Lottery myths, checked against the maths
In a fair draw every combination has exactly the same chance, every time. Hot numbers, overdue numbers, patterns and lucky shops change nothing. One choice does matter, though not for your odds: how many other people picked the same numbers.
"Hot" and "cold" numbers
After many draws some numbers have come up more often than others. That is exactly what chance produces: perfectly equal counts would be the suspicious result. The balls have no memory, so a number that came up often is no more and no less likely next time.
"Overdue" numbers
The same fallacy the other way round. A number that has not appeared for a long time is not "due". Each draw starts from scratch; the chance of any number in the next draw does not depend on the last one.
Patterns and "random-looking" tickets
1, 2, 3, 4, 5, 6 has exactly the same chance as any other six numbers: 1 in 13,983,816 in a six-from-49 lottery. It looks less likely only because we notice patterns and do not notice the millions of unremarkable combinations.
Quick picks versus your own numbers
A machine pick and a hand pick have identical odds. The difference is what happens if you win.
The one thing that matters: sharing the jackpot
A jackpot is split between every ticket with the winning numbers. Many people play birthdays, which only go up to 31, and simple patterns such as a column on the play slip. If those numbers are drawn, the prize is shared by more winners. Numbers above 31 and irregular combinations do not win more often, but when they win they are shared less often. That changes what you might win, never how likely you are to win it. The ticket value page puts numbers on it.
Lucky shops and lucky days
Shops that sell many tickets sell many winning tickets, in proportion. The draw does not know where or when a ticket was bought.
Prediction software and "systems"
No program can predict a fair draw. A system that sells you number lists is selling ordinary combinations with ordinary odds; the only certain winner is the seller.