What is crux for FFA puzzles is that any player can throw the game in the favor of an another player, as such making most of the positions practically unsolvable, hence FFA puzzles are usually too easy to solve, and are never complicated. As such, I wanted to amend this issue by introducing the following FFA puzzle classification format:
a. Constancy. This defines how well should players play in order for the key player to win.
1. Fixed Constancy. This means no matter what the other sides play, the key player will always win, and there is absolutely nothing the others can do about this.
2. Irresolute Constancy. This means that the key player can always win given that at least one player will not throw the game but instead try to maximize the winning their winning chances.
3. Practical Constancy. This means that players will only throw the game when they cannot maximize their winning chances, but otherwise will play optimally as to halt an immediate win / advantage.
4. Deterministic Constancy. This means that every player will play optimally and will not throw the game as long as there is a very slim chance of winning, i.e. imagine a 2700+ game.
b. Goal.
1. Victory, win by force, quite obvious I assume.
2. Practical Victory, a victory that can be prevented only by extreme teaming play or by extreme throwing. Extreme here counts as an incredibly accurate move sequence that players would cease to even think of in practical games, to see this idea one must see all the attacking idea aforehand.
3. Practical Edge, obtain a non-winning advantage that in a real, live game the key player would be definitely able to convert against players of the same level as the key player.
4. Practical Advantage, obtain a certain advantage, i.e. eliminating a flank as to secure one's own comfortable gameplay. No one guarantees the key player will win against same-strength opponents, but they must be equal at least.
c. Any FFA puzzle that has a line that ends up in a forced king-making or encourages one to throw as one cannot change the game outcome is considered as "practically invalid".
d. It is assumed that all the players are of the same level for practical constancy and deterministic constancy.
Let me take the following example puzzle:
[StartFen4 "Y-0,0,0,1-0,0,0,0-0,0,0,0-32,41,39,0-0-{'royal''h2','a7','h14',''),'pawnBaseRank':3,'noCorners':true}-x,4,X,1,yW,X,3,yU,x/1,x,x,2,X,yU,yK,X,2,x,x,dU/1,x,x,3,X,X,3,x,x,1/2,dγ,1,dα,5,yR,dγ,1,dΔ/4,bK,1,bδ,2,yN,2,dC,1/X,X,bU,1,bY,bδ,2,yδ,yM,2,X,X/2,X,bR,3,dI,3,X,dY,dW/bW,bN,X,2,rδ,2,yG,1,yδ,X,dK,dK/X,X,1,bδ,2,rδ,rN,dF,1,dδ,1,X,X/2,bγ,1,bδ,2,rδ,1,rγ,rγ,dδ,dC,dN/bC,5,rK,rY,1,rB,2,dγ,dR/1,x,x,3,X,X,3,x,x,1/1,x,x,rR,1,X,1,rW,X,2,x,x,dU/x,4,X,2,X,4,x"][Variant "FFA"][RuleVariants "AllowPassing Anonymous BarePieceLoses PromoteTo=M Prom=10 Sideways"][CurrentMove "0"]
Yellow to move, Irresolute Constancy, Practical Victory, Blue to win.
Difficulty: pretty difficult.