* China shares have biggest single-day gain since 2013
* Banks, brokerages lead charge as rumours of more easing swirl
* Gap between dual listed values in Shanghai, HK widens
* Illustrates diverging views of mainland rally
By Pete Sweeney
SHANGHAI, Dec 2 (Reuters) - China stocks had their best day in more than a year on Tuesday, as speculation of further policy easing boosted financial services stocks on the mainland and Hong Kong.
Retail investors added fuel to institutional buying, analysts said, pushing many banks and brokerages to their 10 percent daily limit.
The CSI300 index of the largest listed companies in Shanghai and Shenzhen rose 3.7 percent to 2,923.94, its largest daily rise since July 2013, while the Shanghai Composite Index gained 3.1 percent to 2,763.54 points, its best day since Sept 2013.
China's surge helped the Hong Kong China Enterprises Index gain 2.8 percent to 11,125.79, but the wider Hang Seng Index added only 1.2 percent to 23,654.30 points.
The CSI300 Financial Services Index closed up 6.66 percent. Tuesday's move, on the back of steady rises in blue chip financials, has steadily chipped away at the long-standing superior performance of small-cap shares on Shenzhen's ChiNext growth board.
ChiNext is still up nearly 40 percent year-to-date, but the CSI300FS is now up 31.66 percent, with most of that gain coming from a rapid spike beginning in late October.
The widening gap in perception between Hong Kong and Chinese investors has grown increasingly dramatic in recent weeks.
Analysts say that mainland sentiment, driven mostly by retail investors, is celebrating monetary easing policies, which are seen as providing more liquidity for the current rally and also relieving Chinese banks from having to recognise bad loans by making it cheaper for borrowers to roll over debt.
China's central bank cut interest rates unexpectedly on Nov. 21, stepping up support for the economy as it confronts slowing economic growth and mounting bad debts. Sources involved in internal policy discussions have told Reuters the central bank is ready to loosen policy again.
Investors appear to be betting on more stock gains, with the China CSI300 stock index futures for Dec. 4 delivery up 4.6 percent at 2,936, a positive spread of 12.1 points versus the underlying index.
Sudden investor enthusiasm has turned China's once-necrotic exchanges into world-beaters, with the Shanghai Composite Index up 30 percent since the start of the year, compared with 12 percent for the S&P 500 and a negligible 1.5 percent rise for Hong Kong's Hang Seng.
Foreign investors appear to be more worried about the steady drip of soft economic indicators out of the world's second-largest economy, and concerns the market is overbought.
The spike came in the run-up to the announcement of the Shanghai-Hong Kong stock market connect programme and may also have partly priced in an interest rate cut.
Editing by Jacqueline Wong