However, people retiring in decades to come are more likely to lose out financially from the reformed system.
The new UK state pension, aimed at simplifying the system, will see a bigger payment of £155 a week made to many new pensioners from April 2016.
Not all new retirees will receive the full amount.
Chancellor George Osborne has set the new pension at £155.65 a week, compared with the current £119.30.
It includes all the extra payments available at the moment, such as means-tested Pension Credit and the earnings-related State Second Pension.
Under transitional arrangements, most people retiring will not receive the headline figure. They will get more or less, depending on their National Insurance contributions.
Now the Department for Work and Pensions (DWP) has calculated that in the first 15 years, some 73% of people who reach pension age will find they are getting more than if the old system had carried on. The typical gain for them is £10 a week.
In the early years, the typical loss for those getting less will average £7.
By the time people just starting out in the world of work, aged in their 20s, come to retire, virtually all will qualify for the full flat-rate payment.
However, this younger group will do much worse than if the current rules were left alone. Some 69% of those retiring in 2050, now in their 30s, will lose out compared with staying in the current system, typically by £14 a week.
Some 76% of those aged in their 20s will typically get £15 a week less.
One reason is that they will no longer be able to contribute to the earnings-related State Second Pension, one of the payments which is being rolled into the new flat rate pension to make it affordable for the Treasury.
Existing pensioners are not affected by the change. They will continue to receive their current basic state pension with annual upratings.
The majority of new pensioners will gain from the "flat-rate" state pension in the early years after it is launched in April, government figures suggest.