Di prɔbabiliti fɔ strik na rulɛt
Lɔng strik fɔ wan kɔla kɔmɔn. Bɔt dɛn nɔ min natin fɔ di nɛks spin.
Fayv rɛd wan afta di ɔda: 2.7%. Tɛn: 0.074%. Na sɛshɔn we gɛt 200 spin, strik fɔ siks pan wan kɔla de kam mɔ tɛm pas we i nɔ kam.
Ɔmɔs tɛm lɔs strik kin kam
Ivin-mɔni bɛt pan wil wit wan ziro de lɔs 19 spin pan 37. Ɛni lain na di chans se ɔl di spin dɛn insay wan strik go lɔs, ɛn wetin Martingale pleya, we de dɔbul afta ɛni lɔs, dɔn lɔs bay da tɛm de.
| lɔs wan afta di ɔda | chans | lɛk 1 pan | wetin yu dɔn lɔs te naw | nɛks bɛt |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Di chans na 19/37 we yu mɔltiplay bay insɛf wan tɛm fɔ ɛni lɔs, frɔm wan spin we yu pik. Lɔng sɛshɔn gɛt bɔku spin usay dis kayn strik kin bigin, so insay wan ivintɛm i izi fɔ apin pas aw wan lain de sho.
Wan strik
Di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → se di nɛks k spin go ɔl bi rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → na (18/37)ᵏ. Tu: 23.7%. Fayv: 2.7%. Tɛn: 0.074%, lɛk 1 na 1,350. Twɛnti: 1 na 1.8 milyɔn. Twɛnti siks, di Monte Carlo rɛkɔd: 1 na 137 milyɔn. Dɛn ya na di prɔbabiliti fɔ wan patikula strik we bigin pan wan patikula spin. Na kwɛstyɔn we ɔlmɔs nɔbɔdi rili de aks.
Na wan sɛshɔn
Di kwɛstyɔn we pipul rili min na “strik fɔ k go kam sɔmsay na mi sɛshɔn?” Di ansa big pas (18/37)ᵏ bad bad wan, bikɔs sɛshɔn we gɛt 200 spin gi ɔlmɔs 200 ples usay strik kin bigin. Strik fɔ siks ɔ mɔ pan di sem kɔla, rɛd ɔ blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, de kam na sɛshɔn we gɛt 200 spin lɛk 94% fɔ di tɛm; et ɔ mɔ lɛk 47%; tɛn ɔ mɔ lɛk 14%. If yu nem di kɔla bifo, di chans dɛn go dɔŋ to lɛk 75%, 27% ɛn 7%. Pleya we sidɔm fɔ wan ivintɛm go si lɔng strik ɛni ivintɛm.
Wetin mek Martingale de wɔri bɔt am
Ɛni prɔgrɛshɔnstratɛjiPrɔgrɛshɔnƐni rul we de chenj di bɛt mɔni bay di rizɔlt dɛn we dɔn pas. Nɛgativ prɔgrɛshɔn de es am afta lɔs, pɔzitiv wan afta win.Rid ɔl → we de ad mɔni afta lɔs gɛt wan strik lɛnt we de brok am: siks lɔs frɔm $10 bigin bɛt wit $500 limit, tɛn fɔ FibonaccistratɛjiFibonacciPrɔgrɛshɔn we de fala di sikwɛns 1, 1, 2, 3, 5, 8, 13…: wan stɛp bifo afta yu lɔs, tu stɛp bak afta yu win.Rid ɔl →, fayv if yu de mɔltipay bay tri pan dɔzinbɛtDɔzin1–12, 13–24 ɔ 25–36, i de pe 2:1.Rid ɔl →. Di prɔbabiliti fɔ lɔs strik fɔ siks pan ivin-mɔni na (19/37)⁶ ≈ 1.8% fɔ ɛni tray, ɛn sɛshɔn we gɛt 200 spin kin gɛt lɛk 100 tray. So di brok de kam na lɛk fɔ sɛshɔn na fayv we gɛt da lɛnt de. Di prɔbabiliti fɔ strik na rulɛt na di tin we mek di kliff nɔ rɛr.
Ɔt ɛn kol nɔmba
Di sem kalkul de wok fɔ bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl →. Na 300 spin, ɔmɔs tɛm yu fɔ ɛkspɛkt fɔ ɛni nɔmba na 8.1; di standad diviyeshɔnmatematiksStandad diviyeshɔnDi skwɛ rut fɔ varians; di nɔmal distans bitwin wan rizɔlt ɛn di valyu we fɔ ɛkspɛkt.Rid ɔl → na lɛk 2.8. Sɔm nɔmba go kam 15 tɛm ɛn sɔm 2 tɛm jɔs bay chans, ɛni tɛm. Rizɔlt bɔd we de sho “ɔt” nɔmba de sho di tɔp pat fɔ nɔmal distribyushɔn. Di Lab de ɛksplen ɔmɔs spin i de tek bifo ɔt nɔmbalay-lay tɔkƆt nɔmbaNɔmba we dɔn kam mɔ pas aw yu ɛkspɛkt nɔ te. Pan fɛr wil, i nɔ de tɛl yu natin bɔt wetin de kam.Rid ɔl → min ɛni tin (tawzin tawzin, frɔm wan wil we yu no).
