet over the phone once a match has started.
Occasionally betting sentiment differs from the original set of odds offered by the bookmakers. Betters place a disproportionate amount of bets on a particular outcome, which forces the bookmaker to change their odds.
For the first game between Australia and New Zealand in the 2008 rugby league world cup, I remember a bookmaker offering 1.20 for Australia to win. This struck me as being strange because they were only offering 1.20 for Australia to win the whole tournament. By kick off, however, the odds had reduced to 1.10. I bet on Australia for that match so I don’t have all of the original details with me, but suppose the following odds were offered at the time.
| | | Initial Odds | | | Odds just before kick off | |
| Australia | | | 1.20 | | | 1.10 |
| New Zealand | | | 5.50 | | | 8.50 |
| Draw | | | 31.00 | | | 31.00 |
If I had placed a $100 bet on Australia initially, and then a 100*(1.2/31)= $4 bet on a draw and a 100*(1.2/8.5)= $14 on a New Zealand win just before kick off, I would have a guaranteed profit. With Australia winning that match I would have won $2.00. This figure may not blow you away, but it represents a guaranteed 1.7% return on your investment in a matter of days.
Most bookmakers offer sign up bonuses in the form of free bets for new members. If you sign up for two or more agencies, you could pit your free bets against each other between the bookmakers. Consider the odds for a Sunderland v Fulham game below.
| Sunderland | | | 2.25 |
| Draw | | | 3.20 |
| Everton | | | 3.20 |
If you were to sign up for three agencies and obtain $100 in free bets for each possible outcome, you would be guaranteed at least a $125 return, keeping in mind you only receive the net profit.
There are a number of caveats to this strategy. First, most agencies require that you bet on an event with odds of at least 2.00. Second, most agencies require that you “turn over” your winnings at least twice before withdrawing them from your account. So if you won $125 with an agency, you would have to make at least $250 worth of bets before that $125 could be withdrawn.
If you have betting accounts in different currencies, be sure to keep in mind potential exchange rate fluctuations when calculating arbitrage bets. Personally I would only enter into an arbitrage bet across two currencies if the guaranteed profit margin was substantially larger than the exchange rate volatility.
So there you have it. My mini-series on arbitrage betting is now complete. I will likely post further arbitrage related posts in the future, but this initial series was designed to get you onto the same page as myself. If you haven’t done so already, be sure to check out my homemade arbitrage calculators in the Tools section.
A three-outcome arbitrage calculator is now available.
The calculator determines arbitrage strategies for three-outcome sports given two disparate sets of odds. Three-outcome sports represent matches where a win, draw or loss is possible. The “unbiased” strategy aims to provide equal payouts for each betting outcome, while the “biased” strategy aims to provide a better payout if your tip wins, with no loss if it doesn’t.
You can learn more about three-outcome arbitrage betting here.
In my first arbitrage post I laid the groundwork for arbitrage betting with two possible outcomes: win and lose. This is case for sports where draws aren’t possible. Some examples are tennis, baseball, and basketball (with extra time included). For sports like test cricket and soccer, however, draws are not only a possibility, but occur frequently. This post, the second in my arbitrage series, covers arbitrage betting with three possible outcomes.
Part 3: Arbitrage Opportunities is now available
If you haven’t done so already, be sure to check out the three-outcome arbitrage calculator.
As with two-outcome betting, you can obtain a betting agency’s margin on their odds by summing the inverses of the odds. So if an agency offers the following odds for a soccer match:
| Everton | 1.80 |
| Draw | 3.35 |
| Tottenham | 4.40 |
The sum of the inverses of the odds is 1/1.80 + 1/3.35 + 1/4.40 = 1.081. The larger this figure, the greater the margin that the bookmaker is taking. Because the sum is greater than 1, if you placed equitable bets (i.e. providing the same profit) on all three outcomes, you would be guaranteed a loss due to this margin.
If you can find differing sets of odds for the same event, you may be able to come up with a combination of win, draw and loss bets that guarantees a profit, regardless of the event outcome. The different betting odds could be provided by different bookmakers, as in the example below, or it may be due to odds changing over time as the game or series progresses. Arbitrage opportunities will be discussed in more detail in upcoming posts.
