what is the least amount of mateirial you can force a checkmate with?

so I am mostly talking about endgames like 3 knights vs a king but if you have intersting positions pls share =D

also what is the most amount of mateirial that it is still impossible to force a checkmate?

You can force a checkmate with a single pawn... but if you mean the opponent has no pieces and the king starts in the middle of the board then I guess a rook.

ok asuming kings are worth 0 points each....

I assume you mean "still possible." The answer is either a pawn or a rook, depending on how you look at it, since the pawn has to promote to at least a rook.

It is possible with a knight and a bishop vs king.

(forced)

wow pure guinius scottrf.... =D

I remember such a position from Hans Kmoch "Pawn power" "L'art de jouer les pions " in french.

 An unlikely position to emphasize the power of knights in a closed position

... so is the minimum amount of material required infinity + 1? Infinity + 2?

Just infinite.

This is an epic win!

3 knights + king vs king can force a mate. I am not 100% sure but I think I have read somewhere it is always a foced mate in 17 or less moves reagrdless of the starting position. Of course, my "regardless" doesn`t include positions where the side with K only can win a knight and their opponent has no move to avoid it.

Well, 2 pawns is certainly less material than pawn and bishop.

Rook is just 1 piece, so would use the least amount of wood/plastic.

I think the opposite question is more interesting

In both of those positions it's possible for white to force a win.

No it isn't?

For KNNNK

Longest mate score (WTM): MateIn21
Sample WTM longest mating position: 8/8/8/8/8/8/2k4K/1N4NN w - - 0 1

Optimal move sequence from the above WTM longest mating position:

1. Na3+ Kb3 2. Nb5 Kc4 3. Nc7 {Nd6+} Kc5 4. Ne2 {Nf3} Kb6 {Kc6} 5. Nd5+ {Ne6}
Kb5 {Kc5 Kc6} 6. Kg2 {Kg3 Ndc3+ Ne3 Nec3+ Nef4 Nf2 Nhg3} Kc4 {Kc5 Kc6} 7. Nef4
Kb3 {Kb5 Kc5 Kd4} 8. Kf2 {Kf3 Nf2 Ng3} Ka3 {Ka4 Kc2 Kc4} 9. Ke3 {Ne6 Ng3} Ka4
{Kb3} 10. Kd4 {Nc7 Ne6 Nf2 Ng3} Ka5 11. Kc4 {Kc5 Nd3 Ne6 Nf2 Ng3} Ka6 12. Kc5
{Ne6 Nf2 Ng3 Ng6 Nh5} Ka5 {Ka7 Kb7} 13. Nb4 {Nb6 Nd3 Ne6 Nf2 Ng3} Ka4 14. Kc4
Ka5 15. Nfd5 Ka4 16. Nf2 {Ng3} Ka5 17. Ne4 {Nfd3} Ka4 18. Nc5+ Ka3 19. Nc3 Kb2
20. Ncd3+ Ka1 {Ka3} 21. Nc2#