Gambula in mistek
Di bilif se wan rizɔlt “fɔ kam” bikɔs i nɔ kam fɔ sɔm tɛm.
Afta tɛn rɛd, di prɔbabiliti fɔ blak stil na 18/37. Di wil nɔ de kip rɛkɔd ɛn i nɔ de ɔwɔ ɛnibɔdi natin.
Di mistek
If rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → dɔn kam tɛn tɛm, bɔku pleya de fil se blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl → “fɔ kam”, ɛn dɛn de bɛt pan am. Ɔda wan dɛn de fil se rɛd “ɔt”, ɛn dɛn de bɛt pan dat. Di tu dɛn de tink frɔm sikwens we dɔn dɔn, to spin we nɔ apin yet. Di bɔlikwipmɛntBɔlDi smɔl bɔl we dɛn trowe na di rod agens di rotɔ. Di nyu bɔl dɛn na ivorine ɔ Teflon, 18–21 mm.Rid ɔl → nɔ no wetin di las tɛn spin bin bi; di pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → dɛn big di sem we dɛn bin big wan awa bifo; di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → fɔ blak na 18/37, lɛk aw i bin de ɔltɛm.
Wetin mek i de fil lɛk tru
If yu ple lɔng tɛm, di pat fɔ rɛd ɛn blak de kam nia 18/37 ɛni wan. Di lɔ fɔ big nɔmbamatematiksLɔ fɔ big nɔmbaDi avrej fɔ rizɔlt dɛn we nɔ dipen pan wan ɔda de go nia di valyu we fɔ ɛkspɛkt as di nɔmba fɔ tray de bɔku.Rid ɔl → de mek shɔ fɔ dat. Bɔt i de apin bikɔs di nɔmba dɛn de dilyut, nɔto bikɔs sɔntin de kɔrɛkt am. Afta 1,000 spin mɔ, di tɛn ɛkstra rɛd na smɔl tin na di pat, nɔto bikɔs blak dɔn ech, bɔt bikɔs di sampul dɔn gro. Natin nɔ de we de mek blak gɛt mɔ chans, ɛn di lɔ fɔ big nɔmba nɔ nid ɛni tin lɛk dat.
Monte Carlo, 18 Ɔgɔst 1913
Blak bin kam 26 tɛm wan afta di ɔda pan wan tebul na di Casino de Monte-Carlo. Frɔm lɛk di fiftin blak, pleya dɛn bin rɔsh fɔ bɛt pan rɛd. Dɛn bin de dɔbul ɛn dɔbul bak, ɛn ɛni spin bin de fil “mɔ shɔ” pas di wan bifo. Di kasino bin win milyɔn milyɔn frank. Frɔm di fɔs blak, di strik bin gɛt prɔbabiliti 1 na 137 milyɔn, ɛn di prɔbabiliti se i go apin wan de sɔmsay na di wɔl in kasino dɛn bin ɔlmɔs na wan. Na dat mek dɛn kin kɔl di gambula in mistek bak di Monte Carlo mistek.
Natin spɛshal. I de apin wan tɛm na 44.
Pleya dɛn bigin fɔ notis. Rɛd “fɔ kam”.
Di tebul ful. Dɛn de dɔbul di bɛt mɔni pan rɛd afta ɛni lɔs.
Pipul dɔn lɔs big big mɔni. Ɛni nyu blak de mek rɛd fil mɔ shɔ.
Di strik dɔn. Di kasino dɔn win milyɔn milyɔn frank frɔm pipul we bin de bɛt agens strik we nɔ bin ebul “no” se i na strik.