Suppose two agencies offered the following odds:
| Agency 1 | Agency 2 | |
| Everton | 1.80 | 2.30 |
| Draw | 3.35 | 3.25 |
| Tottenham | 4.40 | 2.95 |
If you sum the inverses of agency 2′s odds for an Everton win along with agency 1′s odds for a draw and an Everton loss, you get 1/2.30 + 1/3.35 + 1/4.40 = 0.961. This figure is below 1, so an arbitrage does opportunity exist. Note that a number of cross-combinations can be tested. To find the best combination, take the largest odds for each possible outcome.
To calculate the amount to bet on each outcome, determine the total amount you would like to bet. Then calculate the amounts to bet on each particular outcome as follows:
Definitions:
b1 = bet (in dollars) on outcome 1 (Everton win).
b2 = bet (in dollars) on outcome 2 (draw)
b3 = bet (in dollars) on outcome 3 (Everton loss)
B = b1 + b2 + b3 = combined bet amount
o1 = odds for outcome 1 (Everton win).
o2 = odds for outcome 2 (draw)
o3 = odds for outcome 3 (Everton loss)
In this example I will bet $1,000 in total. Calculate the bets for each outcome as follows:
b1 = B / (1 + o1/o2 + o1/o3)
b2 = B / (1 + o2/o1 + o2/o3)
b3 = B / (1 + o3/o1 + o3/o2)
b1 = $1000 / (1 + 2.30/3.35 + 2.30/4.40) = $452.63
b2 = $1000 / (1 + 3.35/2.30 + 3.35/4.40) = $310.76
b3= $1000 / (1 + 4.40/2.30 + 4.40/3.35) = $236.60
Each bet equals the total bet amount divided by 1 plus the sum of the ratios of that outcome’s odds to the other outcomes’ odds
Calculate the guaranteed profit as b1o1 – B (or as b2o2 – B, etc)
$452.63 x 2.20 – $1000 = $41.06
$310.76 x 3.35 – $1000 = $41.06
$236.60 x 4.40 – $1000 = $41.06
Betting $452.63 on an Everton win, $310.76 on a draw, and $236.60 on an Everton loss would guarantee a profit of $41.06, which is a 4.1% return on the total bets.
If you were confident of a particular result, you could employ a biased arbitrage strategy and make a larger profit if the pick is correct, with no loss if it isn’t.
In the following example let’s predict Everton will win.
Calculate the bets for a draw and an Everton loss as follows:
b2 = B / o2
b3 = B / o3
The bet on an Everton win will equal the total bet amount minus the bets for the other two outcomes:
b1 = B – b2 – b3
b2 = $1000 / 3.35 = $298.51
b3 = $1000 / 4.40 = $227.27
b1 = $1000 – $298.51 – $227.27 = $474.22
If a draw or Everton loss occurs there is no profit or loss. If Everton wins the result is a profit of $474.22 x 2.20 – $1,000 = $90.71, which represents a 9.1% return as opposed to a 4.1% return for an unbiased arbitrage bet.
Using whole dollar bets to reflect most betting agency rules, the possible outcomes for this example are displayed below. The no arbitrage bet involves a simple bet of $1,000 for Everton to win.
| | | No Arbitrage | | | Unbiased Arbitrage | | | Biased Arbitrage | |
| Everton Win Bet | | | $1,000 | | | $453 | | | $474 |
| Everton Draw Bet | | | $0 | | | $311 | | | $299 |
| Everton Loss Bet | | | $0 | | | $237 | | | $227 |
| Profit if Everton Wins | | | $1,300 | | | $41.90 | | | $90.20 |
| Profit if Everton Draws | | | -$1,000 | | | $41.85 | | | $1.65 |
| Profit if Everton Loses | | | -$1,000 | | | $42.80 | | | -$1.20 |
The unbiased arbitrage strategy provides a profit of between $41.85 and $42.80 depending on the result, whereas the biased arbitrage strategy provides a $90.20 profit if Everton wins, with minimal profit or loss for the other results.
With the basics of arbitrage theory out of the way, my next post will cover some practical arbitrage betting opportunities, with references to actual previous bets I have made.
Arbitrage betting involves placing bets on each possible outcome of an event to make a guaranteed profit, regardless of the event outcome.
Most people associate sports betting arbitrage with opportunities where different agencies offer sufficiently different odds to make a guaranteed profit. However, the majority of my own opportunities have involved varying odds over time rather than inter-agency discrepancies. For example, the odds for Australia to beat South Africa in a test match will change each day depending on the previous day’s results. This also applies to intra-game betting, like soccer, where the odds drastically change with each goal scored. While there are many people who do engage in disparate odds arbitrage, you typically need accounts with 25+ betting agencies to take advantage of it on a regular basis.
