In the Bulgarian case, with six numbers (calculated in exactly the same manner as the 42, 41, 40 method), there are 6 x 5 x 4 x 3 x 2 x 1 = 720 different ordering combinations.  Thus our earlier number of 3.78 billion actually represents 720 identical results. 

So, dividing our very large odds by 720 gives us the true odds of 1:5.24 million.  In other words, there are only 5.24 million unique combinations of numbers in the entire lottery.  You want a guaranteed win in the lottery?  That's how many unique entries you'd have to submit!

Incidentally, Microsoft Excel has a formula to calculate exactly this value.  If you open Excel and type into a cell =COMBIN(42,6) you will see the correct result.  You can use this to calculate the odds in your own country.

Now, here's where people's intuition starts to go a little crazy.

If I were to ask 100 people what are the odds of the sets of numbers on successive draws being identical, most would start trying to multiply 5.24 million by itself to get some kind of fantastical result.

That's wrong - it would only be correct if I have provided a specific set of numbers and asked for the odds of getting exactly those numbers twice.

Instead, in this instance, we really don't care what the first set of numbers are - we simply want to know the odds of getting them again.  Interestingly, this is exactly the same as asking what my chances are of selecting the same numbers in the original draw.
 

So, the final question - how unusual is this?