Four-year-old Abraham has spent a year preparing for Delhi's school admissions process. Every evening, under the watchful eye of his mother, he has practised counting and writing, hoping to impress the gatekeepers of at least one good private institution.

His chances of getting into an Ivy League university in the US would be twice as good, if he were old enough.

"He couldn't hold a pencil until he was three," said his mother, Sangeeta, looking apologetic. "Otherwise, I would have started his training much earlier."

Each year, up to half a million children in India's capital attempt to win a nursery place at 1,300 private schools. The competition is so intense parents often begin to worry while their children are still babes in their arms. Many schools resort to lotteries, which until now have taken place behind closed doors, presenting opportunities for abuse.

With a population of 16 million, greater Delhi faces an acute schools crisis. State-run schools are free. But they often cram 50 to a class and lack adequate toilets. And they are obliged to take children only from age six.

So each year, desperate parents apply to multiple private schools. In the past, many bribed their way in. One father promised his daughter's school principal free dry cleaning at the family-run establishment until the child left. Others have donated school buses.

At playgrounds and in offices across the capital, parents are busy trading war stories and comparing notes. School principals are sought out like living deities by crowds of anxious parents.

Last year, Shantnu Mehrotra, a business analyst, applied to 23 schools for his daughter, Sunakshi, but failed to get a single place. This year, he has applied to 21 schools. Sunakshi has so far been shortlisted at one. "It's absolutely killing," he said. "You feel so unfortunate that you can't get your little girl into school for a second year running. It really makes me bonkers."

In past years, parents were grilled separately about their own achievements and personal values. But in 2007, a court-appointed committee set about trying to simplify the admissions process.

It recommended a points system based on a student's proximity to the school, whether a sibling was already enrolled and if parents were alumni. Schools were allowed to allocate some points as well as "management quota" places at their discretion. A quarter of all private school places were set aside for poor and disabled children.

However, legal challenges have shifted the goalposts every year since, often in the middle of the admissions process, sending already tense families into fresh bouts of anxiety.

The management quota, traditionally a way in for wealthy or influential parents, was scrapped last year, at least democratising the misery.

And on Wednesday, Delhi's directorate of education scrapped the five points that were awarded, bizarrely, to parents who had moved to Delhi from elsewhere at any time in their lives. The court heard that the "transfer" points made no sense, and that parents were lying to get them.

Caught in the middle of this administrative battle are the preschoolers whose parents simply want a nice place for them to play and learn.

Fresh chaos broke out on Thursday as schools scrambled to decide whether or not to honour places already granted on the basis of transfer points.

"There is an essential supply and demand problem in Delhi. Our schools are not equally distributed and no land has been allocated for schools in a decade," said Sumit Vohra, founder of a parent pressure group called Nursery Admissions.

The government argues it has a right to dictate the admissions criteria of many private schools because they were given land at subsidised rates. Principals, not surprisingly, disagree.

"The government should upgrade the conditions of its own schools, not shift the burden to private schools," said DR Saini, principal of Delhi Public School RK Puram. "They should be allocating land for new schools; instead they're telling private schools to set aside seats for poor children. That simply increases the pressure on everyone."