This is the first in a series of posts which will cover arbitrage theory, opportunities to look out for and how to best take advantage of them. Please keep in mind that I am no expert on sports betting and these posts are intended for your amusement only. Please don’t rely on my mathematics and logic! Verify everything for yourself. You can view the Wikipedia article on arbitrage betting here.
Part 2: Three-outcome Betting is now available
Part 3: Arbitrage Opportunities is now available
Arbitrage betting involves placing multiple bets on the same event that combine to provide a guaranteed profit.
Arbitrage with Bookmakers
When an agency offers betting odds for an event, the sum of the inverses of the odds will always sum to greater than one. So if an agency offers the following odds for a tennis match:
| Andy Murray | 1.68 |
| Andy Roddick | 2.20 |
The sum of the inverses of the odds is 1/1.68 + 1/2.20 = 1.05. This means the betting agency will earn 5% on all bets for this game. It is worth remembering this, as it enables you to see which bookmakers offer better rates than others. The higher the figure, the greater the profit the bookmaker is taking.
If you placed equitable bets (providing the same profit) on both Murray and Roddick, you would be guaranteed a loss due to the agency’s margin, but if two agencies offered different odds, you may be able to bet on Murray with one agency and Roddick with another. Suppose two agencies offered the following odds:
| Agency 1 | Agency 2 | |
| Andy Murray | 1.68 | 2.20 |
| Andy Roddick | 1.40 | 2.98 |
When you sum the inverses of agency 1′s odds for Murray with agency 2′s odds for Roddick, the result is less than one, which means an arbitrage opportunity does exist.
1/1.68 + 1/2.98 = 0.931
If you placed a $100 bet on Murray with agency 1 and a $100 x (1.68/2.98) = $56.38 bet on Roddick with agency 2, you would receive a guaranteed profit of $11.62 regardless of the result. If you were confident Andy Murray would win, you could instead bet $100 on Murray with agency 1 and $100/(2.98-1) = $50.51 on Roddick with agency 2. This would provide a profit of $17.49 if Murray won with no profit or loss if Roddick won.
In general terms, if you set the second bet equal the first bet multiplied by the ratio of the odds, you will get an equal payout regardless of the result. If you are confident of a particular result but would like protection from being wrong, you can set the second bet equal to the first bet divided by one less than the second bet’s odds. I call the first type unbiased arbitrage and the second type biased arbitrage.
b1 = Bet amount on outcome 1
b2 = Bet amount on outcome 2
o1 = Odds for outcome 1
o2 = Odds for outcome 2
Unbiased Arbitrage
b2 = b1 x (o1 / o2)
Biased Arbitrage
b2 = b1 / (o2 – 1)
If you had a total bet amount in mind and wanted to calculate your two bets, you can use these formulas.
B = b1 + b2 = combined bet amount
Unbiased Arbitrage
b1 = B / (o1/o2 + 1)
b2 = B / (o2/o1 + 1)
Biased Arbitrage – where you predict b1 will be correct
b2 = B / o2
b1 = B – b2
Using whole dollar bets to reflect most betting agency rules, the possible outcomes for the Murray vs. Roddick example are displayed below.
| | | No Arbitrage | | | Unbiased Arbitrage | | | Biased Arbitrage | |
| | | | | | | ||||
| Murray Bet | | | $100.00 | | | $100.00 | | | $100.00 |
| | | | | | | ||||
| Roddick Bet | | | $0.00 | | | $57.00 | | | $51.00 |
| | | | | | | ||||
| Profit if Murray Wins | | | $168.00 | | | $11.00 | | | $17.00 |
| | | | | | | ||||
| Profit if Roddick Wins | | | $-100.00 | | | $12.86 | | | $0.98 |
I suggest you set up a spreadsheet to regularly test for arbitrage opportunities. Also, I have created an arbitrage calculator which is available in the tools section.
My next post will provide theory on arbitrage betting with three possible outcomes: win, draw and lose. This is important for sports like soccer and test cricket.
An arbitrage calculator is now available in the Tools section.
The calculator enables you to see if an arbitrage opportunity exists for a particular event, and if so, what the available arbitrage strategies are.
I will be posting articles on arbitrage betting soon.
The following is a review of the betting agency SportingBet. I will update this review periodically to keep the details up to date.
SportingBet was the second agency that I signed up with and is one of the agencies I use the most. It is licensed in the Northern Territory but is available to all Australians as well as internationally.
