OnlyTellsthetruth - i'm sorry, you're simply wrong. Changing to your dice example is unhelpful because you have not specified what constitutes a "match," whether order is important, etc etc.
let's keep to the lotto example, but a much more simplified case. There are 5 balls. 1,2,3,4,5. The machine will draw 2 at random. If they match the two balls you've chosen, you win.
You have (5 choose 2) = 10 different combinations possible.
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
Therefore you have a 1/10 chance of winning.
Now in order to choose which numbers to pick,
player 1 uses a glitched generator which always picks 1 and 2
player 2 use a non glitched generator which can pick any 10 with equal likelihood
So
On the day of the big draw,
player 1 has 1,2
player 2 has (say) 4,5
When the draw is made they both have 1/10 chance of winning.
If the draw was made again
player 1 having 1,2
player 2 having (say) 2,5
they would both still have 1/10 chance of winning.
No mattter how many times the draw was made, both player 1 and player 2 would have the same odds of winning the lotto.
