Khai 2/3 ê pîng-kun

Tio̍h 1 ê sò͘-jī. Tsit lé-pài ta-ke chhai ê pîng-kun ê 2/3 siōng kin ê lâng to̍h siūⁿ. Bái-sài, m̄-bián tēng-kì.

Helibrain ê tiōng-tsèng ê lângTùi Robert(Ióng-bûn) kàu-kòe, seng-bu̍t li̍k-ha̍k PhD tshù-pī-seng hu-pò͘Siōng-kīn chi̍t pái kàu-kòe

Án-tsuánn khòaⁿ lí ê kiat-kó

  • Lí ê tsàn-tuānn sī khòaⁿ lí siūⁿ kàu kuí pō͘. Khai kin 50 sī tsàn-tuānn 0: bô siūⁿ kàu pa̍t-lâng ē khai siáⁿ-mi̍h. Kin 33 sī tsàn-tuānn 1: “lâng ē khai ta̍i-iok 50.” Kin 22 sī tsàn-tuānn 2: “lâng ē siūⁿ tsi̍t pō͘ tī-tsîng.” Muí tsi̍t pō͘ sī tsîng tsi̍t pō͘ ê 2/3 [1].
  • Kēng-tsuí lī-lūn ê tap-àn sī 0. Nā-sī tsuân-pō͘ lâng lóng siūⁿ kàu-té, tsuân-pō͘ ê khai-sò͘ lóng ē sió kàu 0. Si̍t-tsè ê kēng-tsiá bô lâi án-ni tsò, só͘-í 0 bô tī kong-khai pí-kài ti̍t-ti̍t tshiúⁿ-kòe [1][2].
  • Bē-sái-iūⁿ tshiúⁿ: khai kóe 66.7 to̍h bē-sái-iūⁿ tshiúⁿ, in-uī to̍k-sǹg tsuân-pō͘ lâng lóng khai 100, te̍k-pia̍t ê tiāu-tsún sī 66.7.
  • Tsit lé-pài ê tshiúⁿ-ka ē tī tsit-lūn kiat-sok ê sî tshut-hiān (muí lūn sī tsi̍t lé-pài , UTC ê pài-it kàu pài-ji̍t). Tsit-lūn bô kiat-sok tsîng, lán bô hō͘ lí khòaⁿ tio̍h si̍t-sî pîng-kun, in-uī án-ni ē phá-huī kēng. Tsit-lūn ài tsì-tsió 30 ê kēng-tsiá, tsiah ē ū kiat-kó.

Khai kuí ê sò͘-jī siōng hó?

Bô tsi̍t ê kó͘-tēng siōng hó ê sò͘-jī: ài khòaⁿ pa̍t-lâng lóng khai siáⁿ-mi̍h. Tāi-hîng ê kong-khai pí-kài, te̍k-pia̍t ê tiāu-tsún tī tāi-iok 13 kàu 22 ê tiong-kan. Financial Times ê tha̍k-tsiá pîng-kun khai 18.9, só͘-í te̍k-pia̍t ê tiāu-tsún sī 12.6 [2]. Tī Tān-bia̍t chi̍t pún pò-tsu̍t ê pí-kài, ū 19,196 ê tha̍k-tsiá, pîng-kun khai 32.4, te̍k-pia̍t sī 21.6 [3].

Thn̂g-tiâu-tô͘: sì tiûⁿ ū ho̍k-tshun ê pí-kài ê pîng-kun khai-sò͘ kap te̍k-pia̍t. Tshì-giām-kak tshù-lí 1995: pîng-kun 36.7, te̍k-pia̍t 24.5. Politiken 2005: pîng-kun 32.4, te̍k-pia̍t 21.6. Spektrum 1997: pîng-kun 22.1, te̍k-pia̍t 14.7. Financial Times 1997: pîng-kun 18.9, te̍k-pia̍t 12.6.
Tô͘ 1. Sì tiûⁿ ū ho̍k-tshun ê pí-kài ê pîng-kun khai-sò͘ kap 2/3 te̍k-pia̍t. Tsū-liāu: Nagel 1995, thâu tsi̍t lūn, 67 ê ha̍k-sing [1]; Politiken 2005, 19,196 ê tha̍k-tsiá [3]; Spektrum der Wissenschaft 1997, 2,728 ê tha̍k-tsiá, kap Financial Times 1997, 1,476 ê tha̍k-tsiá [2].

Ín-iōng chit ê bāng-ia̍h: Khai 2/3 ê pîng-kun. Helibrain. 2026. https://helibrain.com/nan/guess-two-thirds-of-the-average. CC BY 4.0.

