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Manchester City increased their offer for Raheem Sterling this week to £35m – with another £5m worth of add-ons to follow.

After their initial offer, dismissed out of hand, that takes City’s latest bid up to £40m.

A significant sum. Not eye-watering, but enough to buy you players of the quality of Alexis Sanchez … provided they can be persuaded to move to Merseyside.

But, like the Cincinnati Kid holding all the aces, Liverpool have looked their City counterparts in the eye and refused to budge.

And the Reds are right to hold out for their stated £50m.

That’s not because Sterling is on a par with fellow £50m-rated forwards Edinson Cavani, Radamel Falcao or Fernando Torres (the 2011 version).

Not yet, anyway.

But simple mathematics say Liverpool should hold out for more than £40m.

Now it may be back of a ciggy packet maths, admittedly, but it’s maths nonetheless.

Let me talk you through it.

Raheem Sterling still has two years left on his Liverpool contract – a deal which presently sees him paid £35k a week.

Since he turned down the Reds’ original offer of more than £100k a week, several months ago, Liverpool have been saving £70k every time Sterling picks up his weekly pay packet.

Over two years that works out at more than £7m.

Then there is the tribunal fee Liverpool would be due at the end of his contract for a player aged under 24, should Sterling be persuaded to stick around.

That fee is decided by the Professional Football Compensation Committee – and is rising all the time.

Daniel Sturridge cost Chelsea £6.5m in 2010, Danny Ings will almost certainly cost Liverpool more.

Tottenham Hotspur were reported to be ready to bid £12m for Ings, which the committee could consider ‘substantiated interest’ in the player when awarding Burnley compensation.

And with City having already bid £40m for Sterling, that ‘substantiated interest’ could see Liverpool receive anything up to £15m for developing Raheem Sterling if he sees it to the end of his Liverpool contract.

That would see Liverpool £22m to the good – and still have the player for two seasons – which is why £40m is not enough to see Liverpool throw down their cards and fold.

Not yet anyway.

Of course Sterling’s commitment during the next two years cannot be gauged, but he has never looked like the kind of kid to down tools like Torres.

Like Torres, Liverpool will almost certainly, one day, have to say goodbye to Sterling too.

But not yet. Not until the asking price is much closer to their stated £50m.

That’s not good poker playing. It’s just economics.