Due column betting

'Due-column Betting' (also: 'due column betting') is a type of fixed-profit betting strategy whereby a bettor increases the amount he wagers on a single proposition after each successive loss. According to this system, the bettor determines a target profit before he begins betting. Then he increases his bet on propositions following a loss in such a way that a win will recover the sum of all amounts he lost from his preceding bets plus gain him his predetermined profit.

While similar to both the Martingale and Labouchere strategies, "Due-column betting" differs from other like betting systems in that it accounts for the odds variance in successive parimutuel propositions. Still, it is often used interchangeably with the casino gambling term "progression system", which refers to several similar betting systems typically employed at casino gaming tables.

System explanation

Due-column wagering is considered a fixed-profit system because the due-column bettor determines his desired profit before he begins betting. However, whereas with percentage-based money-management systems the bettor varies his bets as a percentage of his bankroll, with a series of Due-column bets he bets the amount necessary to make his desired profit plus the total amount necessary to recuperate what he has lost in all previous wagers. The idea is to double the subsequent bet after each loss and reduce it to the original amount after each win. In the end, the winnings cover all losses of previous bets. The basic difference from the Martingale strategy is that you need to double your bet size every time you win, instead of every time you lose.

Supposedly betting this way ensures that if the better correctly calls a single race at any point in the series he will have profited and can cease betting or begin a new series. Proponents of the system argue that the probability of experiencing ten consecutive losses if the bettor is an average, 33 percent handicapper is 1.82 percent. Consequently, they conclude, a Due-column bettor has a given probability of profiting from slightly more than 98 percent of all 10-race series. And, they therefore believe, a Due-column bettor will win the product of his designated profit times the expected percentage of wins per the number of series played; or, assuming the bettor's desired profit is $100, he will win about $9,800 per 100 series played.

The coining of "Due-column" is due to bettors' creating charts to track their bets. A typical Due-column chart is as follows:

Race	Due	Odds	Bet	Result
1	$3.00	3:2	$2.00	Lost
2	$8.00	7:5	$6.00	Lost
3	$17.00	7:5	$12.00	Lost
4	$32.00	6:5	$27.00	Lost
5	$62.00	6:5	$52.00	Lost
6	$117.00	7:5	$84.00	Lost
7	$204.00	4:5	$255.00	Lost
8	$462.00	1:1	$462.00	Won

Mathematical analysis

There are several problems with the assumptions that Due-column bettors make, not the least of which is that the mathematical basis for the system is flawed. Assuming a bettor in any series of horse races is a 33 percent handicapper with an average mutuel of $5.00. Such a bettor's mathematical expectation can be expressed as follows:

E(x) = .33 <--> ($1.50) - .67 = -$.175

According to this analysis, the average bettor's mathematical expectation would not provide a profit, but a loss because his expectation is a negative gain every bet. As a result, the bettor's playing the Due-column system will only multiply his losses over time. After 10 losses given the expression above, for instance, the bettor would average a loss of $1.75, thus making an upward-sloping expectation impossible.

Theoretically, the solution to this flaw in the Due-column system is for the bettor to consistently handicap and have a mutuel above the average rates. If, for example, a bettor had a handicap of 35 percent and mutuel of $6 his expectation could be expressed as follows:

E(x) = .35 x (2) - .65 = .05

This above-average bettor would then have a positive expected gain of 5 percent or $.05 every race. Still, should that bettor attempt to apply the Due-column system to increase his gains he will run into a second problem: Diminishing returns.

The bettor would run into diminishing returns because, as seen in the example Due-column chart above, the bets he must make increase exponentially compared to each preceding bet with each successive loss. Because of the nature of parimutuel betting, then, the bettor's larger wagers will depress his payout odds. As a result, the bettor's real expected return for the session will deflate far below his original target profit.

Furthermore, in horse racing no single horse runs more than one race. So, though jockeys might ride more than one race, each race is arguably an "independent event" and the Due-column bettor will therefore run afoul of the Law of Independent Trials; that is, believing the outcome of each event is significantly dependent on the outcome of the last he will commit the Gambler's Fallacy.

Indeed, insomuch as jockeys do ride in multiple races, horse races are not entirely independent events. The poor morale and physical enervation of a jockey who recently lost a close race previously could undermine his ability to win the following race. But even the worst jockey will have minimal effect on an outcome if riding a horse that performs far better than the other racers.

As with any series of independent propositions, then, only with trials numbering in the thousands can a Due-column bettor ensure that, on average, his historical number of wins will match his probable number of wins. Consequently, experiencing more than 10 losses in a single series is likely to occur according to the Law of Large Numbers, and as the chart above shows, continuing to play the Due-column system will require risking a bankroll proportionately far too large to wager for the expected return.

For all these reasons using the Due-column system is not only unproductive, but counterproductive. Because of this many contemporary gambling strategists strongly advise players not to consider it a winning strategy.