memo1 = {programs,for,checking,equivalence,of, expressions,relating,to,general,games,of,three, players} all4[k$g_] := all3[k$g] /. uabcdsubs all3[zw_] := eevvs[zw] /. symmch eevvs[xy_] := xy /. eesimp /. gensimp eesimp = {e3 -> 1/101, e4 -> 1/103, e5 -> 1/107} kall4[k$g_] := kall3[k$g] /. uabcdsubs kall3[zw_] := kill[zw] /. symmch kill[xy_] := xy /. killDen /. gensimp killDen = {e4 -> 1, e5 -> 1} gensimp = {b3 -> 1/2, b2 -> 1/3, b1 -> 1/5, a1f2 -> 1/7, a1f3 -> 1/11, a2f1 -> 1/13, a2f3 -> 1/17, a3f1 -> 1/19, a3f2 -> 1/23, a12 -> 1/29, a13 -> 1/31, a21 -> 1/37, a23 -> 1/41, a31 -> 1/43, a32 -> 1/47, af21 -> 1/53, af23 -> 1/59, af32 -> 1/61, af13 -> 1/67, af31 -> 1/71, af12 -> 1/73} symmch = {b3 -> b, b2 -> b, b1 -> b, d1 -> da, d2 -> da, d3 -> da, n1 -> n, n2 -> n, n3 -> n, a1f2 -> aa, a1f3 -> aa, a2f1 -> aa, a2f3 -> aa, a3f1 -> aa, a3f2 -> aa, a12 -> ab, a13 -> ab, a21 -> ab, a23 -> ab, a31 -> ab, a32 -> ab, af21 -> ac, af23 -> ac, af32 -> ac, af13 -> ac, af31 -> ac, af12 -> ac, d12 -> db, d13 -> db, d21 -> db, d23 -> db, d31 -> db, d32 -> db, df12 -> dc, df13 -> dc, df21 -> dc, df23 -> dc, df31 -> dc, df32 -> dc, u2b1r23 -> ua, u3b2r31 -> ua, u1b3r12 -> ua, u1b2r13 -> ua, u3b1r32 -> ua, u2b3r21 -> ua, u3b12r3 -> ub, u1b23r1 -> ub, u2b31r2 -> ub, u3b21r3 -> ub, u2b13r2 -> ub, u1b32r1 -> ub, u2b12r3 -> uc, u3b23r1 -> uc, u1b31r2 -> uc, u1b21r3 -> uc, u3b13r2 -> uc, u2b32r1 -> uc, u3b1r23 -> ud, u1b2r31 -> ud, u2b3r12 -> ud, u3b2r13 -> ud, u2b1r32 -> ud, u1b3r21 -> ud} uabcdsubs = {ua -> 1/79, ub -> 1/83, uc -> 1/89, ud -> 1/97} ratof[uu_] := Module[{s, t, v}, {s, t} = uu; v = s/t; Return[v]; ] equal[uu_] := Module[{v}, v = ratof[all4[uu]]; Return[v]; ] diffof[uu_] := Module[{s, t, v}, {s, t} = uu; v = Simplify[s-t]; Return[v]; ] equal2[uu_] := Module[{v}, v = diffof[all4[uu]]; Return[v]; ] memo2 = {programing,device,for,substitutions, useful,for,comparing,expressions,relating,to, games,symmetric,between,players,P1,and,P2} csubs = {bz -> 1/2, b3 -> 1/3, e3 -> 1/8, e4 -> 2/7, e5 -> 3/11, y1 -> 1/5, y2 -> 1/7, y3 -> 1/11, y4 -> 1/13, y5 -> 1/17, y6 -> 1/19, y7 -> 1/23, y8 -> 1/29, y9 -> 1/31, y10 -> 1/37, y11 -> 1/41, y12 -> 1/43, y13 -> 1/47, y14 -> 1/83, y15 -> 1/53, y16 -> 1/59, y17 -> 1/61, y18 -> 1/67, y19 -> 1/71, y20 -> 1/73, y21 -> 1/79}