Football pools systems really do work if they are based on sound statistical analysis. Why do systems work? Simply, because the performance of football teams is not in the long run random - teams do in fact play broadly to form.
There are two parts to solving the problem of how to win the football pools. The first is the statistical analysis - the designer of the system will have looked at past results of teams and matches, and then produced a mathematical model which explains the results with a reasonable degree of accuracy, and enables predictions to be made on that basis.
Actually accuracy only needs to be slightly better than random. In roulette, the casino makes its money on a 2-3% edge, in the long run. In the football pools, that margin is adequate in the long run, but we would expect to do much better occasionally, and win. Of course, we want to win enough to cover the stakes on those weeks we did not win, so that it becomes a profitable exercise.
The second part in the football pools problem is the coverage. It is not economic to cover every possible combination on a coupon of 49 matches - there are 450 million ways of lining up any eight score draw matches. Of course, they may not even be eight score draw results in a given coupon. That is where 'plans' and 'perms' come in. These are ways of covering say 20 selections on a coupon in such a way that when there are maybe 12-15 score draw results on a given coupon, then we can have a reasonable expectation of winnings if we have picked say six or eight of those draws. Put simply, the plan may cover the 20 selections in such a way that 25,000 possible 8 match combinations are staked. This reduces the odds significantly.
There are a number of systems available. Some are described in books available, for example, from Amazon; others are downloadable online; there are spreadsheets available; there is software. There are books which specialize in 'perms' and software which also does so. So, quite a choice for those who are prepared to dig around.
However, the whole process is based on sound prediction of match results. To do that (assuming that you cannot afford to regularly stake thousands of pounds or dollars), then, having bought a system, the user has to put in work to maintain the basic data on which the analysis is based. There are organizations which offer tips and there are comprehensive sets of match data and predictions available online (these are usually subscription only). If the pools punter does not want to subscribe, then several hours work will be required to prepare each entry.

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