Thoma 2/3 ya Mũigana

Ta namba. Mũthaana nĩ ũrĩ na namba ĩrĩ hakuhĩ na 2/3 ya mũigana wa andũ othe kĩyumweru gĩkĩ. Nĩ wa mbere, ndũrĩ na haja ya kwandĩka.

Nĩ andũ a HelibrainNĩyaretiirwo na Robert(Gĩkĩngeresa), mũndũ ũrĩ gũthoma PhD ya biophysicsYandĩkĩtwo Nĩyaretiirwo rĩngĩ mũthenya wa mũthia

Ũrĩa wa gũthoma macookio maku

  • Kĩero gĩaku kĩonesagia namba ya mathambĩa ũciirĩirie mbere. Kũruta namba hakuhĩ na 50 nĩ kĩero 0: ndũciirĩirie ũrĩa angĩ no ta. Hakuhĩ na 33 nĩ kĩero 1: "andũ nĩmakũruta ta 50". Hakuhĩ na 22 nĩ kĩero 2: "andũ nĩmacooke kũciiria gacũũru kamwe". Gĩtugĩ kĩmwe nĩ 2/3 ya gĩtugĩ gĩrĩa gĩatũũrĩte mbere [1].
  • Macookio ma game theory nĩ 0. Angĩtuĩka o mũndũ aciirĩirie nginya hingo ya mũthia, o namba ingĩthii ikĩhũthĩrĩra ikĩruta 0. Atheethi a tene matigĩkaga ũguo, nĩ ũndũ ũcio 0 itigĩaka ithaana rĩa andũ [1][2].
  • Ĩtingĩthaana: namba ĩrĩ igũrũ ya 66.7 ndĩngĩthaana, tondũ o ta andũ othe mabataririe 100, gĩtangĩro gĩgũtuĩka 66.7.
  • Mũthaana wa kĩyumweru gĩkĩ nĩakoneka rũciinĩ rwa mũthenya wa mũthia wa gĩcigo (gĩcigo gĩothe nĩ kĩumweru, kuuma mũthenya wa mbere nginya wa ĩtandatu, UTC). Tũtiũonesagia mũigana wa rĩu mbere ya mũthia: nĩgũthiiria ũrĩa wa gũthaana. Gĩcigo nĩ kĩrĩ na haja ya athiithi atarĩ o mahiũ 30 nĩguo gĩtuĩke na macookio.

Namba njega ya gũthaana nĩ ĩrĩkũ?

Gũtirĩ namba ĩmwe njega ya gũthaana: nĩ ũndũ wa namba iria andũ angĩ magũthaana. Magerio ma andũ maingĩ, gĩtangĩro kĩarĩ hakuhĩ na 13 nginya 22. Athomi a Financial Times maarĩ na mũigana wa 18.9, nĩ ũndũ ũcio gĩtangĩro kĩarĩ 12.6 [2]. Kũrĩ kĩgerio kĩa rũrĩrĩ rwa ndeto rũitwo Danish rĩarĩ na athomi 19,196, mũigana warĩ 32.4 na gĩtangĩro 21.6 [3].

Chati ya itamba: mũigana wa namba iria ciahanĩtwo na gĩtangĩro kĩa magerio mana marĩkĩtwo. Kĩgerio gĩa lab 1995: mũigana 36.7, gĩtangĩro 24.5. Politiken 2005: mũigana 32.4, gĩtangĩro 21.6. Spektrum 1997: mũigana 22.1, gĩtangĩro 14.7. Financial Times 1997: mũigana 18.9, gĩtangĩro 12.6.
Gĩcunjĩro 1. Mũigana wa namba iria ciahanĩtwo na gĩtangĩro kĩa 2/3 kũrĩ magerio mana marĩkĩtwo. Data: Nagel 1995, mũrongo wa mbere, 67 athomi [1]; Politiken 2005, athomi 19,196 [3]; Spektrum der Wissenschaft 1997, athomi 2,728, na Financial Times 1997, athomi 1,476 [2].

Taũra karatathi gaka: Thoma 2/3 ya Mũigana. Helibrain. 2026. https://helibrain.com/ki/guess-two-thirds-of-the-average. CC BY 4.0.

Ciugo cia kwĩhũthĩra

  • Kĩonesagia atĩa: namba ya mathambĩa ũciirĩirie mbere ũkĩrora ũrĩa andũ angĩ megũka gwĩka. Athomi a mĩario ya ũthũũri nĩmetaga level-k thinking [1][4].
  • Kĩgerio kĩa tene: mũrongo wa mbere wa kĩgerio gĩa Rosemarie Nagel kĩa 1995, athomi maathomire 36.7 na mũigana, na namba iria ciahanĩtwo mũno nĩ ciaikaraga hakuhĩ na 33 na 22 [1].
  • Magerio makũru: athomi 1,476 a Financial Times maathomire 18.9 na mũigana (namba ya gũthaana yarĩ 13), na athomi 19,196 a Politiken maathomire 32.4 [2][3].
  • Kũhũtũka kwa 33: mũhũthĩro wa New York Times wa 2015 warĩ na athomi ta 56,000; 33 nĩyo namba yarĩ ciahanĩtwo mũno [5].
  • Kũruga kwa ũciarĩ: ũthomi John Maynard Keynes nĩaageranĩtie soko rĩa mĩgũnda na kĩgerio kĩa mũndũ mwega, harĩa ũgũthaana ũrĩa andũ angĩ magũthaana nĩguo wĩthaane [6].

