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flaw in chess rules ?

it just crossed my mind that this checkmate doesnt make much sense

if im not mistaken chess is based on war and old military units, the main idea is, if king dies the whole army dies.

this might be a silly question but after the last move, if black king went to D4 wouldnt white king get eaten immediately after by black pawn? or is there some sort of barrierpreventing w king from stepping into d4 lol

also, since chess is such an old game, do you think theres room for any improvement on its rules or is it already perfect the way it is?
Taking the war analogy, if the king of one side of the battle runs into reach of the murder zone of the other king, what do you think he would do?

Kill on sight, no mercy.
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yeah but wouldnt white king get eaten immediately after by the pawn on e5? - i would consider that a draw :)
@colin_ni yeah but if thats true then its based on game rules rather than real war

because in real war if u kill the enemy king then immediately after ur own king gets killed then its basically a draw, no?
If you're using that as an analogy then think of it this way. As soon as the king is captured all of its pieces now no longer know what to do. To be direct you can assume as a rule the two kings at war can never be on adjacent squares.
In real war there would be a lot of people ready to take over, many of whom would contribute to their king's downfall if they felt safe enough doing it. My apologies for the lack of romanticism, but the analogy only works so far.
I suggest you look at atomic, where this would be a legal move for the reasons you stated. However, in real chess, it's about who can checkmate, and essentially take, the king FIRST. In this case, white would take the king first, so he wins.

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