(Repeats Tuesday item)

* Polls give widely varying signals on referendum

* Betting odds point clearly to Britain staying in EU

* Majority of bets staked on "leave" vote next month

* But big money placed on Britons opting to remain

* Neither bookies nor polls saw outright Cameron victory

By Jemima Kelly

LONDON, May 24 (Reuters) - Investors seeking guidance on whether Britons will vote to leave the European Union are relying as much on bookmakers and punters as the established trackers of political trends, opinion pollsters.

A month before the referendum, bookmakers' shops on British high streets and betting exchanges on the internet are offering something that the polling industry has failed to provide: a clear trend.

Bookmakers are offering odds of 1/6 - indicating a more than 80 percent probability - that Britain will vote to remain in the EU on June 23. By contrast, opinion polls present a confusing picture of voters' intentions, with some saying the "remain" camp has a big lead while others have put the two sides neck-and-neck.

"Betting is the market's attempt to summarise the polls and adjust for all of their fragilities," said Insight Investment currency fund manager Paul Lambert. He says he looks more at the odds than the polls when deciding how to trade currencies affected by the vote - particularly sterling, but also the euro.

With most economists agreeing that the British economy would take at least a short-term hit from a "Brexit", financial markets are sensitive to any signals on how the nation will vote, including opinion polls. Sterling strengthened sharply last week after an IPSOS-MORI poll showed 55 percent supported remaining in the EU, with only 37 percent backing Brexit.

But the polls' fragilities were exposed in last year's parliamentary elections, when they failed to signal that Prime Minister David Cameron's Conservatives would win a majority.

This is one reason why investors are turning to the likes of

William Hill and Ladbrokes, betting-shop chains more commonly associated with horse racing and football than politics.

The bookmakers say they can set the odds to incorporate nuances that the polls cannot, such as psychological research suggesting that undecided voters tend to opt in the end for the status quo. In this case, that means voting to keep Britain in a bloc that it joined more than 40 years ago.

Investors also like the fact that the "bookies" and online betting exchanges can adjust the odds in real time to reflect developments that could affect the vote, allowing them to make trading decisions faster.

THE PRICE THAT PEOPLE ARE PAYING

When President Barack Obama warned last month that Britain would be at the "back of the queue" for a trade deal with the United States if it left the EU, the probability of Brexit on betting website Betfair immediately fell to 31 percent from 33 percent before he began speaking.

"The price is the price that people are paying - it doesn't get any more live than that, whereas polls have lags," said Mizuho's head of hedge fund currency sales, Neil Jones.

While sterling jumped immediately on Obama's remarks, investors had to wait several days for the first polls incorporating the voters' reaction to be published. In the end, they suggested Obama's intervention had little overall effect.

Bookmakers naturally aren't infallible. For instance, Matthew Shaddick, head of political odds at Ladbrokes, said his firm lost more than 1 million pounds ($1.45 million) on the 2015 election mainly because the Conservatives won an outright majority - an event that few if any bookmakers, pollsters or pundits saw coming.

However, Shaddick said the betting odds had clearly signalled that the Conservatives would be the largest party in parliament, whereas the polls implied a very close result.

A Scottish referendum in 2014 marked a more comfortable victory for the bookies as the betting odds consistently implied that voters would reject independence by a wide margin. In the final run-up to the vote, one opinion poll put the independence camp ahead, prompting sharp moves on the financial markets, before the Scots voted "No" by 55 to 45 percent.

In some cases, the odds are set by the punters themselves. Websites such as Betfair, owned by high-street bookmaker Paddy Power, work as peer-to-peer gambling exchanges so punters bet with each other.

Such sites allow gamblers to get in and out of positions, much like stock or currency traders, so the odds react even faster to news than traditional bookies' odds.



INFLUENTIAL CUSTOMERS

These are set by political betting specialists who consider a wide variety of factors ranging from where the money is going to their personal opinions, though they say they try to remain as unbiased as possible.

They also watch which way influential customers are betting. "Some customers' bets shape the market more than others, for example political journalists' punts," said Paddy Power politics specialist Stephanie Anderson.

That said, Britain's top reporters also failed to predict the Conservative majority last year.

With the referendum odds stacked in favour of a vote to stay in the EU, those wanting to "take a punt" with a small sum tend to choose the more potentially profitable option, however unlikely it is, bookies say. A 10-pound winning bet on "remain" yields a return of less than 1.50 pounds after a month's wait at the current odds. The same sum staked on a Brexit would return 40 pounds at the current 4/1 odds.

Paddy Power says 60 percent of its individual bets have been on a Brexit, yet they make up only 14 percent of the total amount staked. While the average size of a "leave" bet has been 36 pounds, the average bet on a "remain" vote is almost 10 times that, at 333 pounds.

Some people in the financial markets are also placing personal referendum bets, such as 69-year-old trader Simon Cawkwell. Nicknamed "Evel Knievel" after the late motorbike stunt rider for his audacious bets, Cawkwell is going against the trend that Brexit punts are more modest: he has staked a four-figure sum on a British departure from the EU.



PRIVATE BRIEFINGS

Political betting has become a serious business in recent years for Britain's 6.3-billion-pound gambling industry, with about 100 million pounds thought to have been staked on last year's general election.

Bookies say the referendum could be Britain's biggest political betting event, though the amount taken will probably equate only to that staked on a single big football match.

Those who set the odds are increasingly in demand for advice. Shaddick, who has a degree in political science and a masters in statistics, says he is frequently invited to give private briefings to investors.

"Ten years ago, political betting was just a novelty, PR-led loss-leader for bookmakers," he said. "Now it's a serious part of our business."

Outside the world of financial markets, views vary on the wisdom of betting on the referendum.

Alastair Meeks, a 48-year-old lawyer, is going with the flow; he plans to put several thousand pounds on Britain staying in the EU. "I got into gambling through politics, rather than into politics through gambling," he said. "I will increase my commitments as we get closer (to the vote)."

But in southeast London, 67-year-old George Squires is unenthusiastic. He visits the William Hill branch on Deptford High Street four or five days a week to bet on horse racing. Although he will vote in the referendum - to leave, because he says "there are too many immigrants" - he will not bet on it.

"I watch the races on the telly. I can't watch an EU on the telly," Squires said, adding that he wouldn't stay up to watch the results on referendum night. "There's no fun at all in it." ($1 = 0.6912 pounds) (additional reporting by Sudip Kar-Gupta; editing by David Stamp) ((jemima.kelly@thomsonreuters.com; +44)(0)(20 7542 7508; Reuters Messaging: jemima.kelly.thomsonreuters@reuters.net))