Mchezo ũrĩa ũtwaraga

  1. Ta namba yothe kuuma 0 nginya 100 na ũikane nayo.
  2. Namba iria andũ othe magũthomera kĩyumweru gĩkĩ nĩigĩtangĩrwo hingo gĩcigo gĩcio kĩrĩkia, na gĩtangĩro kĩa namba nĩ 2/3 ya mũigana ũcio.
  3. Mũndũ ũrĩ na namba ĩrĩ hakuhĩ nĩ ũgũthaana. Angĩtuĩka nĩ aathaani aingĩ, nĩmagĩgaihana ũthaana. Mũthenya wa mbere, karatathi nĩkĩonesagia athiithi a kĩyumweru gĩkĩathira, mũigana, gĩtangĩro, namba ĩathaana na ũrĩa o namba yathomirwo.

Gĩcigo gĩothe, nĩ gĩtũũra gĩtangĩra thomoro ĩmwe ya mũndũ. Tũtangaga thomoro ĩmwe kwa browser na ĩmwe kwa muungano wa internet, nĩ ũndũ ũcio andũ arĩa marĩ hamwe kũrĩ muungano (thukuru, ofisi kana nyũmba) matangagwo ta mũndũ ũmwe kĩyumweru. Thomo ya keerĩ ndĩtangagwo. Rĩrĩa ũrĩkia gũthoma, karatathi nĩkĩonesagia harĩa namba yaku yathiiire kũrĩ rũrigi rwa kũciiria na ũrĩa ingĩathire kũrĩ magerio marĩa marĩtũũrĩtwo igũrũ.

Ũrĩa mchezo ũgeragia, na kũruga gwagu

Athomi a mĩario ya ũthũũri metaga mchezo ũyũ p-beauty contest, na p = 2/3 haha. Rosemarie Nagel nĩetire ũtuĩke kĩgerio kĩa lab kĩa mũno mwaka wa 1995 [1]. Kĩrĩa kĩaiguĩrwo: andũ matigĩkaga kũciiria nginya 0, na matirũtaga namba hĩndĩ ya kũthirĩrĩria. Aingĩ nĩmatigaga thutha wa mathambĩa 1 kana 2 ma "acio nĩmeciiria atĩ niĩ nĩndeciiria".

Gĩciaro kĩu, atĩ andũ nĩmeciiria mathambĩa matano matheru ma ũrĩa angĩ, nĩgĩtũũkĩtie level-k na cognitive hierarchy models cia kũciiria ũthũũri [4][7]. Magerio ma marũa ma ndeto maathirire thuutha, o hamwe na athomi ngiri, nĩmoonyirie mathambĩa macio macio ma 33 na 22, hamwe na gĩkundi kĩa andũ methire 0 kana 1 [2].

Ũrĩa mchezo ũyũ ũhota na ũtahota kũkuonia

Kĩero gĩaku nĩ kĩrorete thomoro ĩmwe ya mchezo ũmwe. Gĩtirĩ kĩgerio kĩa ũmenyo, na kĩero kĩrĩ igũrũ ti kĩega gũkĩra: ũthaana nĩ wa mũndũ ũrĩ na ũhoti wa gũtũma mũingĩ wa andũ, na mũingĩ wa andũ nĩmatigaga thutha wa mathambĩa 1 kana 2. Thomo ya kĩero 4 nĩ ũciari mwega wa kũciiria, no mĩhĩrĩga mĩingĩ nĩyũmĩrĩra thutha wa gĩtangĩro.

Athiithi a haha nĩ arĩa moingaga kĩyumweru kĩu, ti gĩcunjĩro kĩa athiithi gĩtũũraga kĩmwe, nĩ ũndũ ũcio gĩtangĩro nĩkĩhũthĩrĩraga kuuma kĩyumweru gĩmwe nginya kĩrĩa kĩngĩ. Magerio marĩa marĩtũũrĩtwo marĩ na mawatho magĩtũũra mehitĩte: Financial Times nĩyendaga namba cia mũgongo mũthaka, na Politiken na Spektrum nĩciarĩtĩrĩtie namba cia decimals [2][3].

Ciũria iria ciũragwo mũno

Namba ya gũthaana 2/3 ya mũigana nĩ ĩrĩkũ?

Thoma 2/3 ya mũigana ndĩrĩ na namba ĩtũũraga ĩrĩ ĩmwe. Game theory yaria 0, tondũ o mũthiithi arĩ na mũtugo wa gũthiĩ thĩ ya andũ angĩ othe. No andũ a rĩu nĩmatigaga thuutha wa mathambĩa 1 kana 2, nĩ ũndũ ũcio kũrĩ magerio marĩtũũrĩtwo namba ya ũthaana yarĩ gatagatĩ ka 13 na 21.6 [2][3]. Namba njega ya gũthaana nĩ 2/3 ya ũrĩa ũciirĩirie andũ angĩ nĩmagũthoma na mũigana.

