• With the Australian Federal election tomorrow, now is your final chance to place your bets!

    Below are some of the latest odds. Please note that these odds could change quickly and radically. These odds are accurate as of 5:17 PM on August 20th. Also, as a warning, Sportsbet currently offers odds on who will be PM at the 2013 Federal Election, which some punters may misinterpret as the winner of the 2010 election. These bets won’t pay out for years!

    Note that an arbitrage opportunity exists! Provided the odds don’t move, you can profit by betting against a hung parliament with Centrebet and for a hung parliament with Sportingbet. Remember, an arbitrage opportunity exists whenever the reciprocals of the odds sum to less than one. In this case 1/3.00 + 1/1.64 = 0.943. Use the arbitrage calculator to calculate your strategy. Note that you are exposed to some risk, because a bookmaker may reject your bet or change the odds after you have placed a bet with the other agency. Update: Sportingbet has shortened its odds, but the arbitrage opportunity still exists, so you better be quick!

    Australian Federal Election – Winner

      Labor Party     Coalition
    Sportsbet 1.45 2.75 (any other party)
    Sportingbet 1.48 2.60
    Centrebet 1.48 2.62
    Luxbet 1.50 2.55
    Sports Alive     1.48 2.60
    IASbet 1.45 2.75 (any other party)


    Hung Parliament

      Yes No
    Sportsbet 2.90 1.37
    Sportingbet 3.00 1.35
    Centrebet 2.15     1.64
    Luxbet N/A N/A
    Sports Alive      N/A N/A
    IASbet N/A N/A


PinnacleSports.com Online Sports Betting
  • I’m used to seeing discrepancies in odds between bookmakers, but there are some massive inconsistencies between bookmaker odds for the 2010 football World Cup winner at the moment.

    I mentioned in a previous post the substantial variation in odds for the Miss Universe 2009 competition. Well, there are currently discrepancies on a similar scale for the 2010 football World Cup winner. For example, why bet on Australia to win the tournament with Sportsbet with 51.00 odds when you can back Australia with Betfair at 130.00 odds? North Korea has odds of 501.00 on Sportsbet and 920.00 odds on Betfair.

    This highlights the merits of shopping around for the best odds before you make any bet. I find that the longer the odds, the greater discrepancies that exist between bookmakers.

    Arbitrage opportunities


    Such odds discrepancies do offer occasional arbitrage opportunities. This is where having accounts with numerous bookmakers comes in handy. One bookmaker in particular that suits arbitrage betting is Betfair because of the ease with which you can bet against a particular team rather than for a team. Last week you could back Ivory Coast with Sportsbet for 30.00 odds and bet against Ivory Coast for 26.00 odds. Say you bet $100 for Ivory Coast with Sportsbet and against Ivory Coast with Betfair. If Ivory Coast wins the tournament you pay out $2,600 in Befair but receive $3,000 from Sportsbet. If Ivory Coast does not win then you lose $100 in Sportsbet and pocket $100 from Betfair. Note, due to the Befair fees you would need to adjust the bet amounts accordingly if you want to guarantee no net loss.

    Betting on odds changes

    One thing you can count on before, but especially during, the tournament is changes in odds over time. Prior to the tournament team odds will vary based on sentiment and the group draws. During the tournament, the odds will move drastically as results come in and as teams progress to the knockout stages.

    I have been selecting teams for which I believe the odds will shorten in the future. Using Betfair, I bet money on these teams, and if and when their odds shorten, I place corresponding bets against them to lock in a risk-free profit. Note this isn’t arbitrage betting because if the odds don’t move in the direction I want then I am left exposed to the actual end result of the tournament.

    Likewise you can bet against teams for which you believe the odds will lengthen. If the odds do get larger, you can then bet on them and lock in a safe profit.

    For whom could the odds change? Obviously every team, but some that stand out to me are:

    Odds to shorten:
    South Africa – as the host nation South Africa will be seeded so only one other seeded team will be in their group for the round robin stage. When the groups are determined their odds (currently 101.00 on Sportsbet, 120.00 on Betfair) could fall if they get the likes of New Zealand or North Korea in their group. Remember, both South Korea and Japan got through their respective groups in 2002. South Korea made it to the semi final!
    Other teams worth considering: France (currently 17.00 on Sportsbet, 18.50 on Betfair), Portugal (currently 17.00 on Sportsbet, 21.00 on Betfair).

    Odds to lengthen:
    Any team that has little or hope of winning, and that is unseeded, such as New Zealand and North Korea.


    One caveat is the Betfair odds I’ve mentioned represent the best available price, and some of these prices aren’t backed by a substantial amount of depth. For example, if you want to back Australia to win the tournament you could get $47.00 at 130.00 odds. To bet more than that you would only get 120.00 odds for the next $104 placed, and so on.

    Also, you need a large amount of money in your Betfair account to bet against a team with high odds. While you can be assured New Zealand won’t win the tournament, to lay a bet against them you would need $4,995 in your Betfair balance to accommodate a $5 bet on New Zealand by an opposing punter.

  • Arbitrage 22.08.2009 3 Comments

    It’s fascinating to look at the disparity in betting odds for the Miss Universe 2009 contest. How on Earth do you derive odds based on looks? Bookmakers have settled into a supply and demand approach to determine the odds, and of course the result is a huge level of disparity between countries.

    Australia is bullish on the chances of Miss Australia, with Sportsbet offering 3.20 odds for her to win. Meanwhile Paddy Power has Miss Honduras installed as the favourite with 12/1 odds. Miss Australia, meanwhile, is available at 16/1 odds with the Irish bookmaker.

