▁had ▁followed ▁this ▁rule ▁( ass uming ▁that ▁bet s ▁have ▁infinite ▁gran ular ity ▁and ▁there ▁are ▁up ▁to ▁ 3 0 0 ▁coin ▁toss es ▁per ▁game ▁and ▁that ▁a ▁player ▁who ▁reaches ▁the ▁cap ▁would ▁stop ▁bet ting ▁after ▁that ), ▁an ▁average ▁of ▁ 9 4 % ▁of ▁them ▁would ▁have ▁reached ▁the ▁cap , ▁and ▁the ▁average ▁p ayout ▁would ▁be ▁$ 2 3 7 . 3 6 . ▁ ▁In ▁this ▁particular ▁game , ▁because ▁of ▁the ▁cap , ▁a ▁strategy ▁of ▁bet ting ▁only ▁ 1 2 % ▁of ▁the ▁pot ▁on ▁each ▁toss ▁would ▁have ▁even ▁better ▁results ▁( a ▁ 9 5 % ▁probability ▁of ▁reaching ▁the ▁cap ▁and ▁an ▁average ▁p ayout ▁of ▁$ 2 4 2 . 0 3 ). ▁ ▁Stat ement ▁▁ ▁For ▁simple ▁bet s ▁with ▁two ▁out comes , ▁one ▁involving ▁losing ▁the ▁entire ▁amount ▁bet , ▁and ▁the ▁other ▁involving ▁winning ▁the ▁bet ▁amount ▁multip lied ▁by ▁the ▁pay off ▁odd s , ▁the ▁Kelly ▁bet ▁is : ▁ ▁where : ▁▁▁ ▁is ▁the ▁fraction ▁of ▁the ▁current ▁bank roll ▁to ▁w ager ; ▁( i . e . ▁how ▁much ▁to ▁bet , ▁expressed ▁in ▁fraction ) ▁▁ ▁is ▁the ▁net ▁odd s ▁received ▁on ▁the ▁w ager ; ▁( e . g . ▁bet ting ▁$ 1 0 , ▁on ▁win , ▁re wards ▁$ 4 ▁plus ▁w ager ; ▁then ▁) ▁▁ ▁is ▁the ▁probability ▁of ▁a ▁win ; ▁▁ ▁is ▁the ▁probability ▁of