Blaise Pascal: roulette ntwahonan ho tetesɛm

Akontaabufoɔ no

Blaise Pascal yɛɛ nkontaabu afidie a ɛyɛ adwuma ne nkyɛn bere a na wadi mfeɛ dunkron, ɔkyerɛɛ projective geometry mu nsɛm bere a na ɔyɛ abrantɛ, ɔyɛɛ nhyɛsoɔ ne baabi a hwee nni mu ho fapem adwuma, na wɔ 1654 mu, wɔ nkrataa a ɔne Pierre de Fermat kyerɛɛ mu no, ɔbuaa “nkyekyɛmu asɛmmisa” (problem of points) no: sɛdeɛ wɔbɛkyɛ sika a wɔde ato agorɔ a ɛgyinaeɛ ntɛm mu no pɛpɛɛpɛ. Wɔn mmuaeɛ no, sɛ wɔnkyɛ no sɛdeɛ agorɔfoɔ biara hokwanakontaabuHokwanHokwan a biribi bɛba, firi 0 kɔsi 1 anaa 0% kɔsi 100%. Nɔma baako: 1/37 = 2.70%.Kenkan ne nyinaa → a anka ɔbɛdi nkonim sɛ agorɔ no kɔɔ so a, ne boɔ a wɔhwɛ kwanakontaabuBoɔ a wɔhwɛ kwanNsunsuansoɔ mfinimfini boɔ wɔ bɛt biara so wɔ bere tenten mu. Bɛt sika no −1/37 wɔ Yuropu bɛt biara a ɛyɛ daa deɛ so.Kenkan ne nyinaa → no fiase. EV nkontaabu biara a ɛwɔ saa wɛbsaet yi so fi saa nkrataa no mu.

Blaise Pascal roulette afidie bi wɔ hɔ anaa?

Wɔ 1650 mfeɛ no mfinimfini no, Pascal yɛɛ afidie a ɛkɔ so daa ho adwuma, na wɔka sɛ ɔyɛɛ ntwahonan bi a ne mu duru kari pɛ a ɛkyinii bere tenten a ɛnnom biribiara. Asɛm a ɛka sɛ saa ntwahonan yi na ɛbɛyɛɛ roulette rotornneɛma a wɔde diRotorNtwahonan no fa a ɛkyini a ntokuru no wɔ so.Kenkan ne nyinaa → no, abakɔsɛm nwoma pii ka bio, nanso fiase nkrataa no mu biara nkyerɛ. Ɛbetumi aba sɛ nsuo hyeɛ nkuro mu kasino wuranom wɔ afeha a ɛtɔ so 18 mu de saa din no tuu adwuma no ho dawuro. Nanso nhwehwɛmu dan no rennye nto mu wɔ adansedie a ɛwɔ hɔ no so.

Hokwan, wɔ ne kasa ne yɛn kasa mu

Nkrataa a ɛfiri 1654 no mmɔ roulette din, ɛfiri sɛ na ɛmmaa ase. Wɔbisa sɛ: agorɔfoɔ mmienu hia nkyerɛnneɛ mmiɛnsa na wɔadi sika kuo bi so nkonim; wɔgyina 2–1; ɛkwan bɛn so na ɛsɛ sɛ wɔkyɛ sika no? Pascal mmuaeɛ no de deɛ ɛnnɛ yɛfrɛ no conditional expectation ne nkyerɛkyerɛmu a ɛsan ba ne ho so a ɛsiane kɔ akwan a agorɔ no betumi afa so nyinaa mu na edi dwuma. Huygens kenkanee nkrataa no na wɔ 1657 mu ɔtintim nwoma a edi kan a ɛkyerɛkyerɛ deɛ wɔhwɛ kwan ho. Asɛmfua “expectation” no yɛ ne deɛ.

Bɛt kɛseɛ no

Pascal nkyerɛkyerɛmu a agye din sene biara a ɛfa bɛt ho no, ɛnfa roulette ho na mmom ɛfa Onyankopɔn ho: “bɛt” a ɛwɔ Pensées mu a ɛde gyidie to hɔ sɛ bɛt a n'akatua nni awieeɛ. Ɛyɛ boɔ a wɔhwɛ kwan ho nkyerɛkyerɛmu, na ɛhɔ na obiara de gyinaeɛ ho nimdeɛ (decision theory) dii dwuma kan de kyerɛɛ biribi. Roulette agorɔfoɔ a wɔbɔ Pascal din wɔ ntwahonan no ho no, wɔbɔ Pascal a ɛnyɛ no din; deɛ ɛho hia ne deɛ ɔkyerɛɛ sɛdeɛ wɔbu sika agorɔ bi boɔ no.

Nwanwa a ɛwɔ mu

Sɛ Pascal na ɔyɛɛ roulette ntwahonan a edi kan anaa ɛnyɛ ɔno a, agorɔ no yɛ ne nokorɛ adwuma no ho nhwɛsoɔ pa: afidie bi a ɛfiri onipa a ɔkyerɛɛ sɛ worentumi nnya biribi kwa (afidie a ɛkɔ so daa nyɛ adwuma; deɛ wɔhwɛ kwan no nsesa) hɔ, a wɔde kyerɛ saa asɛm korɔ no ara agorɔfoɔ ɔpepem kakra afe biara.

Nsɛmmisa