Giaman Tingting bilong Gembla
Bilip olsem wanpela namba o kala “i mas kam nau”, long wanem em i no bin kamap longpela taim.
Bihain long tenpela ret, sans bilong blak em i 18/37 yet. Wil i no save holim tingting long wanpela samting, na em i no gat dinau long wanpela man.
Giaman tingting
Sapos retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta → i kamap tenpela taim, planti pleia i pilim olsem blakbetBlakBet wan-long-wan long 18 namba blak. Tok Frans: noir.Ritim olgeta → “i mas kam nau”, na ol i putim bet olsem. Ol narapela i pilim olsem ret i “hat”, na ol i putim bet long en. Tupela lain i tingting long wanpela lain namba i pinis pinis, na ol i ting em i makim wanpela tanim i no kamap yet. BaltulBalLiklik bal dila i sutim long rot i go long narapela sait long rota. Ol nupela bal i ivorine o Teflon, 18–21 mm.Ritim olgeta → i no save wanem samting i kamap long tenpela tanim i go pinis; ol hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta → i gat wankain sais olsem wanpela aua i go pinis; sansmatematikSansSans bilong wanpela resal, long 0 i go 1 o 0% i go 100%. Wanpela namba: 1/37 = 2.70%.Ritim olgeta → bilong blak em i 18/37 olsem em i save stap oltaim.
Bilong wanem em i luk olsem tru
Long longpela taim, hap bilong ret na blak i kam klostu tru long 18/37 wan wan. Lo bilong planti nambamatematikLo bilong planti nambaAvarej bilong ol resal i no hangamap long narapela i kam klostu long ekspektet velyu taim namba bilong ol traim i go antap.Ritim olgeta → i tok klia long dispela. Tasol em i kam klostu long rot bilong i go daun liklik liklik insait long planti namba, i no long rot bilong stretim: bihain long 1,000 tanim moa, tenpela ret i winim em i samting liklik tru long hap bilong olgeta. Em i no long wanem blak i kisim bek, em i long wanem samting yu kaunim i kamap bikpela moa. I no gat wanpela samting i mekim blak i gat sans moa, na lo bilong planti namba i no nidim kain samting olsem.
Monte Carlo, 18 Ogas 1913
Blak i kamap 26 taim long lain long wanpela tebol long Casino de Monte-Carlo. Klostu long namba fiftin blak, ol pleia i pulap long putim bet long ret, ol i dabelim na dabelim gen, na ol i ting olgeta tanim i “klia moa” long tanim bipo. Kasino i winim planti milion frank. Ran i gat sans 1 long 137 milion long namba wan blak, na sans olsem em bai kamap long wanpela taim long wanpela hap long ol kasino bilong graun em i klostu wan tru. Olsem na giaman tingting bilong gembla i gat narapela nem: giaman tingting bilong Monte Carlo.
Samting nating. Em i save kamap wanpela taim long 44.
Ol pleia i stat long luksave. Ret “i mas kam nau”.
Tebol i pulap long manmeri. Ol i dabelim mani bilong bet long ret bihain long olgeta lus.
Ol bikpela mani i lus. Olgeta nupela blak i mekim ol i pilim olsem ret i klia moa.
Ran i pinis. Kasino i winim planti milion frank long ol manmeri i putim bet i birua long wanpela ran i no inap “save” olsem em i ran.
Han i hat
Sapos yu putim bet long wanpela kala long wanem em i stap long ran, em i wankain rong, tasol i go baksait: yu ting ran bai i go yet, i no pinis. Ol saveman bilong tingting i kolim han i hattingting i no truHan i hatBilip olsem planti win, o planti wankain resal, i mekim narapela i ken kamap moa. Long wil, em i giaman tingting bilong gembla i tanim i go baksait.Ritim olgeta →. Nem i kam long wanpela stadi bilong Gilovich, Vallone na Tversky long 1985. Ol i painim ol ran long sutim bal long basketbal, na ol i no painim wanpela ran i winim sans tasol. Long 2018, Miller na Sanjurjo i soim olsem tes yet i bin slip i go long wanpela sait: long sotpela rekot, hap bilong ol sut i go insait stret bihain long wanpela sut i go insait i save daun liklik long avarej bilong man, olsem na man i no gat han i hat i luk olsem han bilong em i kol liklik. Taim ol i stretim, wankain namba i soim liklik han i hat. Man inap kamap hat; wil i no gat pasin olsem. Sampela pleia i holim tupela bilip wantaim: ran bai i go yet inap em i “longpela tumas”, na bihain em i pinis. Long stretpela wil, olgeta kain i gat wankain ekspektet velyumatematikEkspektet velyuAvarej resal long wanpela bet long longpela taim. −1/37 bilong mani bilong bet long olgeta bet olpasin bilong Yurop.Ritim olgeta → olsem yu makim kala long tromoi koin: −2.70% bilong mani bilong bet.
