Probability - How does it work?!

Been telling people that for years; people who buy five tickets with different numbers in order to 'increase' their chance of winning. Or not choosing 1,2,3 4, 5, 6 as mentioned above. Or numbers below 31.
Mostly I tell people not to take part in work lottery plays. Then, if you do win, you will be left with a very small share. That you collectively put in 50 tickets increases the chances of winning minutely. The counter-argument is that you don't want to see your colleagues win and not take a share yourself. Which is fair enough.
People also get trapped sticking to the numbers they have always used for fear that the one week they choose a new set, the old lot win.
I have never played the lottery. I would do, perhaps, but I would be too embarrassed to go in a shop and have to ask how to play it after all this time.

When the lottery first came out some enterprising contingency insurance underwriter tried to sell a policy to protect small businesses against losing their entire workforce in a syndicated win. That was until it was pointed out that the cheaper way of buying sufficient protection was probably to join the syndicate.