[Beestie]

Each drawing is independent - there is no carryover. Think of it this way - if the assumption were true, then every number not drawn became more likely not just your buddy's. It is easy to see that all combinations (all possible outcomes) less one can't become equally more likely. Odds are a zero sum game - they must total 100%.

The source of the fallacy comes from the following scenario. The odds of flipping a coin to heads ten straight times is very low - odds are that it will not happen. Now, if you flip nine straight heads, there is a temptation to think that the odds of yet another head are less than 50% (a carryover from the previous nine flips) when, in fact, it is exactly 50% (provided the coin is not biased, etc.).

Your friend's odds of winning are the same regardless of whether he sticks to the favorite numbers or chooses new numbers each time. But, as someone pointed out, if you have a lucky set, always play it - buy a second ticket with random numbers because if the lucky set is a winner and he didn't buy it, then he's gonna be in a bad way for the rest of his life. Most lottery's offer an option for them to automatically play the same # for you each time without having to buy the ticket. If he's that superstitious perhaps he should explore it.