The outcome is totally random - yes. As I mentioned, a historical simulation may show a more or less universal distribution of drawn numbers, in which case the odds and the probability would be the same for all practical purposes. However, a historical simulation may show certain combinations of number drawn more often than others material enough to be a pattern or series of patterns emerging that increases the probability of sets of numbers being drawn. The draw is stall random, but the probability - and that is all it is - a probable and no guaranteed - set of drawn numbers may become higher than any old random selection. This could be because of say manufacturing imperfections of the balls where minutely different weight distributions result on some balls being more likely to be scooped than others.. And it could be that the probability if subsequent balls being drawn changes depends on what ball/s were previously drawn for the same reasons. In order to prove it, you would need a lot of data, including that of the factors that we define as determinative to the probability - but without those factors, we can only rely on the historical number draws.
Given the permutations and combinations, coming to a single set of numbers likely to be drawn using a historical simulation would improve the probability - but only marginally at best. These simulations predict probable outcomes over various scenarios and normally a confidence level is provided. And it will be a probability map. So for example, it may give a probability for each number of that number being drawn first. For each number, it will give the probability of every other number being drawn second. Then for each number drawn second of the number that was drawn first, it will come up with a probability of each number not drawn yet to be drawn third, and so on. Taking this approach, there are 130m nodes in the map for each number drawn first. So, if 1 is drawn first, there will be a map of 130m possible permutations and combinations. Now multiply by 6 and that is how big the probability map will be.
You can use a binary coefficient approach to reduce it, but you attenuate the probability calculation as a result because we don't know the factors that are causing some numbers to be picked more than others.
Anyway, for a 6/45 lottery draw, the probability map reaches something like 900m nodes, each with a confidence factor. Of course, if we could pick our numbers just before each number is drawn, we could really improve our probability of winning. But we can't, so the only way to really improve the probability is to try and predict what the first through 6th number is going to be dependent on what we think the first number is going to be. So, in defining our confidence level, we have to look for any other correlations. As we have virtually no other known factors, the only thing I can think of is to look at time based cycles and add that to the algorithm to predict the different potential numbers to draw. And that is the rub. Coming up with one most likely to draw is not really going to to reduce it much; intuitively, I would reckon you need to put around 200k minimum bets on it spread across the different scenarios. And, it is still not guaranteed.
I have no idea what the cost of a singe entry is, or 200k entries are against the normal prize value. So, it may be futile.. buit the above is a glimpse of algo trading (well, that would get smashed in the markets.. so I would not recommend it).
Now I am rambling as I have had my first wine in 6 months - a Jim Barry McLaren Vale.. and very nice. What impressed me is my local Majestic Wines knew exactly which aisle I was heading for when I entered the shop...
I digress.
Anyway, chasing the single winning entry will probably not yield too much more likelihood than the basic odds.. it is how you play the probability map.