Unfortunately, after hours of searching I was unable to find an answer to the following scenario:
Let's assume I play five unique combinations in a weekly 6/49 lottery, where the chance of matching all six numbers in this one draw will be 5/13983816 or p=0.0000017878.
However, how would I calculate the winning probability if I played the same number of tickets in 52 weekly draws (that is, a total of 260 unique lines altogether).
The probability that you do not win with this draw $n$ times in a row is $$(1-\frac{5}{13983816})^n$$ hence the probability that you win at least once is $$1-(1-\frac{5}{13983816})^n$$ If you plug in $n=52$ , you get $1.859\cdot 10^{-5}$ , which is very near to $\frac{260}{13983816}$, but the exact value is in fact a bit smaller.