Nĩ kĩĩ gĩtũma 0 itithaana?

Namba 0 no ĩthaane angĩtuĩka o ta andũ othe meciirĩtie nginya mũthia. Kũrĩ magerio ma rĩu, andũ aingĩ magũthoma hakuhĩ na 33 kana 22, na angĩ magũthoma namba nene, iria igũtũũra mũigana ũrĩ igũrũ. Kũrĩ kĩgerio kĩa Financial Times, mũigana warĩ 18.9 na gĩtangĩro 12.6, harĩa haatari na 0 [2].

Nĩ atĩa mũciiri wa "kĩero 2"?

Mũciiri wa kĩero 2 nĩarora atĩ andũ angĩ nĩmaciirĩria gĩtugĩ gĩmwe mbere (nĩmagũthoma ta 33), nake acooke gũthiĩ gĩtugĩ gĩmwe mbere: 2/3 ya 33 nĩ ta 22. Mchezo-inĩ wa Helibrain, kĩero gĩaku nĩ gĩtugĩ kĩa rũrigi rwa kũciiria (50, 33, 22, 15, 10) harĩa namba yaku ĩrĩ hakuhĩ mũno [1].

Nĩngĩhota kũruta thomo inyingĩ?

Ĩĩ, no thomo yaku ya mbere kĩyumweru gĩothe nĩyo ĩtangagwo kũrĩ gĩcigo. Thomo iria ikuihĩ nĩikonekania kũrĩ rũrigi, no ititangagwo, nĩ ũndũ ũcio gũtirĩ mũndũ ũngĩhota kũhũthĩra macookio kwa gũthoma marĩa maingĩ. Gĩcigo kĩerũ gĩambĩrĩria o mũthenya wa mbere.

Mchezo wa Helibrain 2/3 nĩ wa mahũthĩro ta ũrĩa?

Ĩĩ. Mchezo wa Helibrain 2/3 na macookio mothe ma kĩumweru nĩma mahũthĩro: gũtirĩ kwandĩka, gũtirĩ barua ya email, gũtirĩ kũrĩha. Helibrain nĩĩgĩa mbeca kuuma kĩhĩtũ kĩayo, kĩrĩ na mũgawo wa mahũthĩro na mĩgawo ya kũrĩha; ndũrĩ na haja ya kĩhĩtũ gĩkĩ nĩguo ũthome.

Magerio marĩ hamwe

Ona magerio mothe ma ũbongo ma bure 43

Ũkwenda kwĩthaa wĩra ũyũ o mũthenya? App ya Helibrain (rĩu nĩ Gĩkĩngeresa tu) ĩrĩ na gahunda ya bure na gahunda iria cia kũrĩha.

Taũra karatathi gaka: Thoma 2/3 ya Mũigana. Helibrain. 2026. https://helibrain.com/ki/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 →

Ithandĩko

  1. Nagel R (1995). Kũhũthĩra namba kũrĩ magerio ma gũthoma: kĩgerio gĩa kũrora. American Economic Review 85(5):1313–1326. www.jstor.org/stable/2950991
  2. Bosch-Domènech A, Montalvo JG, Nagel R, Satorra A (2002). Ĩmwe, igĩrĩ, (ithatũ), na ũrĩa ũtangĩrĩra, …: magerio ma marũa na lab ma kĩgerio kĩa mũndũ mwega. American Economic Review 92(5):1687–1701. doi.org/10.1257/000282802762024737 (namba kuuma thandĩko rĩa 1999: econ-papers.upf.edu/papers/438.pdf)
  3. Schou A (2005). Kĩgerio kĩa gũta namba kĩonania atĩ tũtirĩ na meciiria marĩa marĩ na ũhoti. Politiken, 22 September 2005. politiken.dk/oekonomi/art5698526
  4. Camerer CF, Ho T-H, Chong J-K (2004). Mũtugo wa cognitive hierarchy wa mĩchezo. Quarterly Journal of Economics 119(3):861–898. doi.org/10.1162/0033553041502225
  5. Quealy K (2015). Ũrĩa athomi maathire kũrĩ kĩũria kĩa namba kĩa Upshot. 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). Mĩhianano ya athiithi kũrĩ athiithi angĩ: mũhianano na ũira wa kĩgerio. Games and Economic Behavior 10(1):218–254. doi.org/10.1006/game.1995.1031

Ũrĩa tũgĩĩte ũtari ũyũ: wandĩkĩtwo nĩ andũ a Helibrain, makĩhũthĩrĩra ithomithia iria ciandĩkĩtwo igũrũ, na ũkĩretiirwo na Robert(Gĩkĩngeresa) (mũndũ ũrĩ gũthoma PhD ya biophysics) mũthenya wa 4 Mwere wa ikũmi na ũmwe 2026. Tũũcookereria rĩrĩa mĩhĩrĩga ya ũhoro yacooka gucooka.