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Joe Joyce wrote: "...Just as in FIDE chess there is a condition called "opposition" in K+P vs K endings which prevents the pawn from successfully promoting, the same sort of thing happens when you try to get your king onto the same 2D level in Hype. The opponent's king stays as close to your king as possible, in both a neighboring big and little square, preventing your king from ever actually getting on the same board as your opponent's king to hold it to a specific 2D level..."

Thanks Joe. What you explained about an analogy in Hyperchess4 to the opposition of Ks in standard chess (an analogy given by you elsewhere too, I think) I independently finally realized (or it sunk in) today, and I meant to make an edit to my previous post to that effect, but I saw that you beat me to it. I found that even with the lone king in a corner cell of some little 2D board, it can never be smoked out by just two pieces (K & Q), say if they are placed on adjacent cells to it, but on an adjacent little board, since there would be always be one of the three adjacent cells available to the lone K on the same little board as its corner cell.