▁ ▁History ▁▁ ▁The ▁first ▁suitable ▁definition ▁of ▁a ▁random ▁sequence ▁was ▁given ▁by ▁Per ▁Martin - L ö f ▁in ▁ 1 9 6 6 . ▁Ear lier ▁research ers ▁such ▁as ▁Richard ▁von ▁M ises ▁had ▁attempted ▁to ▁formal ize ▁the ▁notion ▁of ▁a ▁test ▁for ▁random ness ▁in ▁order ▁to ▁define ▁a ▁random ▁sequence ▁as ▁one ▁that ▁passed ▁all ▁tests ▁for ▁random ness ; ▁however , ▁the ▁precise ▁notion ▁of ▁a ▁random ness ▁test ▁was ▁left ▁vague . ▁Martin - L ö f ' s ▁key ▁insight ▁was ▁to ▁use ▁the ▁theory ▁of ▁computation ▁to ▁formally ▁define ▁the ▁notion ▁of ▁a ▁test ▁for ▁random ness . ▁This ▁contrast s ▁with ▁the ▁idea ▁of ▁random ness ▁in ▁probability ; ▁in ▁that ▁theory , ▁no ▁particular ▁element ▁of ▁a ▁sample ▁space ▁can ▁be ▁said ▁to ▁be ▁random . ▁ ▁Since ▁its ▁in ception , ▁Martin - L ö f ▁random ness ▁has ▁been ▁shown ▁to ▁admit ▁many ▁equivalent ▁character izations ▁— ▁in ▁terms ▁of ▁compression , ▁random ness ▁tests , ▁and ▁g amb ling ▁— ▁that ▁bear ▁little ▁out ward ▁res embl ance ▁to ▁the ▁original ▁definition , ▁but ▁each ▁of ▁which ▁satisfy ▁our ▁intuit ive ▁notion ▁of ▁properties ▁that ▁random ▁sequences ▁ought ▁to ▁have : ▁random ▁sequences ▁should ▁be ▁in com press ible , ▁they ▁should ▁pass ▁statistical ▁tests ▁for ▁random ness , ▁and ▁it ▁should ▁be ▁difficult ▁to ▁make ▁money ▁bet ting ▁on ▁them . ▁The ▁existence ▁of ▁these ▁multiple ▁definitions ▁of ▁Martin - L ö f ▁random ness ,