Ua nīnau ʻo Thomas M. Cover i kēia nīnau kamahaʻo i ka makahiki 1987 ma "Open Problems in Communication and Computation": Kākau ʻo Player \(X\) i nā helu kūlohelohe ʻelua a koho wale ʻia \(A\) a me \(B\) i ʻelua mau mea like ʻole. ʻĀpana pepa a kau i ke alo i lalo i ka papa. Koho ka mea pāʻani \(Y\) kēia manawa i kekahi o kēia mau ʻāpana o ka pepa, ʻike i ka helu a i kēia manawa e hoʻoholo inā ʻoi aku ka liʻiliʻi o kēia helu a ʻoi aku paha ma mua o ka helu ʻē aʻe e kū nei i lalo ma ka papa.
ʻAʻole hiki i ka mea pāʻani \(Y\) ke hoʻohuli i ke kāleka i lalo ke alo. Ua ʻae ʻo ia i ka ʻāpana kālā e hoʻoholo a ua loaʻa kahi hoʻolālā me kahi hiki lanakila o \(50\%\) . Aia kekahi hoʻolālā me kahi kiʻekiʻe kiʻekiʻe?
Ma mua o ke koho wale ʻana o ka mea pāʻani \(Y\) i kekahi o nā ʻāpana ʻelua o ka pepa, hoʻoholo ʻo ia i kahi helu kūlohelohe kūlohelohe \(C\) . A laila hoʻohuli ʻo ia i hoʻokahi o nā ʻāpana pepa ʻelua ma ka manawa kaulele. I kēia manawa ua hoʻoholo ʻo ia penei: Inā ʻo ka helu huli ʻo \( \leq C \) , koho ʻo ia i ka helu ma ka ʻāpana pepa ʻē aʻe e like me ka nui; inā ʻo \( > C\) ka helu i huli ʻia, koho ʻo ia i ka helu i huli ʻia e like me ka helu nui. Kupaianaha, ʻo ka manawa lanakila i kēia manawa \( > 50\% \) .
Ua hoʻonohonoho mua mākou i ka inoa o nā helu ʻelua iā \(A < B\) . A laila kikoʻī kekahi o nā hihia aʻe ʻekolu e kū koke ma hope o ke koho ʻana o \(C\):
- ʻO ka hihia 1: \( C \leq A < B \) : A laila ʻo ka likelika o ka lanakila ʻo \(50\%\) , ʻoiai ʻaʻohe ʻike e pili ana iā \(A\) a me \(B\) .
- Nānā \( A < B \leq C \) : \( A < B \leq C \) : A laila ʻo ka likelika o ka lanakila ʻo \(50\%\) , ʻoiai ʻaʻohe ʻike e pili ana iā \(A\) a me \(B\) .
- Hihia 3: \( A < C < B \) : A laila, i ka pahiki o eo ka \(100\%\) , no ka mea, ina \( B \) ua huli ma mua, hoʻokahi ma \( B \) i koe, a ina \(A\) Huli mua ʻo \(A\) hoʻololi ʻoe iā \(B\) , no laila koho mau ʻoe i ka helu nui aku.
ʻO ka mea kupaianaha, hoʻohana ʻia kēia hoʻolālā i ka nohona o kēlā me kēia lā: Eia kekahi laʻana, inā ʻoe e hoʻoholo koke no a i ʻole kūʻē ʻana i ke kūʻai ʻana i kahi huahana me ka hiki ʻole ke loaʻa i kahi hāʻawi hoʻohālikelike, hoʻonoho ʻoe iā ʻoe iho i kahi palena kālā ma mua. Inā hoʻokō kēia palena i ke kumukūʻai maoli, kūʻai ʻia ke kūʻai - a i ʻole ʻaʻole.