In the long history of Anglo-German incomprehension, it is not yet clear what place will come to be occupied by David Cameron and Angela Merkel.

The Prime Minister and the Chancellor will smile at each other at this afternoon’s press conference in Downing Street, which will be preceded by a joint visit to the Germany: Memories of a Nation exhibition at the British Museum, and followed by an early dinner.

The host, one can guess, will be on his best behaviour, while the guest will display the amiable inscrutability for which she has such a remarkable gift.

But having written a piece at the beginning of November entitled Nine things the British don’t understand about the Germans, I now realise it might be supplemented by a short companion piece, in no way intended to be more than a first shot at the subject, on the things the Germans don’t understand about us.

The two leaders are like two bridge players with wildly different styles, who unexpectedly find themselves paired in an important European tournament. Their conventions, modes of thought and attitudes to risk present a stark contrast.

Merkel has strong cards, but is not inclined to play them, or even to let her partner know what they are. The German Chancellor prefers to smile sweetly, and give nothing away, until the moment comes, just when everyone least expects it, for her to impose herself with ruthless efficacy.

Cameron has weak cards, and could be obliged to retire from the game as early as next May. But he hopes by a series of audacious finesses, conducted with outward calm, to force his opponents into error and win an implausible victory.

In some ways, Cameron makes a welcome change for Merkel from the Greeks, who want to play yet another game of poker with her, and still more from Vladimir Putin, who is always itching to play Russian roulette.

On the question of how to control Putin, Cameron is a more reliable ally than either François Hollande or Matteo Renzi, both of whom are tempted to relax sanctions on him.

But every so often, Cameron shocks Merkel by doing something so irresponsible that she does not wish any longer to be his partner. One such moment came in 2009, when he withdrew Tory MEPs from the European People’s Party. “This decision made Merkel’s blood boil,” as her authorised biographer, Stefan Kornelius, puts it.

A list of things the Germans don’t understand about the British (or at least don’t sympathise with) might begin with

1. The British propensity to take risks

For example, Cameron’s promise, in his Bloomberg speech in January 2013, of an In/Out referendum on Britain’s membership of the EU if the Tories win the next general election. He had warned Merkel he would do this, but she was still deeply critical, at least within her own circle, for as Kornelius explains,

“in Merkel’s opinion, Cameron was making two mistakes. First of all he was taking an enormous risk for the sake of short-term political gain at home. A referendum is no small matter and can have unforeseen consequences. Merkel would never leave herself at the mercy of such uncontrollable political forces. And secondly, it was naive to expect that the promise of a referendum would silence the critics. In fact it had the opposite effect: Cameron had played his trump card, but was still subject to coercion.”

Yesterday morning I spoke to Norbert Röttgen, the Christian Democrat who chairs the Foreign Affairs Committee of the Bundestag, and he confirmed that Berlin still loathes referendums. In any renegotiation of EU membership terms, the Germans are determined to avoid treaty change, because this would require ratification by the 28 member states, which in turn would require referendums, which in Röttgen’s words would be “a way in for left-wing and right-wing anti-European populists”, who would seize the opportunity to try to destroy the European Union.

Given the way that populists seized the opportunity to try to destroy the United Kingdom during the recent referendum in Scotland, one cannot dismiss this German warning as groundless.

The risk Cameron is running with the In/Out referendum horrifies the Germans, and prevents them feeling the slightest admiration for the way he has finessed the question. I suggested at the time, in an article for Standpoint, that the Prime Minister has turned the Eurosceptics’ weapon on themselves: they can have their referendum, but the chances are that they will lose it. That kind of reasoning cuts no ice in Berlin.

2. Casino capitalism

Anglo-Saxon capitalism still seems to the Germans (and to some Anglo-Saxons) deplorably short-term.

3. Adversarial politics

The rude combats of Westminster are alien to the Germans. West Germany developed a tradition of consensus politics. Merkel herself is at present running a coalition with the Social Democrats, the main opposition party. Perhaps Cameron should ask her for tips about how to do this.

4. Insularity

Germany likes to act in tandem with other nations. Britain when push comes to shove likes to go for the “island option”. As Winston Churchill explained in 1930, in an article for the Saturday Evening Post: “We are with Europe but not of it. We are linked, but not comprised. We are interested and associated, but not absorbed. We belong to no single continent, but to all.” Emotionally, the British are more likely to be stirred by a cricket match in Australia than by events in Europe: though counter-examples could be quoted from football.

5. British self-deprecation.

Germans are inclined to take this literally.

6. British self-aggrandisement.

Again in danger of being taken literally, and as a sign of old Empire arrogance.

7. British flippancy.

Liable to be regarded as mere lack of seriousness.

But it is only fair to add that a list of countervailing similarities and affinities might also be compiled. Kornelius claims that as an East German Protestant, Merkel “feels closer to Anglican sensibilities than to the Roman Catholicism of southern Europe”. It is not fanciful to suggest, at least on questions such as economic competitiveness and control of the EU Budget, a northern European solidarity between Britain and Germany.

And in both countries, the new party demanding a tougher line on Europe has run into trouble. UKIP has suffered embarrassments as it tries to select candidates for the parliamentary seats it has the best hope of winning. Alternative für Deutschland, which is pro-EU but anti-euro, is rent by bitter feuding among its leading figures: they have denounced each other in furious emails which have been reprinted in the last few days in the German press.

AfD is also divided by the question of how tolerant or condemnatory to be of the anti-Islamic demonstrations being held each Monday in Dresden. Merkel used her New Year’s message to condemn the demonstrations. Wolfgang Schäuble, the Finance Minister, this week added that “Germany needs immigrants”: a point made about Britain by Owen Paterson in his piece a few days ago for ConHome.

And one observes that Cameron has been making strenuous efforts, in his efforts to frame a new immigration policy, to adopt positions which have already been advanced by Berlin: notably the denial of welfare payments to new migrants.

One of Berlin’s chief concerns about tomorrow’s meeting is that British expectations of German support for EU reform should not be raised too high. That is exactly right. It is only if we do not seek a short cut to happiness in our relationship with Germany that it will sometimes be quite helpful in the interminable negotiations that go on in Brussels.