Kóng-kài ê tsu-liāu

  • I ē hián-sī siáⁿ-mi̍h: lí tùi pa̍t-lâng ē án-tsuánn tsò, siūⁿ tī-tsîng kuí pō͘. Keng-tsè-ha̍k-ka kiò-tsò level-k siūⁿ-khó͘ [1][4].
  • Keng-tián ê si̍t-giām: tī Rosemarie Nagel 1995 nî gián-kiù ê thâu-lūn, ha̍k-sing pîng-kun khai 36.7, siōng tsuē lâng khai ê sò͘ kin 33 kap 22 [1].
  • Tāi-hîng pí-kài: 1,476 ê Financial Times tha̍k-tsiá pîng-kun khai 18.9 (tshiúⁿ ê khai-sò͘ sī 13), 19,196 ê Politiken tha̍k-tsiá pîng-kun khai 32.4 [2][3].
  • 33 ê hút-lik: tī 2015 nî New York Times ê pán-pún, ū tāi-iok 56,000 ê tha̍k-tsiá, 33 sī siōng suan-siú ê khai-sò͘ [5].
  • Tsit-ê sióng-hoat tùi tó-uī lâi: keng-tsè-ha̍k-ka John Maynard Keynes kā ku-tsiáu chhiong-pì chò͘ suí-lūi pí-kài; ài suan-siú pa̍t-lâng ē suan ê bīn-khang tsiah ē tshiúⁿ [6].

Kēng án-tsuánn tsò

  1. Suan tsi̍t ê tsíng-sò͘ tī 0 kàu 100 tiong-kan, koh kā i khǹg-tēng.
  2. Tsit lé-pài tsuân-pō͘ lâng ê khai-sò͘ tī tsit-lūn kuan-pí ê sî sǹg pîng-kun, te̍k-pia̍t ê tiāu-tsún sī pîng-kun ê 2/3.
  3. Khai siōng kin ê lâng tshiúⁿ. Nā-sī pêng-kio̍k, to̍h kap-lâng tsuân-kòng tshiúⁿ. Pài-it ê sî, ia̍h-bīn ē hián-sī kàu-lē-pài ê kēng-tsiá, pîng-kun-sò͘, te̍k-pia̍t, tshiúⁿ ê khai-sò͘, kap muí tsi̍t ê sò͘-jī hō͘ lâng khai ê tình-hêng.

Muí tsi̍t lūn, muí lâng tsi̍t ê khai-sò͘ ē kā-sǹg. Lán muí ê liām-phīⁿ-pò͘-á kap muí ê internet liân-tsuann lóng kā tsi̍t ê khai-sò͘; só͘-í kap-lâng kiong-iōng tsi̍t ê liân-tsuann ê lâng (ha̍k-hāu, kong-si, ka-tîng) tsi̍t lé-pài kā tsi̍t ê lâng. Tē-jī pái khai bô-sǹg. Lí khai liáu-āu, ia̍h-bīn tùi-sî hián-sī lí ê sò͘ tī siūⁿ-khó͘ thiⁿ-thang ê tó-uī, kap tī í-tsîng kóng ê tsai-miâ pí-kài tiong ē án-tsuánn.

Tsit-ê kēng sǹg siáⁿ-mi̍h, koh i ê lâi-gûan tī tó-uī

Keng-tsè-ha̍k-ka kiò tsit-ê kēng-tsò p-beauty contest, tī chia p = 2/3. Rosemarie Nagel tī 1995 nî hō͘ i sîng-tsò tsai-miâ ê tshì-giām-kak tshù si̍t-giām [1]. I ê kiat-kó sī: lâng bô su̍t-khó͘ kàu 0, mā bô tùi-ì khai-sò͘. Tāi-pō͘-hū lâng siūⁿ tsi̍t, nn̄g pō͘ to̍h thang: “i siūⁿ-kóng guá ē án-tsuánn siūⁿ”.

Tsit-ê sióng-hoat sī lâng tùi pa̍t-lâng ê tāng-tsok, tsí ū-hān-tō͘ ê kuì-tō͘ siūⁿ-khó͘, āu-lâi to̍h sîng-tsò level-k kap kám-tsai tsàn-lio̍k siūⁿ-khó͘ ê bûn-hêng [4][7]. Āu-lâi ê pò-tsu̍t pí-kài, muí pái lóng ū tsian-tsi̍t ê tha̍k-tsiá, mā khòaⁿ tio̍h 33 kap 22 ê tsàn-tuānn, koh ū tsi̍t tsū lâng suan 0 á-sī 1 [2].

Tsit-ê kēng ē-kàu kap bē-kàu hō͘ lí tsai siáⁿ-mi̍h

Lí ê tsàn-tuānn sī siáu-sit tī tsi̍t pái kēng ê tsi̍t ê khai-sò͘. I m̄-sī tsìng-tiōng ê tiōng-thàu, siūⁿ koh khuànn-khùi mā bô pí-kàu hó: tshiúⁿ ê sī siōng ē-tàng tsai-tsiáu tuā-tsiòng ê lâng, tuā-tsiòng pîng-siông siūⁿ tsi̍t á-sī nn̄g pō͘ to̍h thang. Tsàn-tuānn 4 ê khai-sò͘ sī khiáu-khì ê suy-lūn, m̄-koh siông-siông lóng ē tī te̍k-pia̍t ê tiāu-tsún ē-té.

