lottery tickets, better to buy all for one game or play X number of games

#1
Im wondering which would be better. Im assuming the following, chance of winning = 10,000 for a particular ticket. So if i bought 10 tickets, the probability of winning one would be 1/1,000

2nd scenario, if i bout all 10 for one particular game, is there a difference?

I originally used a tree diagram for the 2nd scenario but im starting to wonder if thats correct.

Would appreciate it if someone could point out how this should be done and why.

Thanks