fp3[p_, a_, b_] := (1 + b)*p - b*(p^a)
v3[fp3_, p_, a_, b_] := 1 - fp3[1 - p, a, b]
pbar[pi_, ph_, pl_] := pi*pl + (1 - pi)*ph

valSplit2[v3_, fp3_, ph_, pl_, a_, b_, pi_, pbar_] :=
(fp3[pi, a, b]* v3[fp3, pl, a, b] - v3[fp3, pbar, a, b])) + (1 - fp3[pi, a, b])*(v3[fp3, ph, a, b] - v3[fp3, pbar, a, b])

maxSplit2[valSplit2_, v3_, fp3_, ph_, pl_, a_, b_, pi_, pbar_] :=
 FindMaximum[{valSplit2[v3, fp3, ph, pl, a, b, pi, pbar], 1 >= ph > pl >= 0, pi*pl + (1 - pi)*ph == pbar, 1 >= pi >= 0}, {ph, pl, pi}]

N[maxSplit2[valSplit2, v3, fp3, ph, pl, 20, .05, pi, .03], 8]

Plot[maxSplit2[valSplit2, v3, fp3, ph, pl, 20, .05, pi, x], {x, 0, 1}]