Long tebol tru
Croson na Sundali (2005) i lukim 18 aua vidio bilong sekiuriti long wanpela tebol i gat dabel sirowilSiroWanpela grinpela hul we i no gat bet wan-long-wan, dosen o kolam i karamapim; em i as bilong edj bilong kasino. Narapela nem: wanpela siro, 0.Ritim olgeta → long wanpela bikpela kasino long Reno: 139 pleia i putim 24,131 bet. Long ol bet wan-long-wanbetBet wan-long-wanRet/blak, od/iven, antap/daunbilo. 18 namba, pe em i 1:1.Ritim olgeta →, hap bilong ol pleia i bihainim ol sotpela ran na hap i go birua long ol. Bihain long faivpela wankain long lain, ol i go moa long birua long ran, na bihain long sikispela o moa, 85% bilong ol bet bilong ol i stap long narapela sait. Wankain pleia i soim han i hat long ol yet: bihain long win long ol namba, ol i karamapim 13.6 namba long tanim bihain long avarej, na 9.2 bihain long lus. Wil bilong ol i no soim wanpela mak bilong bias, olsem na i no gat wanpela bilong ol dispela samting i senisim samting ol inap wetim.
Ausait long kasino
Dispela kain pasin i kamap tu long ples we ol man i makim ol samting tru. Clotfelter na Cook (1993) i bihainim pilai bilong namba long olgeta de long Maryland: mani ol i putim long wanpela namba i go daun kwik tru taim namba i kamap, na i kisim planti mun long kamap gen olsem bipo, maski pilai i no save holim tingting. Chen, Moskowitz na Shue (2016) i painim dispela long ol man i save gut long wok. Ol jas bilong ol man i askim long stap long Amerika, sans bilong ol long tok nogat long wanpela kot i go antap inap 3.3 pesen poin sapos ol i bin tok yes long kot bipo. Ol ampaia bilong besbal, sans bilong ol long kolim strike i daun 1.5 poin bihain long ol i kolim wanpela, na i winim tupela taim long ol tromoi i klostu klostu. Long wanpela traim long wok tru wantaim ol ofisa bilong givim dinau ol i kisim wankain pe, inap 9% bilong ol tingting ol i makim i senis long dispela rot. Ol kot i kam long oda i rendom, olsem na tingting bipo i no tokaut long wanpela samting long narapela, wankain olsem tanim bipo i no tokaut long wanpela samting long tanim bihain.
Giaman tingting i go baksait
Saveman bilong tingting Ian Hacking (1987) i givim nem long namba tri kain. Wanpela man i go insait long rum, em i lukim tupela dais i pundaun long dabel sikis, na em i ting ol i mas tromoi planti taim pinis. Olgeta tromoi i gat wankain sans long kamap dabel sikis, namba wan long nait o namba wan tausen, olsem na dispela samting em i lukim i no tokaut long hamas taim pilai i bin go. Long rulet, em i pleia i kamap long bod i soim eitpela ret na i ting tebol i mas tanim inap planti aua pinis bilong kamapim ol. Giaman tingting nating i putim samting i go pinis long tanim bihain; dispela i putim wanpela samting i no save kamap planti long taim i go pinis we i no gat man i lukim.
Wanpela saveman bilong tingting i bilipim
Sampela saveman i bin sapotim dispela giaman tingting. Saveman bilong tingting bilong Jemani, Karl Marbe, i lukluk long fopela buk bilong raitim ol pikinini i bon, na wan wan i gat 49,152. Em i painim olsem ran i longpela moa bilong ol pikinini man o pikinini meri long lain em i 17. Em i ting ol longpela ran i no save kamap planti olsem sans i tok, olsem na wanpela ran i mekim narapela samting i gat sans moa. Sans tasol i tok narapela kain: long 196,608 pikinini i bon, ran bilong 17 o moa i save kamap klostu fopela taim long faivpela. Marbe i painim stret pasin bilong lain namba i rendom. Epstein (2013) i stori gen long dispela; “Sans bilong Ol Ran” i givim stori bilong rulet.
