What's fixed is the total number of lottery combinations.
If there are 13.9 million combinations we like to say the
odds are 1 in 13.9 million because one dollar buys one
combination giving the purchaser one chance to win.
Fly to a state where you get two combinations for a dollar
the total number of combinations haven't changed, but the
odds of 1 in 13.9 million are 1 in 6.9 million because now
you have two combinations in hand for one/dollar.
In the same sense, buying two tickets for two dollars also
cuts the odds in half for what each ticket faces, but does
not change the odds for one/dollar.
Of course it's still just two combinations out of 13.9
million, but it is the same division you would use if you
were in charge of any kind of team facing a larger team,
you would divide your numbers into theirs and come up with
a figure for how many each of your team would be facing.
To be precise, the total number of lottery combinations
never change. The odds of winning do change for you
depending on how you play, but generally can't be computed
until after the draw.
For example, the decision to put ten numbers into play
rather then six reduces the odds from 1 in 13.9 million
to one in 66,589.60 of having all six among the ten as
opposed to all six among six.
To fully cover 10 numbers takes 210 combinations and 210
times 66,589.60 gives us 13.9 million so in the background
the odds didn't change overall, but they certainly did for
your chance of having the numbers among yours. Actually
even those odds didn't change, they were the odds you took
or chose to accept by putting 10 numbers into play.
So the odds don't change, but there are odds for everything
possible within the lottery and you can choose to play at
one of those odds positions and by doing so be playing at
better or worse odds of winning then the person ahead and
behind you in line.