There is actually a simple strategy to maximise your winnings on lotteries. Certainly it is pure luck whether the numbers you pick are the winning ones, and there is nothing you can do to maximise your chance of winning. However, if you do win, you can maximise your share of the winnings.
For example, if the lottery is to pick 3 numbers from 1-10... if you pick 1,2,3 then you are exactly as likely to win as if you picked 3,8,10... but it's likely that more people will pick 1,2,3 than will pick 3,8,10... so if you win with the second example you get a great share of the total prize as there are fewer winning participants.
Depending on what the options are, it is advisable to avoid sequential numbers or other patterns, avoid popular 'lucky' numbers, avoid 1-31 as these can be birthdays, etc.