Masalo: Laba Dersin iyo Chip
Laba dersin waxay daboolaan 24 lambar. Ku dar chip eberka waxaad daboolaysaa 25. Caymisku ma bixiyaa?

Maya. Qayb kastaa waa −2.70% sharadkeeda, sidaas darteed isku-darku waa −2.70% wadarta. Masaladu waxay sharraxaysaa sababta, waxay xisaabisaa qaybinta saxda ah, waxayna muujinaysaa waxa isbeddela (qaabka) iyo waxa aan isbeddelin (qiimaha).
Masalada
Waxaad sharadsataa $10 dersinkasharadDersin1–12, 13–24 ama 25–36, wuxuu bixiyaa 2:1.Akhri dhammaan → koowaad, $10 dersinka labaad iyo $1 eberkagiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan →. (a) Waa maxay natiijooyinka suurtagalka ah iyo itimaalkooda? (b) Waa maxay qiimaha la filayoxisaabQiimaha la filayoCelceliska natiijada sharad kasta muddada dheer. −1/37 ee sharadka sharad kasta oo Yurub caadi ah.Akhri dhammaan →? (c) Chip-kalacagChipCalaamad u taagan qadar go'an, oo la dul dhigo shaxda sharadka si sharad loo sameeyo. Sidoo kale: check.Akhri dhammaan → eberku ma hagaajiyaa sharadka?
Xalka (a) iyo (b)
Natiijooyinka: kubbaddaqalabKubbadKubbadda yar ee lagu tuuro jidka iyada oo ka soo horjeedda rotor-ka. Kubbadaha casriga ah waa ivorine ama Teflon, 18–21 mm.Akhri dhammaan → 1–24 (24 godqalabGodMid ka mid ah 37-ka qol ee lambarrada leh ee rotor-ka. Sidoo kale: slot, cup.Akhri dhammaan →): hal dersin wuxuu bixiyaa $20, kan kale wuxuu khasaaraa $10, eberku wuxuu khasaaraa $1: saafi +$9. Kubbadda 25–36 (12 god): labada dersinba way khasaaraan, eberkuna wuu khasaaraa: −$21. Kubbadda eberka (1 god): dersinnadu waxay khasaaraan $20, eberku wuxuu bixiyaa $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 wareeggii $21 oo la sharadsaday: 2.70%.
Xalka (c)
Chip-ka eberka la'aantiis: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54 $20 oo la sharadsaday, sidoo kale 2.70%. Chip-ka eberku wuxuu natiijada eberka ee −$20 u beddelay +$15 (horumar $35 ah hal jeer 37 kiiba, oo u dhiganta $0.95 wareeggii) wuxuuna ku kacay $1 36-ka wareeg ee kale (oo u dhiganta $0.97 wareeggii). Isbeddelka saafiga ah: −$0.03 wareeggii, taasoo ah 2.70% doollarka dheeraadka ah. Caymiska waxaa loo qiimeeyay si sax ah sida wax kasta oo kale.
Sababta ay tani u guud tahay
Qiimayaasha la filayo way isku darmaan. Koox kasta oo sharadyo isku mar ah waxay leedahay EV la mid ah wadarta EV-yada qaybaha, mid kastaana waa −1/37 sharadkiisa. Sidaas darteed isku-dar kastaa waa −1/37 wadarta sharadka. Ma jiro habayn chips ah oo shaxda sharadkaqalabShaxda sharadkaShaxda sharadka ee daabacan ee miiska. Sidoo kale: table, felt, cloth.Akhri dhammaan → ah, intay doonaan ha le'ekaadeene, oo ka baxsada tan; qalabka Dhisaha Sharadka ayaa xaqiijin doona koox kasta oo aad dhigi karto. Waxa isku-darradu beddelaan waa qaybinta: inta jeer ee aad guulaysato, inta ay le'eg tahay, iyo inta ay xun tahay xaaladda ugu xun.
Su'aal xigta oo ka adag
Hel isku-dar sharadyo caadi ah oo daboola dhammaan 37-ka lambar. Saddex dersin ($10 mid kasta) iyo $1 eberka: mid kasta oo 1–36 ah saafigiisu waa −$1 (hal dersin wuxuu bixiyaa $20, labada kale waxay khasaaraan $20, eberku wuxuu khasaaraa $1), eberkuna saafigiisu waa +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 $31 oo la sharadsaday: 2.70%. Waxaad dammaanad qaadi kartaa inaadan weligaa la yaabin, weli waxaad bixinaysaa isla qiimaha mudnaantaas.
Qaacido
Su'aalo
Maya, miis Yurub ah. Miis Faransiis ah, sharadyada lacag isle'eg ahsharadSharad lacag isle'eg ahCasaan/madow, kisi/dhaban, sare/hoose. 18 lambar, wuxuu bixiyaa 1:1.Akhri dhammaan → keligood waa 1.35%; ku darista wax kale waxay kor u qaadaysaa faa'iidada isku-dhafan.
Wuxuu khasaaraa $1 $1 kasta eberka oo keliya, waxbana kuma guulaysto marka kale. EV −2.70% iyadoo aan faa'iido jirin: isku-darka keliya ee gebi ahaanba aan macno lahayn.
Si aad u doorato qaab fadhi oo aad ku raaxaysato. Taasi waa sabab sharci ah, waana tan keliya.
Kaftan yar

Caymiska miiska roulette wuxuu ku kacaa si sax ah inta uu badbaadiyo.
Ilaha
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.