Can I predict the winning lottery numbers

Tags: statistics ml

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in data-science · Sun 29 December 2019

This was one of the questions asked by a colleague of mine who is new to the data analytics and Machine learning space. I had to tell him that this isn’t possible because data itself is not suitable to do any sort of valuable predictions. It usually takes some time to get this intuition. Those who have statistics background can quickly catch-up, others have to put up extra effort to solidify these concepts.

So, back to the question, can we build a model to predict lottery numbers? The short answer is NO, and the long answer is NO :). Now you have to ask why!

Why this post?

This question may be a very trivial one for seasoned ML practitioners, but sometimes experienced one also misses the key basic concepts when it comes to how to deal with data and what data is good for a particular problem. This is my attempt to answer the questions that I had!

Looking into the winning chances

Let’s take one lottery series for this experiment, this lottery number has 2 alphabet and 6 numbers, eg; AG389435. In this case how many unique lottery tickets can be printed?

$$ \begin{array}{l} Total\ number\ of\ lotteries\ for\ number\ sequence\ of\ form\ \mathbf{AB123456}\ \ =\ 26^{2} \ \ 10\ ^{6} \ \ =\ 676\ Million\ \ =\ Chance\ of\ winning\ for\ a\ person\ =\ \frac{1}{676\ Million} \ =\ \mathbf{1.4710^{-9}}\ \ Here\ we\ are\ assuming\ equal\ chance\ for\ all\ to\ win,\ and\ the\ lottery\ system\ will\ ensure\ this\ constraint.\ \ So\ winning\ probability/chance\ is\ \mathbf{0.000000147} \ \ or\ 1\ in\ 676\ Million \end{array} $$

To put this number into context, let's take another study done to identify the cancer risk due to smoking [link]. According to their study, they estimate 1 in 10 men and 1 in 8 women in India can expect to develop cancer of any form, in their lifespan after the age of 35 years. This means getting cancer is a way higher chance than winning a lottery.

Why am I saying lottery data isn't usable for any prediction

Because the lottery prediction is done using some random number generator (RNG), this means RNG ensures that every lottery purchased gets an equal probability of winning, usually the odds of winning are above 1 in Million. And there won't be any relation between historical predicted number and the future numbers, because they are close to independent. So you can't find any relation from the historical winning numbers.

If we are using some faulty RNG machine or RNG system with lesser entropy then the results may be skewed, so we can see patterns in number prediction. So how few individuals broke the lottery system legally, below listed are the two instances people worked hard to increase their chances of winning, here also they aren't predicting the actual winning numbers, instead of increasing the chance of winning probability of each lottery.

1. Michle Memorized live game patterns, video

   This story may come as a Hollywood movie soon.

2. Or you have to run a lottery syndicate to increase the chance of winning by pooling the tickets from multiple contributors. Here is an interesting guy who did this thing across the world. It's purely playing against the odds by purchasing more tickets.

Does an ML model won’t predict the winning numbers at all?

If you run enough times, your model may predict the right answers sometimes, so why are you saying ML models can’t predict correctly at all? We call a model doing good when it produces predictions better than a simple guess. If your model prediction accuracy is close to any other simple guesswork, then why do you need this ML model after all.

The predictions are really based on known patterns. The patterns are coming out of data ( data may be image, sound, simple numbers anything).

When can we do ML

We can do any sort of data analysis or prediction using statistical methods only when the data has some repeating patterns or correlation or some inherent orders.

eg; When you see a different type of cat, you can identify it as a cat, how’s that working, when you look at it objectively there is some underlying order in their pixels and behaviors, and our brain maps those patterns of light signals to the cat. And you can apply this same analogy ( similar technique ) to our ML models here, models learn to identify cat/dog by capturing these common patterns present in the data or image or video. If the data doesn’t bring these patterns, how can any system or our brain identify a particular object?

Similarities with Language Models

The number of sequences in the lottery number can be treated as a finite sequence. The random numbers from RNG usually pick random numbers from this finite sequence. Let's connect this to the Language models in NLP. NLP language models predict the next word from whatever it has seen till now. If we take all the words in the English dictionary, it comes around 171,476 words. If we arrange these words in a particular order it forms a valid sentence, ie; we can't put all combinations of words to form a valid sentence. This means there is a fixed order of word sequence, this is what the NLP models learn internally via word co-occurrence and other methods.

Now come back and see how the sequence predicted by RNG for the lottery has some pattern ?, it shouldn't. So we can't find any sort of significant statistical correlation between two lottery numbers.

How clickstreams are helping for the recommendation

This is another way of pulling out data that has some meaning or patterns present in it. When you browse over any e-commerce site, for a given query your mouse movement leaves out some meaning about those items. They are related items !. So if you pull out the clickstream done by a user for a session we can find the related items and using that data we can do recommendations for a given query.

You can read more about this from this paper from Airbnb

I will be posting one more article to show how those individuals increased their chances of winning.

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