Tī chia ê kēng-tsiá sī hiaⁿ-pài lâi ê lâng, m̄-sī kó͘-tēng ê iú-hūi; só͘-í te̍k-pia̍t ê tiāu-tsún muí-lē-pài lóng ē piàn. Tsai-miâ ê pí-kài ū sió-sió ê kuī-tik bô-kâng: Financial Times tsí-hún khai tsíng-sò͘, Politiken kap Spektrum tsí-hún khai sió-sò͘ [2][3].

Siông-siông ū lâng mn̄g ê tāi-tsì

Khai pîng-kun ê 2/3 ê tap-àn sī siáⁿ-mi̍h?

Khai pîng-kun ê 2/3 bô kó͘-tēng ê tap-àn. Kēng-tsuí lī-lūn kóng sī 0, in-uī muí ê kēng-tsiá lóng ū lī-iû khì khai pí pa̍t-lâng koh khah kē. M̄-koh si̍t-tsè ê lâng siūⁿ tsi̍t á-sī nn̄g pō͘ to̍h thang, só͘-í tī ū ho̍k-tshun ê pí-kài, tshiúⁿ ê sò͘ sī tī 13 kàu 21.6 tiong-kan [2][3]. Siōng hó ê khai-sò͘ sī lí khòaⁿ-khuì pa̍t-lâng pîng-kun ē khai ê sò͘-jī ê 2/3.

0 án-tsuánn bô tshiúⁿ?

Tāi-iok tsuân-pō͘ lâng lóng siūⁿ kàu-té, 0 tsiah ē tshiúⁿ. Si̍t-tsè pí-kài tiong, tsuē lâng khai 33 á-sī 22, koh ū lâng khai khah kuân ê sò͘-jī, hō͘ pîng-kun suah kuân. Tī Financial Times ê pí-kài, pîng-kun sī 18.9, te̍k-pia̍t sī 12.6, lī 0 hun kuân [2].

“level 2 siūⁿ-khó͘ ê lâng” sī siáⁿ-mi̍h ì-sù?

Level-2 siūⁿ-khó͘ ê lâng khòaⁿ-khuì pa̍t-lâng ē siūⁿ tī-tsîng tsi̍t pō͘ (in ē khai tāi-iok 33), koh i koh siūⁿ tī-tsîng tsi̍t pō͘: 33 ê 2/3 tāi-iok sī 22. Tī Helibrain kēng tiong, lí ê tsàn-tuānn sī siūⁿ-khó͘ thiⁿ-thang (50, 33, 22, 15, 10) tiong, lī lí ê khai-sò͘ siōng kin ê hia̍p [1].

Guá ē-tàng khai khah-tsuē pái bô?

Ē-sái, m̄-koh muí-lē-pài tsi̍t-lūn tsí ū sǹg lí thâu-pái khai ê sò͘. Āu-lâi ê khai-sò͘ ē hián-sī tī thiⁿ-thang, m̄-koh bô-sǹg, só͘-í bô lâng ē-tàng khai tsuē pái lâi kā kiat-kó phah-sǹg. Muí pái pài-it lóng khai-sí sin ê tsi̍t-lūn.

Helibrain 2/3 kēng chin-tsiàⁿ bô-hūi bô?

Sī. Helibrain 2/3 kēng kap muí-lē-pài ê kiat-kó lóng bô-hūi: bô-bián tēng-kì, bô-bián email, bô-bián thâu-tsînn. Helibrain tùi i ê app lâi thâu-tsînn, app ū bô-hūi ê pán-pún kap siū-tsînn ê pán-pún; bô-bián ū app mā ē-tàng kēng.

Siong-kuan ê tshì-giām

Khòaⁿ tsuân-pō͘ 43 hông-bîⁿ ê tāu-lāi tshì-giām

Nā beh ta̍k-ji̍t tsò tsit-ê? Helibrain app (hiān-tsāi iáu-koh sī Ióng-bûn) ū bô su-iàu tsînn ê kè-uē kap siu-tsînn ê kè-uē.

Ín-iōng chit ê bāng-ia̍h: Khai 2/3 ê pîng-kun. Helibrain. 2026. https://helibrain.com/nan/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 →

Tsū-liāu

  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 (sò͘-jī tùi 1999 nî ê kang-tsok bûn-kiāⁿ: 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

Tsit-ê ia̍h-mn̂g án-tsuánn tsò--ê: Helibrain ê tiōng-tsèng ê lâng kàu-kòe siōng-bīn liáu-lia̍t ê gián-kiù lâi siá, koh tùi 11/4/2026 hō͘Robert(Ióng-bûn) (seng-bu̍t li̍k-ha̍k PhD tshù-pī-seng) kàu-kòe. Tsu-liāu ū kái-kòe ê sî, guán ē kā tsit-ê ia̍h-mn̂g kái-kòe.