Ples we giaman tingting i no stap
Sapos wil i gat bias tru long bodi bilong en, ol tanim i go pinis bai givim save, long wanem ol bai soim samting long ol hul na i no long gutpela luk. Em i wok bilong Laboratori, na em i nidim planti tausen tanim long wanpela wil yu save long en bilong tokaut long wanpela samting. Long ran bilong tenpela ret long wil yu no save long en, bias i no gat sans olsem sans nating.
Ol askim
Nogat. Em i stap long olgeta samting i kamap planti taim na i no hangamap long narapela: dais, koin, ol namba bilong lotari.
Ol hap bilong tupela bai i kam klostu. Tasol samting i kamap long yu bai i stap klostu −2.70% bilong mani yu betim.
I no gat lo bilong avarej. I gat lo bilong planti namba, na em i wok long rot bilong i go daun liklik liklik insait long planti namba.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Bihain long 10 tromoi, wanpela koin i soim 7 het na 3 tel. Bihain long 1,000 tromoi, em i soim 517 het na 483 tel. Ol tel i kam bihain na kisim ol het?
Soim bekim
Bekim Nogat. Namel long tupela i kamap bikpela long 4 i go long 34. Hevi bilong tupela tasol (ratio) i kam klostu long wankain.
Ratio bilong het long tel i pundaun long 7/3, klostu 2.33, i go long 517/483, klostu 1.07. Em lo bilong planti nambamatematikLo bilong planti nambaAvarej bilong ol resal i no hangamap long narapela i kam klostu long ekspektet velyu taim namba bilong ol traim i go antap.Ritim olgeta → i wok.
Namel long tupela i kamap bikpela, long 4 i go long 34. Wantaim stretpela koin, namel bilong klostu 30 bihain long 1,000 tromoi em i samting nating: namel oltaim i kamap bikpela klostu wantaim skwea rut bilong namba bilong tromoi, na ratio i go isi isi long 1.
Nogat samting i pulim ol tel i kam bek. Ol het i planti long stat i kamap liklik long 990 tromoi i kam bihain, ol i no stretim.
Tromoi koin fopela taim na lukim tasol ol tromoi i kam stret bihain long het. Wanem hap bilong ol em het? Wokim long olgeta 16 lain inap kamap na kisim avarej bilong ol hap. Em 50%?
Soim bekim
Bekim Nogat. Em 17/42, klostu 40.5%. Taim yu lukim olsem, stretpela koin i luk olsem em i kamap kol bihain long het.
Raitim 16 lain. Tupela bilong ol, TTTT na TTTH, i nogat het long tripela tromoi bilong stat, olsem na nogat samting i bihainim het; dispela i lusim 14.
Long olgeta wan wan, kisim ol tromoi i bihainim het na painim hap em het. HHHH i givim 3 long 3. HHHT i givim 2 long 3. HTHT i givim 0 long 2. Taim yu go long olgeta 14: sikispela lain i givim 0, fopela i givim 1/2, wanpela i givim 2/3 na tripela i givim 1 (HHHH, THHH na TTHH).
Putim ol hap wantaim: 4 × 1/2 + 2/3 + 3 = 17/3. Skelim long 14: 17/42 ≈ 40.5%.
Nogat tromoi i laikim tel; olgeta em 50–50. Dispela i kam long pasin bilong kisim avarej lain long lain: lain i pulap long het i gat planti tromoi bilong lukim tasol i kaunim wanpela taim, wankain olsem lain i gat wanpela het tasol. Miller na Sanjurjo (2018) i soim olsem stadi bilong han i hat long 1985 i bin mesarim ol pleia bilong basketbol long dispela rot, olsem na ol pleia i luk olsem ol i no gat ran moa long sans tru tru i bin gat ran liklik moa.
Liklik lap
I go daun liklik liklik, i no stretim. Wil i no gat dinau long wanpela man.
Ol As bilong Save
- 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.”