Yezga 2/3 ya Avareji

Sankha nambara. Wakutonda ni uyo wasankha nambara yapafupi chomene na 2/3 ya avareji ya wose sabata yino. Waulere, palije kulembeska.

Na gulu la HelibrainYawelereskeka na Robert(Chingelezi), uyo wakusambira digiri ya PhD ya sayansi ya physics ya viŵikiliYikafaliskika Yawelereskekaso paumaliro

Umo mungapulikiskira ivyo mwachita

  • Mlingo winu ukulongora masitepu agho mwaghanaghanira panthazi. Usange mwazgora pafupi na 50, muli pa mlingo wa 0: mundaghanaghanireko vya ŵanji. Pafupi na 33 muli pa mlingo wa 1: "ŵanthu ŵaghanaghanenge kuti ŵazamuzgora pafupi na 50". Pafupi na 22 muli pa mlingo wa 2: "ŵanthu ŵazamughanaghana sitepu limoza panthazi". Sitepu lililose ni 2/3 ya ilo lalutapo [1].
  • Zgoro la game theory ni 0. Usange waliyose wangaghanaghanira m'paka kuumaliro, zgoro lililose lingakhira kufika pa 0. Ŵanthu awo ŵakuseŵera nadi ŵakuchita nthena yayi, ntheura 0 yindatondeso mpikisano wa ŵanthu wose [1][2].
  • Yingatonda yayi: zgoro lakujumpha 66.7 lingatonda yayi, chifukwa nanga waliyose wangazgora 100, chandamale chingaŵa 66.7.
  • Uyo watonda sabata yino wazamuwoneka para chizunguliro chamara (chizunguliro chilichose chikuchitika kwa sabata limoza, kwambira pa Mande kuya pa Sabata, UTC). Tikumuwoneska yayi avareji iyo yikusintha pa nyengo yeneiyo, chifukwa vingapoka chimwemwe cha mchezo. Chizunguliro chikukhumbikwira ŵanthu pafupifupi 30 kuti chiŵe na zgoro.

Kasi nambara yiwemi chomene yakuzgora ni nji?

Palije nambara yimoza yiwemi nyengo zose: vikuthemba pa ivyo ŵanthu ŵanyake ŵazgorenge. Mu mipikisano yikuru ya ŵanthu wose, chandamale chikaŵa pakati pa pafupifupi 13 na 22. Ŵaŵazgi ŵa Financial Times ŵakaŵa na avareji ya 18.9, ntheura chandamale chikaŵa 12.6 [2]. Mu mpikisano wa nyuzipepara ya ku Denmark uwo ukaŵa na ŵaŵazgi 19,196, avareji yikaŵa 32.4 ndipo chandamale chikaŵa 21.6 [3].

Chati ya mizati: avareji ya zgoro na chandamale mu mipikisano yinayi yakusindikizgika. Kafukufuku wa labu 1995: avareji 36.7, chandamale 24.5. Politiken 2005: avareji 32.4, chandamale 21.6. Spektrum 1997: avareji 22.1, chandamale 14.7. Financial Times 1997: avareji 18.9, chandamale 12.6.
Chithuzithuzi 1. Avareji ya zgoro na chandamale cha 2/3 mu mipikisano yinayi yakusindikizgika. Vyakuŵerengera: Nagel 1995, chizunguliro chakwamba, ŵasambiri 67 [1]; Politiken 2005, ŵaŵazgi 19,196 [3]; Spektrum der Wissenschaft 1997, ŵaŵazgi 2,728, na Financial Times 1997, ŵaŵazgi 1,476 [2].

Zunurani peji ili: Yezga 2/3 ya Avareji. Helibrain. 2026. https://helibrain.com/tum/guess-two-thirds-of-the-average. CC BY 4.0.

Fundo zakudumura

  • Ivyo vikulongora: masitepu agho mukughanaghanira panthazi pa ivyo ŵanthu ŵanyake ŵachitenge. Ŵasayansi ŵa vyachuma ŵakucema kaghanaghaniro aka kuti level-k [1][4].
  • Kuyesera kwakumanyikwa: mu chizunguliro chakwamba cha kafukufuku wa Rosemarie Nagel wa 1995, ŵasambiri ŵakazgora avareji ya 36.7, ndipo mazgoro ghanandi chomene ghakaŵa pafupi na 33 na 22 [1].
  • Mipikisano yikuru: ŵaŵazgi 1,476 ŵa Financial Times ŵakaŵa na avareji ya 18.9 (zgoro lakutonda likaŵa 13), ndipo ŵaŵazgi 19,196 ŵa Politiken ŵakaŵa na avareji ya 32.4 [2][3].
  • Chifukwa icho 33 yikutemwekera: mu mtundu wa maseŵero agha wa New York Times mu 2015 uwo ukaŵa na ŵaŵazgi pafupifupi 56,000, 33 ndilo likaŵa zgoro lakusankhika chomene [5].
  • Umo fundo iyi yikambira: John Maynard Keynes, wasayansi wa vyachuma, wakayaniska msika wa masheya na mpikisano wa uzuri umo munthu wakutondera para wasankha chisko icho ŵanthu ŵanyake ŵangasankha [6].

