aren't the odds of something happening several times in a row less than the odds of it happening once? Specific problem in description

Question

If in a video game there is a 1/50 chance a monster will drop an item once killed, aren't the odds of it taking 171 kills greater than a smaller amount around like 50 kills? I understand there is still a 1/50 chance for the 171st to drop the item but the odds of it not dropping the item are 49/50 so the odds of it not dropping the item 170 times in a row is slim is it not?

Answer 1

1 kill: 1/50

2 kill: (1/50)(1/50)

3 kill: (1/50)(1/50)(1/50)

4 kill: (1/50)(1/50)(1/50)(1/50)

...and so on.

 

What do you think?