Di ɔt an
Fɔ bɛt pan wan kɔla bikɔs i de pan strik na di sem mistek, we tɔn bak: yu de ɛkspɛkt se di strik go kɔntinyu, nɔto se i go dɔn. Saykɔlɔjist dɛn kɔl am di ɔt anlay-lay tɔkƆt anDi bilif se if yu win bɔku tɛm wan afta di ɔda, ɔ if wan rizɔlt kam bɔku tɛm, ɔda wan go mɔ kam. Na di wil, na gambula in mistek we tɔn ɔp-said-dɔŋ.Rid ɔl →, frɔm wan stɔdi na 1985 bay Gilovich, Vallone ɛn Tversky. Dɛn bin luk fɔ strik we pipul de shut na basketbɔl, ɛn dɛn nɔ fɛn natin pas chans. Na 2018, Miller ɛn Sanjurjo bin sho se di tɛst insɛf bin bɛnt: na shɔt rɛkɔd, di pat fɔ shɔt we de go insay rayt afta wan we go insay de kam lɔ pas di shuta in ol rɛt pan avrej. So pleya we nɔ gɛt ɔt an atɔl de luk smɔl kol. We dɛn kɔrɛkt am, di sem data de sho smɔl ɔt an. Pɔsin kin wam ɔp; wil nɔ gɛt fɔm fɔ de insay. Sɔm pleya de bilif di tu tin di sem tɛm: se strik de kɔntinyu te i “tu lɔng”, ɛn dɔn i de dɔn. Pan fɛr wil, ɛni wan pan dɛn gɛt di sem valyu we fɔ ɛkspɛktmatematiksValyu we fɔ ɛkspɛktDi avrej rizɔlt fɔ ɛni bɛt if yu ple lɔng tɛm. −1/37 fɔ di bɛt mɔni fɔ ɛni nɔmal Yuropian bɛt.Rid ɔl → lɛk fɔ pik kɔla bay we yu trowe kɔpɔ: −2.70% fɔ di bɛt mɔni.
Na rial tebul
Croson ɛn Sundali (2005) bin wach 18 awa sikyuriti vidio frɔm wan dɔbul-zirowilZiroDi wan grin pɔkit we nɔ ivin-mɔni, dɔzin ɔ kɔlɔm bɛt nɔ kɔba; na usay di kasino advantej kɔmɔt. Dɛn kin kɔl am bak: wan ziro, 0.Rid ɔl → tebul na wan big kasino na Reno: 139 pleya we put 24,131 bɛt. Pan di ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl →, di pleya dɛn bin ɔlmɔs sheb ivin: sɔm de fala shɔt strik, sɔm de go agens dɛn. Afta fayv di sem kayn wan afta di ɔda, dɛn bin lin agens di strik, ɛn afta siks ɔ mɔ, 85% fɔ dɛn bɛt bin de pan di ɔda say. Di sem pleya dɛn bin sho di ɔt an bɔt dɛnsɛf: afta dɛn win pan di nɔmba dɛn, dɛn bin kɔba 13.6 nɔmba pan di nɛks spin pan avrej, agens 9.2 afta lɔs. Dɛn wil nɔ bin sho ɛni sayn fɔ bayas, so natin pan ɔl dis nɔ bin chenj wetin ɛni wan pan dɛn kin ɛkspɛkt.
Atsay di kasino
Di sem pul de sho usay pipul de mek rial disizhɔn. Clotfelter ɛn Cook (1993) bin fala Maryland in de-bay-de nɔmba gem: di mɔni we pipul bɛt pan wan nɔmba bin fɔdɔm kwik kwik we dɛn pul am, ɛn i bin tek mɔnt dɛn fɔ kam bak, pan ɔl we di pul nɔ gɛt mɛmori. Chen, Moskowitz ɛn Shue (2016) bin fɛn am wit pipul we sabi dɛn wok. Jɔj dɛn fɔ asaylɔm na Amɛrika bin gɛt te to 3.3 pasɛntej pɔynt mɔ chans fɔ se nɔ to wan kes if dɛn bin se yɛs to di wan bifo. Ɔmpaya dɛn na bezbɔl bin gɛt 1.5 pɔynt lɛs chans fɔ kɔl strayk afta dɛn kɔl wan, ɛn mɔ pas tu tɛm dat pan pich dɛn we kam klos. Na wan ɛkspirimɛnt wit lon ɔfisa dɛn we dɛn pe di sem fi, te to 9% fɔ di disizhɔn dɛn bin tɔn bak dis we. Di kes dɛn bin kam ɛni kayn we, so di las disizhɔn nɔ bin tɛl natin bɔt di nɛks wan, jɔs lɛk aw di las spin nɔ de tɛl natin bɔt di nɛks wan.