    I have no idea who will win the contest, but I do recall that judges tend to be very generous to the local contender, so I have placed a small bet on Miss Bahamas. Also, I noticed that Sportsbet offered considerably longer odds on Miss Mexico than some other bookmakers in Europe, so I have placed a modest wager on Miss Mexico. Perhaps close to the end of the contest I will exploit an arbitrage opportunity if one presents itself. All I need is for one of my picks to still be around near the end of the contest to lock in a profit. Given the huge disparity in he odds at the moment, I think there’s a good chance that will happen. Even from the time I placed a bet on Miss Mexico her odds with Sportsbet have dropped from 13.00 last night to 9.00 today.

    I think this is one of those competitions where mathematics goes out the window and sentiment reigns. Good luck with any bets you make. As for the winner, your guess is as good as mine. I’m in it for the odds changes rather than the outcome itself.

  • Arbitrage 18.05.2009 1 Comment

    It’s always a good idea to keep an eye out for irregularities in available odds, because bookmaker mistakes do happen.

    Last night Sportsbet was offering the following odds on the Super 14 Tournament outright winner.

        |   Winner
    Bulls   |   2.35
    Chiefs   |   3.50
    Hurricanes   |   4.00
    Crusaders   |   6.00


        |   Winning Country
    New Zealand   |   1.53
    South Africa   |   2.40


    The Bulls are the only South African team left in the tournament, hence the disparity in the 2.40 South Africa odds to the 2.35 odds on the Bulls.

    I checked the odds again today and found that the winning country odds are now as follows.

        |   Winning Country
    New Zealand   |   1.55
    South Africa   |   2.35


    So the disparity has been fixed.

    It just goes to show that disparities do exist, although they disappear quickly!

    For the Super 14 tournament I have placed a bet a South African team to win using the 2.40 odds offered last night. Providing the Bulls manage to beat the Crusaders, I will likely hedge my bets by betting on the winner of the Chiefs / Hurricanes match to win the tournament. The Bulls would have home game advantage, and they play at altitude, so providing they can beat the Crusaders I would expect them to be installed as favourites to win the final. Odds of more than than 1.72 on their opponent would enable me to lock in a profit before the final commences. All that needs to happen now is for them to beat the Crusaders! Fingers crossed.

PinnacleSports.com Online Sports Betting
  • Arbitrage 21.04.2009 No Comments

    It’s interesting to see how public sentiment can change leading up to a match.

    Liverpool host Arsenal on Wednesday morning in the English Premier League.

    On April 15 I placed a wager through Sports Alive for Liverpool to beat Arsenal with odds of 2.10. Yesterday SportsBet was offering 1.85 for Arsenal to draw or beat Liverpool. If you sum the inverses of those odds (1/2.10 + 1/1.85) you get 1.017. Because it’s greater than 1.00 an arbitrage opportunity didn’t exist, but one was close, so I have been keeping an eye on the odds ever since.

    I checked back today and found that SportsBet is offering 1.95 for Arsenal to draw or win, while Sports Alive is offering 2.00. Both of these odds offer an arbitrage opportunity alongside my original bet, but of course using the 2.00 odds provides better value.

    Unfortunately, my original bet with Liverpool was modest, but I have entered into the arbitrage opportunity anyway, so I will be guaranteed a risk free profit. To make things more interesting, if had I bet $1,000 on Liverpool to begin with, my arbitrage opportunities, as calculated using the Two-outcome Arbitrage Calculator, would be as follows:


        |   No Arbitrage   |   Unbiased Arbitrage   |   Biased Arbitrage
        |       |       |    
    Liverpool Bet   |   $2,050.00   |   $1,000.00   |   $1,025.00
        |       |       |    
    Arsenal Bet   |   $0.00   |   $1,050.00   |   $1,025.00
        |       |       |    
    Total Bets   |   $2,050.00   |   $2,050.00   |   $2,050.00
        |       |       |    
    Profit if Liverpool Wins   |   $4,305.00   |   $50.00   |   $102.50
        |       |       |    
    Profit if Ars. Wins or Draws   |   $-2,050.00   |   $50.00   |   $0.00

    If I had made an original $1,000 bet on Liverpool and had entered into an unbiased arbitrage bet, I would have been guaranteed at a $50.00 profit.

    It just goes to show the merits of making early bets on events. While I really like SportsBet, one of its downsides is it tends to be slow on providing betting options for upcoming events. I find agencies like Sports Alive and Betfair offer odds much earlier, which enables opportunities like this one to arise. If you can pick the best value odds and the odds move enough in your favour, you can reap a profit before the match even starts!

    Update: Sports Alive is now offering 2.08 for Arsenal to win or draw. Talk about a huge odds shift. Punters seem to be heavily favouring Liverpool.

    If Sports Alive keeps jumping in with early odds like this, I highly recommend you get an account with them! It’s not often you see a betting agency offer odds on a match where one of the teams involved had another game to be played beforehand. In this case, Arsenal were involved in the FA Cup against Chelsea, with Robin van Persie and Emmanuel Adebayor ruled out with injury after the game.

    Update: Liverpool drew Arsenal 4-4! I feel good about my decision to accept the arbitrage opportunity now!

  • Arbitrage 24.01.2009 2 Comments

    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.

    Disparate odds between bookmakers

    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.

    Changing odds during a multi-game series

    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.

    Intra-game betting

    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.

    Changing odds leading up to an event

    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.

    Sign up free bets arbitrage

    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.

    Exchange rate warning

    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.

PinnacleSports.com Online Sports Betting
  • Arbitrage 22.01.2009 No Comments

    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.

  • Arbitrage 20.01.2009 1 Comment

    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.

    Three-Outcome Arbitrage Theory

    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:

    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 12.01.2009 1 Comment

    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 Theory

    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.

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