The referendum, which asks whether the country should accept demands made by its international creditors, was intended to show the resolve of Greeks to push for a better deal. Mr Tsipras and his government have been urging a strong "no" vote to bolster their bargaining power. Yet the latest betting odds suggest that there's a two-in-three chance that the "yes" case will win.

Politically, the key issue is about who best succeeds in framing the debate for voters. Jacob Kirkegaard, my colleague at the Peterson Institute for International Economics, says that "when voters are asked to answer yes or no to a complex issue — like a multipage economic reform program — they almost always choose to answer an entirely different question in the voting booth."

The apparent popularity of the affirmative vote reflects the success of other European leaders in framing the referendum as being "about whether Greece wishes to stay in the euro or not," and the euro remains extremely popular in Greece. Because "narratives can change several times in the course of a referendum campaign," he sees "high levels of uncertainty about the outcome."

In this sort of volatile atmosphere, it can be hard to keep track of public opinion, which is why I turn to political betting markets.

At first, the British bookmaker Ladbrokes concurred with Mr Tsipras: The opening odds last Saturday assessed the "no" case as much more likely. But the flow of money caused a rapid reassessment, and Ladbrokes shifted the odds so sharply that "yes" became the new favourite by the next morning, and it has remained the betting favourite since.

Matthew Shaddick, who heads Ladbrokes' political betting operation, told me that "it's been quite a lively market," although it is also one where he is being cautious, because "obviously it's very easy for events to move rapidly one way or the other." Mr Shaddick reports that "62 per cent of the money has been on for YES." (And the probability is up to 66 per cent in the latest numbers.)

Bettors believe in a deal

How seriously should we take these odds? This is not a deep financial market, and the total amount staked is in the tens of thousands of dollars. That said, my research has shown that even quite small prediction markets can yield useful forecasts.

Mr Shaddick reports that most of the bettors are based in Britain, "and some of them do seem to be from City sources" (the "City" being London's financial district). While there are many reasons to doubt the value of the betting odds, it's hard to think of a more reliable alternative.

I'm not suggesting that bookies have particularly deep insights into the state of Greek public opinion. The value, I suggest, is that as they adjust betting odds in response to the flow of money, their odds come to represent a quantifiable assessment of the conventional wisdom.

That conventional wisdom is this: There remains tremendous uncertainty about the referendum, and both sides have a substantial chance of winning. It has come as a surprise to many to learn that the "yes" case remains somewhat more likely, although it is just as important to note that "no" still has a one-in-three chance of success.

The New York Times