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linBrett = RandomSample[linBrett0];

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(* Initialisierung und Eingabe *)
n = 10; nn = n^2; nSim = 10^5; nErg = {0, 0, 0};
linBrett0 = Table[(-1)^(i + 1)*i, {i, 1, nn}];

(* Simulation *)
For[iSim = 0, iSim < nSim, iSim++,
   rslt = 0; nZmin = nn + 1;
   linBrett = RandomSample[linBrett0];
   zlBrett = Table[linBrett[[n*(i - 1) + j]], {i, n}, {j, n}];
   spBrett = Table[linBrett[[n*(i - 1) + j]], {j, n}, {i, n}];
   diag1 = Table[zlBrett[[i, i]], {i, n}];
   diag2 = Table[zlBrett[[i, n + 1 - i]], {i, n}];
   zlSum = Table[Total[Sign[zlBrett[[i]]]], {i, n}];
   spSum = Table[Total[Sign[spBrett[[i]]]], {i, n}];
   d1Sum = Total[Sign[diag1]];
   d2Sum = Total[Sign[diag2]];
   
   For[i = 1, i < n + 1, i++,
    If[Abs[zlSum[[i]]] == n, nZ = Max[Abs[zlBrett[[i]]]]; 
     If[nZ < nZmin, nZmin = nZ; rslt = Sign[zlSum[[i]]]]];
    If[Abs[spSum[[i]]] == n, nZ = Max[Abs[spBrett[[i]]]]; 
     If[nZ < nZmin, nZmin = nZ; rslt = Sign[spSum[[i]]]]]];
   If[Abs[d1Sum] == n, nZ = Max[Abs[diag1]];
    If[nZ < nZmin, nZmin = nZ; rslt = Sign[d1Sum]]];
   If[Abs[d2Sum] == n, nZ = Max[Abs[diag2]];
    If[nZ < nZmin, nZmin = nZ; rslt = Sign[d2Sum]]];
   nErg[[rslt + 2]]++;
   ]; // Timing

(* Ergebnis *)
nErg
Print[nErg[[3]]/nSim*100., " % Gewinn"];
Print[nErg[[2]]/nSim*100., " % Remis"];
Print[nErg[[1]]/nSim*100., " % Verlust"];