Your quote:
"I think it has something to do with the fact that my chances must increase if my entry is sent in by the most popular format as then I must have a greater breadth of numbers to be randomly chosen from. (Don't I)".
That's exactly what I was trying to illustrate. In my example, Method B was the most popular format so, when the computer selects a random number, there are 650 chances out of 1000 that the an entry from the 'B' group wiil be selected.
You ask about the problem of dealing with incorrect entries. There are two possible solutions. The first is that only correct entries are 'put into the pot'. The second is that, if an incorrect entry is drawn, the process is started again. (i.e. the computer is instructed to select another random number).
Having written that (and my previous reply), I ought to state this: My degree is in 'mathematics as a double subject' and one of my specialist fields was 'probability and statistics'. (So I ought to know the 'theory'). However, I live in the real world and know that most competition organisers aren't interested in 'fairness' or 'equal probabilities'. They probably select competition winners simply on the basis on the easiest way of finding a winner. For example, you might have several sacks containing thousands of postcard entries and a computer system holding details of thousands of e-mail entries. To get your company's software boffins to find a random way of selecting an e-mail entry might take time and money. To shove your hand into a sack will take hardly any time at all and cost nothing. So what do you do?
As I've said, I live in the real world. If you believe that all competitions are fair then, with no offence intended, I have to suggest that you don't.
Chris