▁constraints ▁may ▁override ▁the ▁desire ▁for ▁optimal ▁growth ▁rate . ▁The ▁conventional ▁alternative ▁is ▁expected ▁utility ▁theory ▁which ▁says ▁bet s ▁should ▁be ▁s ized ▁to ▁maxim ize ▁the ▁expected ▁utility ▁of ▁the ▁outcome ▁( to ▁an ▁individual ▁with ▁log arith mic ▁utility , ▁the ▁Kelly ▁bet ▁maxim izes ▁expected ▁utility , ▁so ▁there ▁is ▁no ▁conflict ; ▁moreover , ▁Kelly ' s ▁original ▁paper ▁clearly ▁states ▁the ▁need ▁for ▁a ▁utility ▁function ▁in ▁the ▁case ▁of ▁g amb ling ▁games ▁which ▁are ▁played ▁finit ely ▁many ▁times ). ▁Even ▁Kelly ▁supp or ters ▁usually ▁argue ▁for ▁fraction al ▁Kelly ▁( bet ting ▁a ▁fixed ▁fraction ▁of ▁the ▁amount ▁recommended ▁by ▁Kelly ) ▁for ▁a ▁variety ▁of ▁practical ▁reasons , ▁such ▁as ▁wish ing ▁to ▁reduce ▁vol at ility , ▁or ▁protect ing ▁against ▁non - det erm in istic ▁errors ▁in ▁their ▁advantage ▁( edge ) ▁calculations . ▁ ▁See ▁also ▁ ▁R isk ▁of ▁ru in ▁G amb ling ▁and ▁information ▁theory ▁Pro eb st ing ' s ▁par ado x ▁M erton ' s ▁port folio ▁problem ▁ ▁References ▁ ▁External ▁links ▁ ▁Category : Opt imal ▁dec isions ▁Category : G amb ling ▁mathematics ▁Category : Information ▁theory ▁Category : W ager ing ▁Category : Art icles ▁containing ▁proofs ▁Category : 1 9 5 6 ▁introdu ctions ▁Category : Port folio ▁theories <0x0A> </s> ▁Joseph ▁Dub osc , ▁count ▁of ▁P es qu id oux ▁( 1 3 ▁December ▁ 1 8 6 9 ▁in ▁Sav igny - lès