▁mathemat icians ▁and ▁econom ists . ▁ ▁Multiple ▁out comes ▁Kelly ' s ▁criter ion ▁may ▁be ▁generalized ▁on ▁g amb ling ▁on ▁many ▁mut ually ▁exclusive ▁out comes , ▁such ▁as ▁in ▁horse ▁races . ▁Suppose ▁there ▁are ▁several ▁mut ually ▁exclusive ▁out comes . ▁The ▁probability ▁that ▁the ▁- th ▁horse ▁wins ▁the ▁race ▁is ▁, ▁the ▁total ▁amount ▁of ▁bet s ▁placed ▁on ▁- th ▁horse ▁is ▁, ▁and ▁ ▁where ▁ ▁are ▁the ▁pay - off ▁odd s . ▁, ▁is ▁the ▁divid end ▁rate ▁where ▁ ▁is ▁the ▁track ▁take ▁or ▁tax , ▁ ▁is ▁the ▁re venue ▁rate ▁after ▁dedu ction ▁of ▁the ▁track ▁take ▁when ▁- th ▁horse ▁wins . ▁The ▁fraction ▁of ▁the ▁bet tor ' s ▁funds ▁to ▁bet ▁on ▁- th ▁horse ▁is ▁. ▁Kelly ' s ▁criter ion ▁for ▁g amb ling ▁with ▁multiple ▁mut ually ▁exclusive ▁out comes ▁gives ▁an ▁algorithm ▁for ▁finding ▁the ▁optimal ▁set ▁ ▁of ▁out comes ▁on ▁which ▁it ▁is ▁reasonable ▁to ▁bet ▁and ▁it ▁gives ▁explicit ▁formula ▁for ▁finding ▁the ▁optimal ▁fra ctions ▁ ▁of ▁bet tor ' s ▁wealth ▁to ▁be ▁bet ▁on ▁the ▁out comes ▁included ▁in ▁the ▁optimal ▁set ▁. ▁The ▁algorithm ▁for ▁the ▁optimal ▁set ▁of ▁out comes ▁consists ▁of ▁four ▁steps . ▁Step ▁ 1 : ▁Calcul ate ▁the ▁expected ▁re venue ▁rate ▁for ▁all ▁possible ▁( or ▁only ▁for ▁several ▁of ▁the ▁most ▁prom ising ) ▁out comes : ▁▁ ▁Step ▁ 2 : ▁Re order ▁the ▁out comes ▁so