Di gambula in mistek we tɔn bak
Di filɔsɔfa Ian Hacking (1987) bin gi nem to wan tɔd kayn. Pɔsin waka go insay rum, i si tu dayz fɔdɔm dɔbul siks, ɛn i se dɛn fɔ dɔn trowe dɛn bɔku tɛm bifo. Ɛni trowe gɛt di sem chans fɔ bi dɔbul siks, di fɔs wan fɔ di ivintɛm ɔ di wan tawzin wan, so wetin i si nɔ de tɛl natin bɔt aw lɔng di gem dɔn de go. Na rulɛt, na di pleya we kam rich bɔd we de sho et rɛd ɛn i se di tebul fɔ dɔn de spin fɔ awa ɛn awa fɔ mek dat. Di nɔmal mistek de rid di tɛm we dɔn pas insay di nɛks spin; dis wan de rid tin we nɔ kɔmɔn insay tɛm we dɔn pas we nɔbɔdi nɔ si.
Saykɔlɔjist we bin bilif am
Lan pipul dɔn difɛn di mistek bifo. Di Jamani saykɔlɔjist Karl Marbe bin go tru fɔ rɛjista, ɛni wan wit 49,152 bɔn. I fɛn se di strik we lɔng pas ɔl fɔ bɔy ɔ fɔ gyal wan afta di ɔda na 17, ɛn i se lɔng strik rɛr pas wetin chans alaw, so strik de mek di ɔda rizɔlt gɛt mɔ chans. Chans nɔmɔ de se difrɛn: na 196,608 bɔn, strik fɔ 17 ɔ mɔ de kam lɛk fɔ tɛm na fayv. Marbe bin fɛn rayt rayt wetin rakpa sikwens de luk lɛk. Epstein (2013) de tɛl di kes bak; “Di prɔbabiliti fɔ strik na rulɛt” de gi di rulɛt kayn.
Usay di mistek nɔ de wok
If di wil bin gɛt bayas fɔ fizik, di spin dɛn we dɔn pas go gɛt infɔmeshɔn, bikɔs dɛn go bi pruf bɔt di pɔkit dɛn ɛn nɔto bɔt lɔk. Dat na di Lab in tɔpik, ɛn yu nid tawzin tawzin spin frɔm wan wil we yu no bifo yu kin tɔk ɛni tin. Fɔ strik fɔ tɛn rɛd pan wil we yu nɔ no, di bayas ɛksplen gɛt lɛs chans bad bad wan pas di chans ɛksplen.
Kwɛstyɔn dɛn
Nɔ. I de wok fɔ ɛni tin we de apin bak bak ɛn nɔ de dipen pan wan ɔda: dayz, kɔpɔ, lɔtri nɔmba.
Di pat dɛn go kam nia. Yu rizɔlt go stil bi lɛk −2.70% fɔ wetin yu bɛt.
Lɔ fɔ avrej nɔ de. Lɔ fɔ big nɔmba de, ɛn i de wok bay dilyushɔn.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Afta 10 tɔs, wan kɔyn sho 7 ed ɛn 3 tel. Afta 1,000 tɔs i sho 517 ed ɛn 483 tel. Di tel dɛn dɔn kach ɔp?
Sho di ansa
Ansa Nɔ. Di gap gro frɔm 4 to 34. Na jɔs di reshyo kam nia ikwal.
