Probability inna roulette
Evry roulette probability a jus a count a pocket divide by 37.
p = numba weh di bet cover / 37. One numba: 2.70%. Eighteen: 48.65%. Fi a set sequence, yuh multiply di probability fi each spin.
One spin
Each a di 37 pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → have di same chance, suh di chance fi win pon one spin a roulette a jus a ting yuh count. A bet pon four numba win 4/37 a di time, bout 10.8%. Nutten more nuh deh inna one-spin probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → dan dat, an a dat mek yuh can work out di whole game pon a napkin.
Nuff spin
Di spin dem independent, suh di probability fi a sequence multiply. Two redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → back to back: (18/37)² = 23.7%. Red, den zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting →: (18/37)(1/37) = 1.3%. Seventeen two time straight: (1/37)² = 0.073%, bout one outta 1,369. Di order matta fi a set sequence, but it nuh matta fi a count: “red den blackbet demBlackEven-money bet pon di 18 black numba. Inna French: noir.Read di whole ting →” a 25.0%, but “one red an one black inna two spin, any order” a 50.0%.
At least one time
Use di complement. Di chance fi get no hit pon a straight upbet demStraight upOne single numba, pay 35:1.Read di whole ting → inna 37 spin a (36/37)³⁷ = 36.3%, suh di chance fi get at least one hit a 63.7%, nuh di “sure ting” weh nuff playa expec fram 37 chance at 1 outta 37. Di same calculation seh a numba have bout a 1 outta 3 chance fi nuh show up at all inna 37 spin, an a dat mek di result board always show a few “cold” numba.
Ow long yuh can expec fi wait
Pon average a straight-up numba show up one time evry 37 spin, but di wait jump bout wild: di median wait a bout 25 spin (half di time it come sooner) an one wait outta twenty go past 110 spin. Wait time fi a geometric process have a long tail, an a playa weh “know” seh a numba due afta 60 spin a describe sumting weh happen one time outta five.
Common mistake
Fi add up probability fi ting weh can happen same time (red or odd nuh 36/37; it a 26/37, cause ten numba a both). Fi multiply fi ting pon di same spin (red an odd pon one spin a 10/37, nuh 18/37 × 18/37). Fi count di spin weh done pass as part a di sequence yuh a bet pon now: afta ten red, di chance fi a eleventh one a 18/37, nuh (18/37)¹¹.
Wah di odds dem inna roulette, an ow dem different fram probability?
Casino quote payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting → as odds. A single numba win wid probability 1/37, suh di odds fi win pon a single numba inna roulette a 36 to 1 gainst. A payout a 35 to 1 come up one unitmoney mattaUnitDi base stake weh a system or a playa work wid. Dem describe progression inna unit suh dem work at any table.Read di whole ting → short, an dat a di house edgemathsHouse edgeDi part a evry stake weh di casino keep pon average: 2.70% inna European roulette.Read di whole ting → inna it original form. Fi convert: odds gainst = (1 − p)/p; probability = 1/(odds + 1).
Formula
Question dem
(1/37)² = 1/1369 ≈ 0.073%.
36/37 = 97.3%. Zero a di res.
All 37 a 1/37. Seventeen a di numba weh people bet pon di most, an dat a sumting bout people.
Fun wid maths
Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.
Yuh bet pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting →, spin afta spin. Wah a di chance seh yuh fifth win come pon exactly di eighth spin? An dat yuh have five win inside di fus eight spin?
Show di ansa
Ansa 12.9%, bout 1 outta 8, fi di fifth win pon spin eight. 33.4% fi five win by den.
Di fifth win pon spin eight mean two ting: spin eight win, an di fus seven spin hold exactly four win an tree loss, inna any order. It have 35 way fi put four win mongst seven spin.
Suh di chance a 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%.
Fi five win by spin eight, add di same kind a term fi di fifth win pon spin five, six an seven: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%. Statistician call dis di negative binomial distribution: ow much try a fix numba a success tek. Taylor (2021) work di same question pon a American wheel, 12.2%.
Sumting fi laugh
Count di pocket. Divide by 37. Multiply fi sequence. Done.
Source dem
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.