For a first trial for a solution of general type (not symmetric) we could
start from "sxfr2" below, reduced to a few decimals, and use for the
parameters:

 paramsubs = {b1 -> 1/6, b2 -> 1/5, b3 -> 1/4, e3 -> 1/8, e4 -> 1, e5 -> 1}

  (So Player 1 is favored, Player 3 is disfavored, and Player 2 is in between.)


############################################################


     " soln.4th.725 " is included below


ps = {b -> 1/5, e3 -> 1/8, e4 -> 1, e5 -> 1}
 
sxfr2 = {0.2249231208288102375374538588877156198864732340807737533458377`50, 
     0.7233006827985626950790903629180062466250644711487729953496914618303`50,
     0.6713834891155636761170726674007960910894132772933648733438254421356`50, 
     0.26703722298448075482010890016126340787167534483031174439956578`50, 
     0.26703722298448075482010890016126340787167534483031174439956578`50, 
     0.19156123683529868070543962125644721753362124361205629439026546`50, 
     0.20228233301230830936622767432058834709096940747253102193580912`50, 0, 
     0, 0, 0, 0, 0, 0, 0}
 
sx100 = {0.22229155691330077, 0.6902869839530485, 0.6276417349811777, 
     0.2602074178818153, 0.25923813216686636, 0.18695287183115933, 
     0.19923321203013758, 0., 0., 0., 0., 0., 0., 0., 0.}
 
sx5 = {0.2071827268430749, 0.660075381063681, 0.6033312879011854, 
     0.27904725286198767, 0.2795229645169963, 0.19474679798639674, 
     0.2028797290224437, 0., 0., 0., 0., 0., 0., 0., 0.}
 
paye = 0.772855718973674152020398312581211`20
 
stagespaye = {0.015157426579573844239203392219527`20, 
     0.757698292394100307781194920361684`20}