Di reshyo fɔ ed to tel fɔdɔm frɔm 7/3, lɛk 2.33, to 517/483, lɛk 1.07. Dat na di lɔ fɔ big nɔmbamatematiksLɔ fɔ big nɔmbaDi avrej fɔ rizɔlt dɛn we nɔ dipen pan wan ɔda de go nia di valyu we fɔ ɛkspɛkt as di nɔmba fɔ tray de bɔku.Rid ɔl → de wok.
Di gap bitwin dɛn gro, frɔm 4 to 34. Wit fɛr kɔyn, gap fɔ lɛk 30 afta 1,000 tɔs na nɔmal tin: di yuzhual gap de gro lɛk di skwɛ rut fɔ ɔmɔs tɔs, we di reshyo de sɛtul to 1.
Natin nɔ pul di tel dɛn bak. Di ɛkstra ed dɛn we kam fɔs, na di nɛks 990 tɔs dilyut dɛn; natin nɔ kɔrɛkt dɛn.
Tɔs wan kɔyn fɔ tɛm ɛn luk jɔs di tɔs dɛn we kam rayt afta ed. Wetin na di pat pan dɛn we na ed? Wok am fɔ ɛni wan pan di 16 sikwɛns we fit kam ɛn tek di avrej fɔ di pat dɛn. Na 50%?
Sho di ansa
Ansa Nɔ. Na 17/42, lɛk 40.5%. If yu luk am dis we, fɛr kɔyn tan lɛk se i de kol afta ed.
Lis di 16 sikwɛns. Tu pan dɛn, TTTT ɛn TTTH, nɔ gɛt ed pan di fɔs tri tɔs, so natin nɔ de fala ed; dat lɛf 14.
Pan ɛni wan, tek di tɔs dɛn we fala ed ɛn fɛn di pat we na ed. HHHH de gi 3 pan 3. HHHT de gi 2 pan 3. HTHT de gi 0 pan 2. If yu go tru ɔl 14: siks sikwɛns de gi 0, fɔ de gi 1/2, wan de gi 2/3 ɛn tri de gi 1 (HHHH, THHH ɛn TTHH).
Ad di pat dɛn: 4 × 1/2 + 2/3 + 3 = 17/3. Divayd bay 14: 17/42 ≈ 40.5%.
Nɔ tɔs nɔ de fayvɔ tel; ɛni wan na 50–50. Di tilt de kɔmɔt frɔm we yu tek avrej sikwɛns bay sikwɛns: sikwɛns we ful wit ed gɛt bɔku tɔs fɔ luk, bɔt i kɔnt jɔs wan tɛm, di sem lɛk sikwɛns we gɛt jɔs wan. Miller ɛn Sanjurjo (2018) sho se di 1985 stɔdi bɔt ɔt an bin mɛzhɔ in baskɛtbɔl pleya dɛn dis we, so pleya dɛn we tan lɛk se dɛn nɔ gɛt strik pas chans bin rili gɛt smɔl mɔ strik.
Smɔl jok fɔ ɛz di maynd
Dilyushɔn, nɔto kɔrɛkshɔn. Di wil nɔ de ɔwɔ natin.
Usay wi gɛt am frɔm
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Croson, R. & Sundali, J. “The gambler’s fallacy and the hot hand: empirical data from casinos.”
- Chen, D. L., Moskowitz, T. J. & Shue, K. “Decision making under the gambler’s fallacy: evidence from asylum judges, loan officers, and baseball umpires.”
- Clotfelter, C. T. & Cook, P. J. “The ‘gambler’s fallacy’ in lottery play.”
- Gilovich, T., Vallone, R. & Tversky, A. “The hot hand in basketball: on the misperception of random sequences.”
- Miller, J. B. & Sanjurjo, A. “Surprised by the hot hand fallacy? A truth in the law of small numbers.”
- Hacking, I. “The inverse gambler’s fallacy: the argument from design. The anthropic principle applied to Wheeler universes.”