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If Chess was invented today ...

There are plenty of abstract strategy games invented in the last decade or so: Arimaa and DVONN come to mind. Arimaa has a much deeper game complexity than Chess and held off competitive engines until just recently. It's a good game that borrows a bit from chess: the board size, the number of differently ranked pieces, though it changes quite a lot otherwise. Some consider it a better designed game, but because it lacks the history and wide player base it will never be a realistic alternative. I don't think chess would stand out any more than many of these modern abstract strategy games if it didn't have a 500+ year head start.

That said, I don't think it matters much that chess be the deepest, most well-designed strategy game imaginable. All of these abstract strategy games share the same need for deep calculation coupled with human pattern recognition. In some sense, as long as the game is deep enough to keep a human from ever mastering it, the quality and number of available opponents and learning material is more important than the rules. Chess just happens to capture most of that market in Europe, the Americas, and some other places, just as Go captures most of it in Asia.
My serious response is:
Instead of board game it would be video game, like for example Sid Meier's Civilization. (but one can say a lot in this creative topic)
Warhammer was the 90's version of chess, everyone used to sit and paint their armies. Orks, Space Marines, Hybrids and dwarfs abounded and many had special abilities.

The battles were fought with rolls of the dice etc etc

If it was still more recent it would have a player mall where you could spend money on virtual items that run out.

The reason chess is good is because despite the technology the rules of the game and the objective is simple, unlike the stratergy and tactics. The same can be said of many other games that grab hold of people, like the various forms of poker - the more you learn the more aware you are of how much you have to learn.
I think this topic is quite absurd in many ways.

First, if chess were invented today, it would not be something like Settlers of Catan or Civilization which is what is described by the original poster. These are not abstract strategy games, as you don't have perfect information and there are random elements added.

Second, the political commentary by some posters is intriguing, but rather ill got. The pieces arbitrarily represent a military force, so in a modern setting they would still do so.

And lastly, the idea that W40K and that ilk is anything like chess is again ridiculous...the games are not comparable, the skills are not the same, and the appeal is different. I love chess, I never liked miniature games. If there was no chess, I would not have started playing minature games. They are entirely different animals.

So to boil it down into what was actually asked...if chess was invented today what would it look like. Well, it would reflect changes in modern military. The game must still be "chess" because you're asking what if CHESS were invented today and not thousands of years ago. So fundamentally, the game would be the same. The board would be larger, maybe be divided into more than 2 colors of squares, and the armies would reflect modern themes: tanks, jets, etc. There might also be the option to drop pieces back onto the board under your control like in the Eastern chesses. That's it, otherwise you wouldn't be inventing chess, you'd be inventing another game entirely.
@15
relax man, its just little hypothetical chat . Try not to get all serious and tear down everything that does not make sense to you.
3d chess comes to mind, although for me, I couldn't be bothered with the added complexity.
Most of us would have had to endure extended sufferings as brilliantly described in 'The Master of Go' by Yasunari Kawabata (transl. engl. Seidensticker). Though thanks to a lot of foreign aliens from India, Persia and other unamerican intellectuals we escaped that dreadful fate.

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