Your 6 line argument will do little to sway the other side, there are entire books written on this exact subject

Well lets make it simpler to understand.

Lets say the lottery has 10 different possibilities 0-9.

If you buy 1 ticket, what are your odds? 1/10

If you buy 2 tickets, what are your odds? 2/10

If you buy 3 tickets, what are your odds? 3/10

If you buy 4 tickets, what are your odds? 4/10

If you buy 5 tickets, what are your odds? 5/10

I can keep going and going until my post is as long as the book you'd like to read, but I think you're confused here.