▁of ▁its ▁money ▁that ▁the ▁next ▁bit ▁will ▁be ▁ 0 , ▁and ▁then ▁remainder ▁of ▁its ▁money ▁that ▁the ▁next ▁bit ▁will ▁be ▁ 1 . ▁d ▁doubles ▁the ▁money ▁it ▁placed ▁on ▁the ▁bit ▁that ▁actually ▁occurred , ▁and ▁it ▁los es ▁the ▁rest . ▁d ( w ) ▁is ▁the ▁amount ▁of ▁money ▁it ▁has ▁after ▁seeing ▁the ▁string ▁w . ▁Since ▁the ▁bet ▁placed ▁after ▁seeing ▁the ▁string ▁w ▁can ▁be ▁calculated ▁from ▁the ▁values ▁d ( w ), ▁d ( w 0 ), ▁and ▁d ( w 1 ), ▁calculating ▁the ▁amount ▁of ▁money ▁it ▁has ▁is ▁equivalent ▁to ▁calculating ▁the ▁bet . ▁The ▁mart ing ale ▁character ization ▁says ▁that ▁no ▁bet ting ▁strategy ▁implement able ▁by ▁any ▁computer ▁( even ▁in ▁the ▁weak ▁sense ▁of ▁construct ive ▁strateg ies , ▁which ▁are ▁not ▁necessarily ▁comput able ) ▁can ▁make ▁money ▁bet ting ▁on ▁a ▁random ▁sequence . ▁ ▁Properties ▁and ▁examples ▁of ▁Martin - L ö f ▁random ▁sequences ▁ ▁Ch ait in ' s ▁hal ting ▁probability ▁ Ω ▁is ▁an ▁example ▁of ▁a ▁random ▁sequence . ▁ ▁R AND c ▁( the ▁complement ▁of ▁R AND ) ▁is ▁a ▁measure ▁ 0 ▁subset ▁of ▁the ▁set ▁of ▁all ▁infinite ▁sequences . ▁This ▁is ▁imp lied ▁by ▁the ▁fact ▁that ▁each ▁construct ive ▁null ▁cover ▁covers ▁a ▁measure ▁ 0 ▁set , ▁there ▁are ▁only ▁count ably ▁many ▁construct ive ▁null ▁covers , ▁and ▁a ▁count able ▁union ▁of ▁measure ▁ 0 ▁sets ▁has ▁measure