I've never studied statistics, which might be why I am perceiving this differently.
Having 1/2 odds means that you have 1 of the 2 possible outcomes.
So if 2 unique draws were made, your number would definitely come up.
If you have 10 out of 20 possible draws, it does not equal 1/2, as 2 unique draws could still result in you winning nothing, if 2 of the numbers you don't have are drawn. If would take 11 unique draws to guarantee you a win
So in order to guarantee a win from odds of 4 in 14 million, 13,999,997 unique numbers need to be drawn.
If you change to the lowest common denominator, it becomes 2 in 7million, meaning that a guaranteed win would need 6,999,999 unique numbers to be drawn, which doesn't match the above.
No