Umo mchezo uwu ukuseŵerezgera

  1. Sankhani nambara yizima kufuma pa 0 kuya pa 100 ndipo muyikhome.
  2. Mazgoro gha wose gha sabata yino ghakuŵerengeka pamoza para chizunguliro chamara, ndipo chandamale ni 2/3 ya avareji iyi.
  3. Uyo wazgora pafupi chomene ndiyo wakutonda. Para ŵanthu ŵakwana na zgoro limoza, ŵakugaŵana kutonda. Pa Mande, peji likulongora ŵanthu ŵa sabata yakumara, avareji, chandamale, zgoro lakutonda na umo nambara yiliyose yikazgolekera.

Zgoro limoza la munthu ndilo likuŵerengeskeka pa chizunguliro chilichose. Tikuŵerenga zgoro limoza pa buroza na zgoro limoza pa intaneti yimoza, ntheura ŵanthu awo ŵakugwiliskira ntchito netiweki yimoza (sukulu, ofesi, panji mbumba) ŵakuŵerengeskeka kamoza pa sabata. Zgoro lachiŵiri likuŵerengeskeka yayi. Mwati mwazgora waka, peji likulongora malo gha nambara yinu pa masitepu gha kaghanaghaniro na umo yate yikachitira mu mipikisano yakumanyikwa iyo yili pachanya apa.

Ivyo mchezo uwu ukuyezga, na uko wafuma

Ŵasayansi ŵa vyachuma ŵakucema mchezo uwu kuti mpikisano wa p-beauty, ndipo pano p = 2/3. Rosemarie Nagel ndiyo wakawusambazga chomene nga ni kuyezga kwa mu labu mu 1995 [1]. Ivyo wakasanga: ŵanthu ŵakughanaghanira m'paka kuumaliro kufika pa 0 yayi, kweniso ŵakuzgora mwamwayi yayi. Ŵanandi ŵakuleka para ŵaghanaghanira sitepu limoza panji ziŵiri za kuti "iwo ŵakughanaghana kuti ine nkhughanaghana".

Fundo yakuti ŵanthu ŵakughanaghanira ŵanji masitepu ghachoko waka ndiyo yikazgoka ndondomeko za level-k na cognitive hierarchy pa kaghanaghaniro ka kupanga vyakusankha [4][7]. Mipikisano ya mu nyuzipepara iyo yikachitika pamanyuma, ndipo yikaŵa na ŵaŵazgi masauzandi ghanandi, yikalongora masitepu agha agho ghali pa 33 na 22, pamoza na gulu la ŵanthu awo ŵakasankha 0 panji 1 [2].

Ivyo mchezo uwu ungamuphalirani na ivyo ungamuphalirani yayi

Mlingo winu ukulongora zgoro limoza mu mchezo umoza. Ni chiyezo cha vinjeru yayi, ndipo mlingo wapachanya nguwemi chomene yayi: wakutonda ni uyo wayowoyera makora ivyo gulu lisankhenge, ndipo kanandi gulu likuleka pa masitepu limoza panji ghaŵiri. Zgoro la mlingo wa 4 likulongora kaghanaghaniro kawemi, kweni kanandi likumalira pasi pa chandamale.

Ŵanthu awo ŵakuseŵera pano ni awo ŵiza sabata yiliyose, ni gulu lakuyana nyengo zose yayi, ntheura chandamale chikusintha sabata na sabata. Mipikisano yakumanyikwa yikagwiliskira ntchito malango ghakupambana pachoko: Financial Times yikazomerezga manambara ghazima pera, ndipo Politiken na Spektrum vikazomerezga manambara gha decimal [2][3].

Mafumbo agho ŵanthu ŵakufumba kanandi

Kasi zgoro la kuyezga 2/3 ya avareji ni vichi?

Yezga 2/3 ya avareji yilije zgoro lakukhazikika. Game theory yikuti zgoro ni 0, chifukwa munthu waliyose wali na chifukwa chakuti wasankhe nambara yichoko kuluska ya ŵanji wose. Kweni ŵanthu ŵeneko ŵakuleka para ŵaghanaghanira sitepu limoza panji ziŵiri, ntheura mu mipikisano yakusindikizgika nambara zakutonda zikaŵa pakati pa 13 na 21.6 [2][3]. Zgoro liwemi chomene ni 2/3 ya ivyo mukughanaghana kuti ŵanji ŵazgorenge pa avareji.

