# Sequences

Sequences are probably responsible for more punters failing than any other factor in racing. In previous articles we have attributed that to the average punter’s failure to correctly assess Probability, but in reality, these two concepts are opposite sides of the same coin.

Clearly, if we wish to assess the chance of something happening on a once-off basis, the question of a sequence of events doesn’t enter into the equation. We simply need to weigh the evidence and make our decision accordingly. As soon however, as we want to repeat an action the outcome of which isn’t certain, then the relationship between probability and sequences immediately becomes apparent. For example, what is the probability of getting 4 successive winning bets from a strike rate of 50%? The answer is simply to multiply the probabilities together, since every event is not just part of a sequence, but a stand-alone as well. Thus, 0.5 x 0.5 x 0.5 x 0.5 = 0.0625, or 6.25%. In other words, only about 1:17. Very important to consider if we are trying to string place bets together, for example. If we can achieve a strike rate of 75%, the chances of success in getting 4 in a row rises to just under 1 in 3 or 31.6%, which is almost identical to that mentioned below as the strike rate for favourites winning their races. The average price paid for a winning favourite is a bit under \$3, which is why we will go broke if that is all we ever bet upon. It is not difficult to get an average place dividend of better than \$1.50 however, and 4 of these running into one another amounts to \$5.06. Is it any surprise that the Totes and bookmakers do not advertise place betting in their premises or the media?

Perhaps the easiest and most common example is the coin-tossing experiment. If we toss a coin 10 times, we know that the chance of it landing on either side is exactly 50% or 0.5 in Probability terms. This doesn’t mean of course, that these events will occur precisely in a sequence like this: HTHTHTHTHT. The runs can come in every conceivable order. The reason is the variables that come into each action, such as the speed and/or the height of the spin, the evenness of the surface onto which it is tossed, and so forth. The only thing of which we can be certain is that over a very large series of spins, there will be a relatively minor deviation from the 50/50 split.

Statisticians refer to such things as a ‘normal distribution’, and the examples of the difference from a 50/50 split over a series of say 1,000 spins as falling between a certain number of ‘standard deviations’ from the norm. Without becoming too technical, all measurements of things which can be expected to have a normal distribution curve (such as our coin tosses, or the average height of people in a certain population), will tend to form a bell curve when shown graphically. Over 96% of all these measurements will fall within 1 standard deviation of the ‘mean’ (or mid-point), and over 99% within 3 standard deviations. This tells us that whenever we have measurements that can be regarded as reasonably accurate, the Laws of Probability predict very closely what sort of variations from the norm we may expect.

Now when we come to gambling, consideration of these Laws is vital in making our decisions about where to bet. When betting on roulette for instance, we know precisely what the odds are for every type of bet available, and we only have to worry about the fact that the House, when we are successful, will not pay us our true odds! What this ultimately means is that it’s impossible to play indefinitely and expect to come out ahead. Of course it’s still possible to win, but one must accept that this can only be done by getting temporarily ahead of the Probabilities, and running away with our winnings!
It’s different with horse racing. Here there are so many variables, that a correct assessment of the true odds of any horse is extremely difficult, and is largely a matter of opinion, which is why different bookmakers will offer different prices about the same animal. It also explains why different sections of the large punting population will invest money on every single horse in the race, irrespective of whether they have any objective chance of winning or not.

It’s already been mentioned in one or two of the blogs here, that one of the most famous statistics of all in racing, is that favourites will only win about 31% of races. There are numerous such statistics which have stood the test of time, even though the distribution curve for the prices of winning horses is not a normal bell-curve, but is obviously slanted towards the lower end of the price scale. It would benefit most punters to pay a lot more attention to these collections of statistics than they do.

Having said that, if we look too closely at all the masses of data available these days, it’s very easy to overload ourselves and wind up with too many options to consider. A survey was once conducted, which divided a group of punters into three sections. One section was given very little information, another, a moderate amount, and the third was given a whole load of information to assess. They had to make their assessments based on what they were given.

Perhaps unsurprisingly, the group that did the best was the one with the moderate amount of data to work with. This would tend to suggest that a very effective way of making selections is to have some method of eliminating, instead of considering, the vast majority of horses in a race from our assessment. This not only saves us from a pile of work, but also prevents us from betting on too many horses (a very common failing). Of course, eliminating many runners also means that we will miss out on some winners. The question is though, what is the average price of those that we eliminate and did win? Would including them have improved, or lessened our overall bottom-line result? A corollary to this question is ‘What are the average prices of the horses we are left with, when they win?’ Do these eliminate enough of our losing bets to leave us in front overall?
This brings us back to the question of Probability and sequences. Which is more important: getting a lot of small-to-moderate priced winners, where a losing streak of 10-15 does serious damage to our bank; or scoring some small-to-moderate priced winners, interspersed with some very valuable high-priced successes? The latter can enable us to withstand losing streaks of 20-30 without too much trouble (provided we don’t lose heart).

Let’s refer again to roulette. There are many types of bets available. Mathematically, the House advantage is smallest when a single number is bet. The random distribution of large numbers ensures that of every 36-37 spins (allowing one chance for each number on the wheel to hit), there is an almost 90% chance that there will only be 21-26 different numbers represented. Almost half of that, 40%, will be taken up by series where there are either 23 or 24 different numbers. Therefore, in all these sequences, between 12 and 17 numbers (with 13-14 numbers predominating) will be repeated at least once. Hence, when selecting single numbers to bet, we should focus on those that have already appeared recently. Clearly, there’s no way of predicting exactly how this will happen, how the ball will jump after hitting those little dividers fixed in the wheel, etc. It is not necessary to know how. All we need is the knowledge that these are the probabilities, allied to the probability that of course the numbers adjacent on the wheel to those mentioned, will be hit exactly twice as often. With that knowledge, we should be able to fashion a staking method, involving small stakes, with the possibility of large payouts, especially when two or more consecutive hits occur.

We may not be able to explain fully how it is that a horse with a win strike rate of 12-15% can win a race, beating horses with strike rates double that or more, but is it really necessary to do so? If we can identify some of the common factors in horses which achieve such feats, and we know that the payout on these animals is significantly (sometimes drastically) higher than the probability of this happening, that is a bet that should be made.

Commonly called an overlay, a series of such bets would inevitably lead to handsome profits, over time, provided one has a plan to withstand the inevitable losing streaks. It turns out that some of the probabilities in horse racing have more in common with other forms of gambling, where the odds can be precisely determined, than was previously imagined.

In closing, it remains to emphasise that as we embark on what is essentially an endless series of bets, that we are going to encounter some serious losing sequences (from the win component view).

Bear in mind that these losing streaks could happen consecutively, with only sparse wins separating these runs. Of course, winning spells will balance such events, when everything we touch seems to turn to gold. Our plan must encompass these possibilities.
This is why it is essential to factor in the place bets. With a place strike rate of say 70%, the outlook is much more clement. From 1,000 events, we can be certain that there will be at least one losing streak of 6, with an 80% chance of 7 in a row. However, there’s only an even-money chance of hitting a losing run of 8. With an average place dividend of around \$1.60, it won’t take long to recover from such setbacks. The important point however is the insurance these bets provide against serious drawdowns from losing win bets. Even over a sequence of 10,000 wagers (and that may take years), there’s only a 41% chance of even getting 11 wrong consecutively, and clearly, the winning streaks are much more encouraging, where we may expect plenty of sequences up to 8 or 9, with some going into the high teens.

There is free software available online which enables us to easily perform these sequence calculations (especially regarding expected losing streaks), and it is difficult to overstate how useful such tools can be.