Quote from HolyGrail:
It has a great deal to do with the odds of winning unless of course you chose the same numbers for all 124,000 tickets. As long as you chose a different combination your chances of winning increases because you are playing with a finite number of total numbers.
edit: or said in simpler terms. I will give you three chances to guess the number I am thinking of between 1 and 3. Ya think your odds aren't improved by those three guesses?
You're referring to probabilities of winning, not the odds of any one (or two) games. The news article was outlining the odds of winning two lotto games, not the probabilities as that would be drastically different for every single player based upon their playing history. So the news article was not incorrect as blackjack was saying.
Secondly, he calculated the probabilities wrong, because the "independent event" is two games, not one game.