What are filters, and why use them?
When you play a line, it has the same chance as any other line of being drawn. So filters are not about increasing your chances of winning. However, not all lines are equal in a lottery. "How can that be?" you're probably asking. Well it's not a study of numbers (or perish the thought history analysis), but it is a question of observing human nature.
Before we do this, ask yourself, what are you hoping to do by playing the lottery, either as an individual or in a syndicate. The first hope is to win the jackpot (or one of the other major prizes). If you manage this, you'll probably jump for joy for a bit (I know I would), and then you'll start asking one important question; how much have I/we won? You'll be hoping that no one else has won as well, eating into your winnings.
So ideally we don't just want to win, we want to win big. With the UK lottery for example, prizes for four balls or better are variable in size, and less likely chosen lines are more likely win bigger prizes. This is where filters come in. They do not increase your chances of winning, but they should increase your winnings when you do (on average). The idea is to filter out line selections that are more likely to be chosen by humans, and humans can be fairly predictable.
So what do humans do?
Think about it, you have a play-slip in front of you, and you fill it out. What are you inclined to do? The first 'trap' is to play numbers that are significant to you. These are likely to be birth dates, ages of children, house numbers, lucky numbers, your favourite footballer's number etc. Each of these can increase the frequency of selection of ranges of numbers, i.e. dates 1-31, months 1-12, lucky numbers 1-9, sportsmen 1-15 (Mr Beckham, Keegan, or even Barry Sheene (R.I.P.) would all promote 7, the most frequently chosen number). House numbers could be anything, but would lend a statistical weighting to lower numbers.
The second trap would be to fill in the slip with a pattern. Patterns could be numerical patterns, or patterns on the slips design. Either of these is likely to increase the probability that someone else is playing that line, thus reducing the prize values for those lines should they be drawn.
Humans also try to be clever when they choose lines. It has been written that around 10,000 tickets for each UK Lotto Saturday draw play the line 1,2,3,4,5,6. The jackpot prize for this line would be trivial, so it's not worth playing. Another 'clever' thing to do would be to play numbers that have already been drawn. After all, no one else would play them…
How fussy are our filters?
Around 38 million tickets are bought for each UK Lotto Saturday draw. With there being around 14 million possible lines, the average line will have 2.7 players playing it. Some will have many more players due to human nature others may have none. The job of filters is to not play the lines with many more players than the average. LSMC would never be too strict with its filtering though, because it would then push all of it's users into a limited selection of lines, thus defeating the object of the exercise. Another reason not to be too fussy is that a great many players will purchase generated lines or 'lucky dips', which should improve the spread of lines played. Filters can only benefit us because of the greater percentage of human selections.
Conclusion
Filters are not about increasing your chances of winning, but are about improving your chances of higher winnings when you do. For syndicates in particular, where a great many lines are played, your winnings over time are more likely to be higher, which can't be bad.
Warning
Since filters are about removing certain lines, it is possible to have winning lines removed from your selections, and these may even be jackpot-winning lines. It's a risk you take, but in the same vein, by removing a number of lines from your selections may enable you to play other lines that go on to win. It really is a lottery, and the final decision on which lines you play remains with you.