What is Fixed odds betting and Due Column betting?
By Chris D.

Gambling has been around in our societies for a very long time. Over the time as the stakes involved in gambling rose, so did sophistication in rules in how to gamble rose. Although rules that came into force to govern how to gamble were helpful in reducing the number of complaints for foul play, other rules in terms of how to gamble are more informal and can also be considered as strategies.

Louis Pasteur reminds us that ‘Chance always favors the prepared mind’. Before entering the world of gambling it is imperative that you know what you are getting into after all it’s your money and you are primarily undertaking a financial risk. In gambling terminology the size of this risk involved is given the name of ‘odds’. Odds on bets also roughly express the probability that the bettor will win. There are two main type of betting available; all forms of wagering in the sporting world such as horse racing and football etc. involve fixed odds betting, where as in the financial world spread betting is utilized[i]. This paper shall be focusing on the former.

As the name suggests, fixed odds involve a fixed amount of money put at risk also referred to as the ‘stake’. Bettors bet a stake against the odds offered by the bookmaker or the exchange. This fixed wager in turn results in a fixed reward. Fixed odds are the current fixed price for an event at any given time and will not change after the bet has been placed.

There are three major ways that the fixed odds can be quoted by the bookmaker, they are essentially the same and can be thought of referring to the odds in three different languages. The first one is Fractional odds and is more common in horse racing than sports betting, this is also known as traditional or UK odds as bookmakers in UK and Ireland prefer them. As the name indicates they are presented in a fractional form and no sign precedes them. The fractional from represent that the stake equal to the denominator will result in a winning equal to the numerator.[ii] So what the bettor wagers is in the denominator and what he wins is in the numerator. Payout to the individual would equal the sum of his stake and his winnings when the stake has been paid for upfront.

Winning = Stake * Fraction Odds

Payout = Stake * (Fraction Odds + 1)

= Winning + Stake

For example, odds of 2/1 (two-to-one) imply that the bettor will win £20 from a £10 stake. The payout would be £30.

Odds of 1/1 indicate ‘evens’ or ‘even money’ which means that the winnings are equal to the stake and the bettor this way is able to double his wager.  Where the numerator is greater than the denominator i.e. the winnings are greater than the stake, it is known as odd-against. On the other hand odds-on refers to the situations where the winnings are less than the money wagered.

The second type of fixed odds is Decimal odds, and this type is also the standard way of specifying odds. They are also called European odds and are preferred by bookmakers in Europe, Canada and Australian regions. Mathematically these odds are always greater than one and no sign is used for these as well. The decimal numbers specify how many times the stake the payout will actually be. For example 3.00 indicates that that the payout will be 3 times the stake for each dollar you bet. With a stake of $10 at 3.00 would end in a payout of $30 if the bettor wins. This would imply that the even odds 1/1 are quoted in decimal odds as 2.

Pay-out = Stake * Decimal Odds

Winning = Stake * (Decimal Odds – 1)

= Payout – Stake

Decimal odds are a lot easier to weigh odds against each other in comparison to fractional odds and therefore the most popular way of quoting odds.  Decimal odds are mostly used by trading exchanges.

Lastly the Moneyline odds are famous for being used in sporting event such as football in the US. These odds are also commonly referred to as the American odds. These odds are distinct from the previous two as they are either positively or negatively signed and the numerical values of these are always greater than or equal to 100. Indonesian and Malaysian odds have the same formulas as the US moneyline odds, the difference lies in the fact that their basis is 1 unit and not 100. The signs here indicate whether the winnings at the end of the bet are greater than or less than the stake wagered. The Negative moneyline odds represent how much to wager in order to win $100 while the positive moneyline odds represent how much the winnings will turn out to be if the stake was $100 to begin with. Even moneyline odds in this case are represented by 100 which can be either positive or negative. The sign is often not stated by the bookmakers.

For example odds of -180 indicate that in order to win $100 the stake should be $180. Kochan[iii] elaborates with the example of favorites and underdogs in a football match. With the favorite team (A), you divide the stake by the odds and for the underdog (B) you multiply the stake with the odds. If A is has the odd of -350 and B have the odd of +310 than to calculate your winnings firstly you convert the odds to decimals and multiply and divide accordingly. Therefore, if the bettor wages $1000 on A at -350 and A win the match they will end up with $285.71 as 1000/3.50 =285.71.

