Question about single elimination tournament?

Here is the problem:

In a single-elimination tournament for tennis (1v1), the loser of each match is eliminated from the tournament.

There are 10 players. How many games must be played to determine a winner?

My question is, can someone explain to me why the answer would the answer be 9?

Also, in the same manner, why would the answer be 999 games if there where a 1000 tennis players?

It seems like the trend is if there is x amount of players in the 1v1 tennis tournament, there is always (x-1) games to determine a winner. I really am confused why this is.

Thanks for any help.

PS: I asked a similar question like this a while ago, but screwed up my explanation of the problem (and thus got answers for a problem that I wasn't asking about). This is why I am asking a similar question, but with a added stipulation that I forgot to add the first time.