The American sociologist Leonard Beeghley once proposed an imaginative twist for playing Monopoly. Make different players start with different amounts of cash - some with $5,000, some with $1,000, and some with just $500.
As the game proceeds, an inevitability of outcomes takes its grip, an apparently unstoppable juggernaut delivering predictable successes and failures. Those with the most initial cash are clearly at an advantage: they can afford to buy up every property on the board. The poorest players quickly get caught in a cycle of hefty rental payments and a chronic inability to secure the properties they aspire to.
As Daniel Rigney, who quotes the Monopoly hypothesis in his book The Matthew Effect (Columbia University Press), puts it: "The laws of probability virtually ensure that under these conditions, the rich will get richer and the poor will get poorer, and through no special virtue or vice of their own."
It's not just the case with money. As Rigney and others have demonstrated, it's the same with literacy: the word-rich get richer while the word-poor get poorer. Being a good reader helps me become a better reader. We know, for example, from Department for Education research that a child aged seven in the top quartile will have a vocabulary of around 7,000 words. One in the bottom quartile will have half that - and without extraordinary teaching, will almost certainly never catch up. It's the same with learning generally: knowledge begets knowledge.
The Government education team knows this. They cite ED Hirsch's book The Schools We Need And Why We Don't Have Them (Random House). First published in 1966, it was apparently derided by parts of the British education establishment. I found its arguments pretty compelling. Knowledge, argues Hirsch, is like Velcro: the more you have of it, the more will stick to it. We should, therefore, explicitly teach the foundations of knowledge and the vocabulary with which to express it.
The youngsters who will most benefit from all of this are those from the most deprived backgrounds because - and again he quotes The Matthew Effect - "the rich will get richer and the poor will get poorer".
Many of us came into the education system on a bit of a mission to do the same thing. Whatever our subject specialism, we see ourselves (in Matthew Arnold's phrase) as "preachers of culture". Scratch even the most battle-weary member of the staffroom and you'll often find the husk of a Miss Jean Brodie-esque idealist lurking somewhere within.
Which is why so many of us have concerns with current education policy. Where's the idealism? What in practice are the policies to help the most disadvantaged? If as headteacher I can now exclude pupils permanently, with no financial penalty and no threat of an appeals panel, where will those youngsters - however troublesome they were - end up? Will they inevitably gravitate to a school with surplus places and lower parental support, so that poor schools get poorer? How will the free schools initiative prevent self-serving enclaves of same-class or same-faith groups who may previously have happily interacted?
Is competition genuinely the right solution: can we rely on the market alone to make the poor richer?
We find ourselves in a murky ideological no man's land characterised by what Dylan Wiliam, deputy director of the Institute of Education (IOE), London calls "policy tourism" - ideas picked up from around the world, unpacked, then displayed back home like holiday trinkets. But the unifying principles, especially on equality, are often unclear and worryingly short on detail. And even where there are precedents, they don't build confidence that current reforms are going to make the system better or fairer.
Take the notion of free schools. Last week's IOE study of the impact of do-it-yourself schools in Sweden (I know, it's hard not to think of Ikea) concludes: "school choice has augmented social and ethnic segregation, particularly in relation to schools in deprived areas."
Its author, Dr Susanne Wiborg, an expert in comparative education, suggests what we all suspect when school choice is left to market forces: it benefits the children of "highly educated" families and "the impact on families and immigrants who had received a low level of education is close to zero".
So instead of idealism, we get an apparently gleeful desire to stop lots of previous projects in their tracks, with a hint of yah-boo scorn. When the school buildings cancellation list was made public, it wasn't just the poor attention to detail that depressed us: it was the apparent relish with which the announcement was made. The tone was distasteful.
That same disdain for anyone not "front line" - the assumption that anyone in a school or local authority not teaching is not doing anything important - insults good people who chose a life in public service.
A summer holiday is an important time to replenish our ideals, principles and reserves of optimism. Let's hope that the education team at Sanctuary Buildings takes one.
Geoff Barton, Headteacher, King Edward, VI School, Bury St Edmunds.