As these three types of odds are interchangeable, there exists a conversion system between them. Conversion[iv] from fractional odds to decimal odds is easy as it involves just converting the fraction to its equivalent decimal value and adding one to it. Converting from fractional odds to money line is rather complicated as it involves converting the fraction to an equivalent fraction with the denominator of 100. The numerator of this fraction will be the moneyline odds. Converting from moneyline to decimal odds depends on the sign. If the odds are positive then divide them by 100 and add one, if negative then divide 100 by the absolute value of moneyline odds and add one.

Knowledge of odds enables the bettor to understand the risks associated with each individual wager. However, often people try to get around these risks by employing strategies in the way they bet. Now although these strategies are being used in a manner to reduce risk they might as well backfire. There are some popular strategies that are followed commonly without much understanding. They do appeal to a naïve mind, but when investigated in further detail they reveal the faults in their inherent assumptions. One such theory is partially based on the law of average and partially based on the assumption that any person can make money on any gamble given enough repetitions[v]. The way the system would work is that the bettor would decide what the gambling arena owes him; he would then bet in a manner that his first bet would yield him that amount. In case he loses the first bet, he would then bet in a manner that he is able to win the amount he considered due as well as the amount of money he lost in the first round. This way, as the bettor loses each round he has to increase the amount of money he has to bet in order to get the amount due and is increasingly likely to run out of all the money he had to start out with.

If everyone in the gambling arena would be following the same strategy, it is not hard to see that only a fraction of those people would be able to get their desired result. In effect, the result is that participants, who ran out of capital while following this strategy, simply transferred their capital to everyone that managed to successfully follow the strategy. This is despite the fact that the underlying assumption of this strategy is that everyone should be able to win.

To give more clarity to this system explanation, we can build a table to display what is happening. This table is also the reason why this form of betting is called due-column betting, as the amount in the due column is being tracked by whoever is betting.

As can be seen in the table, during a losing streak the amount of capital required for each successive bet balloons at an extremely rapid pace and subsequently decreases the likelihood that the bettor would remain in the game long enough to be able to recoup his losses. In this example it is easy to see how the system is working. The better had decided on beginning this methodology that he is due $100. As he lost $20 in the first round, he updates the due column to be the sum of what has due in the previous round and what was lost in it. As you can see, the amount bet grow at a very fast pace as the better tries to recoup his losses in addition to the $100 that he had planned on winning.

Although this method is used in betting on racing horses, one should realize that this would not be a true application of the law of averages, and is therefore even less effective. In horse racing, a horse participates only in one race therefore making it impossible to bet on the same horse over and over again. Furthermore, even if the bettor repeatedly bets on the same jockey, the two bets would not be identical as not only has the horse changed but the physical conditions of the jockey as determined by his stamina are also different and therefore affect his winning chances[vi].

Returning to the discussion about how this strategy seems to be easy money considering the basic logic of it, some writers have gone ahead and labeled this strategy as lunacy[vii].  In this argument, the basic premise is attacked by understanding that whoever is running the gambling arena has to be able to make a profit for the arena to stay around. By default, that would mean that in the expected profit in a single bet would always be negative considering purely statistical tools. This can be proven by assuming that 101 people are betting a dollar each to win a prize of $100. In this way, the expected winning for each player statistically is $100/101, however the money one has to pay to get this winning is $1. Therefore, the expected result of the complete transaction is 100/101 – 1 = -$0.0099. Now, no matter how many times you repeat this experiment, you cannot statistically expect to have a positive winning. Replacing this example with another which might be easier and could be used by someone promoting due column betting would be as follows. The better has to be using the due column betting strategy on races that have a 2:1 bet repeatedly. The chance he loses one bet is 0.5, for two it is 0.25, for three it is 0.125, four .0625, five 0.03125, six 0.015625. Therefore, even with as little as 6 consecutive bets there is more than a 98% chance that the strategy would be successful. What is missing in this information is the pain that would be experienced in the 1.5% chance that all six bets are lost. If the better had planned on winning $100, by the time he fails six consecutive bets with 2:1 odds, the amount of money lost is already over $1,000.

Although it would make sense to employ a betting strategy, using a due column strategy is completely without statistical merit. An alternate often described as a useful strategy would perhaps be always betting a fraction of the amount of money you have available for betting before each round. This way losing streaks would lead to progressively smaller bets, thereby allowing more chances to take advantage of the law of averages.