Due Column Lunacy

by Dick Mitchell

There's a betting method that's been sold as a system to be used in just about any parimutuel gambling game anywhere. It's also appeared in many books and articles on horse racing. This method is the ultimate in stupidity. It's the largest money-burner imaginable. If you think I've talked before about dumb things horseplayers do, hold onto your hat. This is the dumbest, most ridiculous form of wagering ever devised. It's called "due column" or the "owes me" technique. This idea is simple to grasp and sounds benign. Let me try to make a case for this method.

If a player wants to earn $100 per day at the racetrack, what he should do is wager in such a way that the first winner he hits during the day assures him of his profit goal. In other words, it takes only one winner per day to guarantee he'll make at least a $100 profit. Suppose the player performs like the public. He's a 33% handicapper. It's very unlikely that he'll experience 10 consecutive losers. The probability of doing so is .67 multiplied by itself 10 times, or roughly .0182. This says that in a 100 sequences of 10 races each, he can expect to lose less than two of them. His chances of not losing (winning) any single sequence are .9818, or greater than 98%! Therefore, what he does is wager enough depending on the odds to have his first bet yield the $100 profit. If he loses he simply adds the amount of his loss to $100. This becomes his due column.

For example, suppose the first playable race offers odds of 4-to-1 on his top selection. He bets $25 to Win. If this selection wins, he's on his way home, mission accomplished. If it loses, he now adds $25 to his original goal of $100 profit. His due column is now $125. He must now wager enough, depending on the odds offered on the next race, to make up for his losses plus his $100 profit goal. Let's suppose the next playable race offers odds of 3-to-1 on his top pick. He now bets $42 to Win on his selection. Once again, if his selection wins, he has achieved his goal and is homeward bound. If the selection loses, he now must add $42 to his due column of $125. His new due column is $167. This sequence continues until he hits a winner. It only takes one winner per day to earn $100 profit at the races. Any handicapper, no matter how unskilled, should be able to pick at least one winner per day. This sounds fairly easy, but the only requirement is a bankroll large enough to withstand a number of consecutive losses.

Let's examine this technique from the point of view of a winning player. The public is a 33% handicapper with an average mutuel of around $5.00. Our friend with the due column is a might bit better. He's a 35% handicapper with an average mutuel of $6.00. The public is, of course, a losing player. Its expectation is approximately as follows:

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

If you simply emulate the public, you're assuring yourself you'll lose in the long run. You'll probably lose pretty close to the track take. If you have a method that does not show a flat-bet profit, there is no betting scheme in the universe will turn this into a profitable situation. If your single-bet expectation is negative, then any number of repetitions of this wager, regardless of bet-size, will still result in a negative expectation. One thing you can do by your betting scheme is to make things worse! The best you can do is achieve your single-bet expectation. Sorry, folks, that's a mathematical law with as many exceptions as the Law of Gravity. If you insist on denying this irrefutable truth, be my guest. I can get you a great buy on a "perpetual motion machine."

Let's take the above winning player and employ the due column technique. His single-bet expectation is a positive 5%.

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

We'll give him a bankroll of $5,800 and use $100 per day as his profit goal. In order to make this scenario simple, let's assume that each wager is paid at odds of 2-to-1. His initial bet is $50. The following table represents the 10-race sequence I mentioned earlier. If he wins one of these wagers, he has achieved his profit goal and a new sequence begins.

Wager # Due Column Bet Size
1 100 50
2 150 75
3 225 113
4 338 169
5 507 254
6 761 381
7 1142 571
8 1713 857
9 2570 1285
10 3855 1928

Look at the rapid escalation of bet-size. The seventh bet is more than ten times the original wager. The tenth bet is almost 39 times the original wager. If he had to go to an eleventh bet, it would be $2,892! At this point he would hit the diminishing returns situation imposed by the pari-mutuel system. A $2,892 bet on a 2-to-1 horse would depress the odds. This method has the seeds of its own destruction sown right into it. It's quite common to experience 10 losing Win wagers in a row. In my case, this happens with greater frequency than I would like to admit. Last year, I had a string of 13 consecutive losses, and another of 11. Imagine betting $1,285 on a 2-to-1 shot? Wouldn't this make you somewhat nervous? You bet. Now you lose. If you were nervous with the last bet, the next one might cause a mild heart attack or seizure.

Let's consider what happens when the due-column-bettor applies this technique to a large number of races, in 10-race sequences. Any sequence will result in either a $100 profit or a $5,783 loss. The expectation per sequence at a 35% win rate is as follows:

E(x) = $100 <--> (.987) - $5,683 (.013) = $24.821

Therefore, he can expect on average to win $24.82 per sequence. After 100 sequences his profits are $2,482. Wow, that's great! He's making money, hence this method is sound, right? Wrong. Dead wrong! What ever happened to his goal of $100 per sequence?

If he were to use a flat-bet strategy with a bankroll of $5,800 and a single-race expectation of 5% at average odds of 2-to-1, his optimum wager would be 2% of his bankroll. (The optimum flat-bet amount is your single-race expectation divided by your average odds.) His wager size would be $145. Since his single-race expectation is 5%, he can expect to make $7.25 per race, hence in a sequence of 10 bets his expectation is $72.50. Now what has the due column bettor accomplished by using this weird system of money management? He's reduced his expectation from $72.50 per sequence to $24.82. That's taking a 66% beating! In addition, he has taken an enormous risk of tapping out. From a risk-management point of view, it's hard to conceive of a worse thing to do.

Please don't be deceived by this type of scheme or any variation of it. It's death on the bankroll. It's a money-burner of the largest magnitude possible. Did you recognize this technique as our old friend Martingale in disguise? Let the profit goal be one unit, the odds even money, and the initial bet one unit. The due column sequence becomes 1, 2, 4, 8, 16 ....

These kinds of techniques sound plausible. They sound wonderful on first hearing. What an easy way to make money. Please be warned that whenever something sounds to good to be true, it usually is. Easy money is the road to the poorhouse. And you can bet your sweet bippy that your residence won't be Easy Street if you use this insane form of betting.