Chifukwa wuli 0 yikutonda yayi?

Nambara zero yikatenge yitonde pekha para pafupifupi waliyose wangaghanaghanira m'paka kuumaliro. Mu mipikisano yeneko, ŵanthu ŵanandi ŵakuzgora pafupi na 33 panji 22, ndipo ŵanyake ŵakusankha manambara ghapachanya, ivyo vikukwezga avareji. Mu mpikisano wa Financial Times, avareji yikaŵa 18.9 ndipo chandamale chikaŵa 12.6, vyakupambanako chomene na 0 [2].

Kasi "munthu wa kaghanaghaniro ka mlingo wa 2" wakung'anamurachi?

Munthu wa kaghanaghaniro ka mlingo wa 2 wakughanaghana kuti ŵanthu ŵanyake ŵaghanaghanirenge sitepu limoza panthazi (ŵazgorenge pafupi na 33), ndipo iyo wakughanaghanira sitepu linyake: 2/3 ya 33 ni pafupi na 22. Mu mchezo wa Helibrain, mlingo winu ni sitepu pa nthowa ya manambara (50, 33, 22, 15, 10) ilo zgoro linu lili pafupi chomene [1].

Kasi ningaseŵera kanandi waka?

Enya, kweni zgoro linu lakwamba pera la sabata ndilo likuŵerengeskeka mu chizunguliro. Mazgoro agho mwazgora pamanyuma ghakulongoreka pa masitepu, kweni ghakuŵerengeskeka yayi, ntheura palije uyo wangasintha ivyo vyachitika mwa kuzgora kanandi waka. Chizunguliro chiphya chikuyamba Mande lililose.

Kasi mchezo wa 2/3 wa Helibrain ngwauchokwadi waulere?

Enya. Mchezo wa 2/3 wa Helibrain na vyakufumapo vyose vya sabata ni vyaulere: palije kulembeska, imelo panji kulipira. Helibrain yikusanga ndalama kufuma mu app yake, iyo yili na pulani yaulere na mapulani ghakulipira; mukukhumbikwira app yayi kuti museŵere.

Mayezgo ghanyake

Wonani mayezgo ghose gha wongo ghaulere 43

Mukukhumba kuchita ivi zuŵa lililose? App ya Helibrain (yili mu Chingelezi pera sono) yili na pulani yaulere na mapulani ghakulipilira.

Zunurani peji ili: Yezga 2/3 ya Avareji. Helibrain. 2026. https://helibrain.com/tum/guess-two-thirds-of-the-average. CC BY 4.0.

How this test works

This is a weekly strategy game. Pick a whole number from 0 to 100. When the week ends, everyone's guesses are averaged, and the winner is whoever comes closest to two thirds of that average. Right after you guess, you see how many steps ahead of other players your number suggests, and how it would have done in famous contests. Economists first ran this game as a lab experiment in 1995.

Version 1 · Cite this test:

Helibrain (2026). Guess 2/3 of the average, v1. https://helibrain.com/guess-two-thirds-of-the-average/methods

Full method →

Vyakufumiskapo

  1. Nagel R (1995). Unraveling in guessing games: an experimental study. American Economic Review 85(5):1313–1326. www.jstor.org/stable/2950991
  2. Bosch-Domènech A, Montalvo JG, Nagel R, Satorra A (2002). One, two, (three), infinity, …: newspaper and lab beauty-contest experiments. American Economic Review 92(5):1687–1701. doi.org/10.1257/000282802762024737 (numbers from the 1999 working paper: econ-papers.upf.edu/papers/438.pdf)
  3. Schou A (2005). Gæt-et-tal konkurrence afslører at vi er irrationelle. Politiken, 22 September 2005. politiken.dk/oekonomi/art5698526
  4. Camerer CF, Ho T-H, Chong J-K (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics 119(3):861–898. doi.org/10.1162/0033553041502225
  5. Quealy K (2015). How readers fared in Upshot's number puzzle. The New York Times, 20 August 2015. www.nytimes.com/2015/08/21/upshot/how-readers-fared-in-upshots-number-puzzle.html
  6. Keynes JM (1936). The General Theory of Employment, Interest and Money, chapter 12. London: Macmillan.
  7. Stahl DO, Wilson PW (1995). On players' models of other players: theory and experimental evidence. Games and Economic Behavior 10(1):218–254. doi.org/10.1006/game.1995.1031

Umo peji ili likapangikira: gulu la Helibrain likalemba kufuma mu kafukufuku uyo walongosoreka pachanya, ndipo Robert(Chingelezi) (uyo wakusambira digiri ya PhD ya sayansi ya physics ya viŵikili) wakaliwelereskaso pa 11/4/2026. Tikulisintha para ivyo vyagwiliskirika ntchito vyasintha.