The dice is loaded against children from poorer backgrounds when it comes to grammar schools, according to a new report.
A study of data from Kent found that about a quarter of all students went to a grammar school in 2016, but children eligible for free school meals (FSM) were less likely to sit or pass the 11-plus.
The report acknowledged that the situation will vary across the country, but said Kent could be a useful case study as it is an area where selectivity "is most heavily embedded" and comprises both rural and urban communities of varying social class.
Kent County Council has said improvement of social mobility in education is one of its priorities and one of the biggest challenges for the selective and non-selective education system.
The data relates to pupils who sat the 11-plus in September 2015 for entry to grammar school in September 2016.
It was obtained under the Freedom of Information Act by the Kent Education Network, a group opposed to selective education.
Some 12% of FSM-eligible students passed the test, compared with 30% of those not eligible for free meals, it said.
Children from less affluent backgrounds also scored particularly poorly in the reasoning element of the test compared with others.
Lead author and Education Datalab director Rebecca Allen said the chances of gaining a grammar school place were like "rolling a loaded dice".
She explained: "If the 11-plus is a dice, then the reasoning component contributes to the dice being loaded against disadvantaged children."
The report noted that Kent state primary schools were explicitly asked not to prepare their pupils for the 11-plus, which suggests only those whose parents help them practise, who receive private coaching or attend private schools will gain familiarity in this area.
Allowing state primary schools in Kent to provide 10 hours of practice on reasoning-style questions to all students could help increase the proportion of children from less affluent backgrounds entering grammars, it said.
If the Conservatives stay in power after the June 8 snap election, Prime Minister Theresa May will have the opportunity to roll out her flagship policy of more grammar schools for England.
She has said the policy will help to create a place at a good school for every child and argued that many children's school choices are determined by where they live or their parents' wealth.
But opponents believe it will entrench social division, with National Union of Teachers (NUT) general secretary Kevin Courtney saying there was "no appetite for this programme".
Currently grammar schools only exist in parts of the country, including in Kent and Buckinghamshire, with a ban on new grammars introduced by Labour in 1997.
Responding to the report, Mary Bousted, Association of Teachers and Lecturers' general secretary, said grammar schools were "not the answer" if the Government was serious about social mobility.
She added: "Grammar schools are a total distraction from the most important issues facing children's education - school funding cuts, the shortage of teachers, the shortage of school places, and the rise in mental health issues among children and young people.
"These are what the Government should be focusing on rather than spending money, particularly when budgets are tight, on policies which will benefit few children."