Fɔ nɔ dipen na di ɔl tin
Strik fɔ tɛn rɛd nɔ de mek blak gɛt mɔ chans, ɛn i nɔ de mek rɛd gɛt mɔ chans bak. Di tu na 18/37. Strik na tin we rakpa sikwens gɛt, ɛn if dɛn nɔ de, dat fɔ mek pɔsin sɔspɛkt. Sikwens fɔ 200 spin we nɔ gɛt strik we lɔng pas fɔ go bi pruf se pɔsin dɔn tamba wit am, pas wan we gɛt strik fɔ twɛlv.
Fɔmula
Kwɛstyɔn dɛn
26 blak na Monte Carlo pan 18 Ɔgɔst 1913 na di wan we pipul no. Dɛn bin ripɔt 32 rɛd wan afta di ɔda na wan Amɛrikan kasino na 1943. Di tu dɛn gri wit chans, if yu tink bɔt ɔmɔs spin kasino dɛn de rɔn.
I na 18/37 ɛni we. Bɛt wetin yu plan se, ɔ nɔ bɛt natin.
Nɔ. Bayas de sho we sɔm pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → de kam mɔ tɛm afta tawzin tawzin spin, nɔto lɛk strik fɔ wan kɔla.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Ɔmɔs spin pan Yuropian wil i de tek, pan avrej, bifo ɔl di 37 nɔmba dɔn kam pan di list wan tɛm ɔ mɔ?
Sho di ansa
Ansa Lɛk 155 spin pan avrej; di midul valyu na 147.
Kɔnt di wet wan nyu nɔmba bay wan nyu nɔmba. Di fɔs spin ɔltɛm de sho nyu nɔmba. We yu dɔn si 1 nɔmba, 36 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → insay 37 na nyu wan, so di nɛks nyu nɔmba de tek 37/36 spin pan avrej. We yu dɔn si k nɔmba, i de tek 37/(37 − k).
Ad di wet dɛn: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 spin.
Di pat we big pas na di ɛnd. Di las nɔmba wan de tek 37 spin pan avrej, ɛn di las fayv de tek lɛk 85. Pan Amɛrikan wil di sem kɔnt de gi lɛk 161. Dis na di prɔblɛm we dɛn kɔl “coupon collector”; di sem avrej de kɔmɔt frɔm di nɔmal kalkuleshɔn.
Insay 37 spin pan Yuropian wil, wan spin fɔ ɛni pɔkit, ɔmɔs difrɛn nɔmba yu fɔ ɛkspɛkt fɔ si?
Sho di ansa
Ansa Lɛk 23.6. Lɛk wan tɔd pan di nɔmba dɛn, lɛk 13, nɔ de kam atɔl.
Tek wan nɔmba, lɛk 17. Pan ɛni spin di chans we i nɔ go kam na 36/37, so di chans we i go mis ɔl 37 spin na (36/37)³⁷ ≈ 0.363.
Ɛni nɔmba gɛt di sem chans, so pan avrej 37 × 0.363 ≈ 13.4 nɔmba nɔ de kam ɛn 37 − 13.4 ≈ 23.6 de kam, ɛn bɔku pan dɛn de kam tu tɛm ɔ mɔ.
Rulɛt pleya dɛn kɔl dis “di lɔ fɔ tɔd”. I nɔto lɔ, na jɔs di kɔnt fɔ nɔmba we de kam bak: insay strik we lɔng lɛk di wil, lɛk wan tɔd pan di nɔmba dɛn de sidɔm nɔ kam, pan fɛr wil lɛk pan ɛni ɔda wan. Pan 38 pɔkit di pat na (37/38)³⁸ ≈ 0.363 bak; fɔ big wil i de sɛtul nia 1/e ≈ 0.368.
Yu padi sho yu tu list we gɛt 50 kɔla, rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → ɔ blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, ɛn i se ɔl tu kɔmɔt frɔm wil we dɛn nɔ kɔnt di 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 → dɛn. Wan de chenj kɔla 25 tɛm ɛn in strik we lɔng pas na siks. Di ɔda wan de chenj 35 tɛm ɛn i nɔ ɛva pas tri. Wish wan na mek-mek?
Sho di ansa
Ansa Di sɛkɔn wan. Rial list de chenj lɛk 24 ɔ 25 tɛm. List we chenj 35 tɛm de kam lɛk wan tɛm insay 500 list, ɛn list we nɔ gɛt strik we lɔng pas tri de kam lɛk tu tɛm insay 100.
Ɛni nyu kɔla de ripit di las wan ɔ i de chenj, af ɛn af, so 49 chans fɔ chenj de gi 24.5 chenj pan avrej, mɔ ɔ lɛs lɛk 3.5. Tati-fayv na tri pan dɛn stɛp de ɔp di avrej; fɛr wil de mek dat ɔmɔs chenj lɛk wan tɛm insay 500 list.
Di strik dɛn de tɔk di sem tin. Rial list fɔ 50 gɛt strik fɔ fɔ ɔ mɔ lɛk 98% pan di tɛm, ɛn in strik we lɔng pas, bɔku tɛm, na fayv ɔ siks.
Pipul we yu aks fɔ mek list we na chans nɔmɔ de chenj tumɔs, bikɔs strik fɔ fɔ ɔ fayv de luk lɛk patɛn to dɛn. Taylor (2021) sho di sem sayn insay list fɔ kɔyn we stiudɛnt dɛn mek-mek: rial chans gɛt mɔ strik pas wetin pipul de ɛkspɛkt.
Wan buk fɔ kasino stori dɛn tɔk bɔt pleya we in nɔmba kam fayv tɛm wan afta di ɔda, ɛn i kɔl am rɛkɔd. Aw dat rial rial pan Yuropian wil? Ɛn ɔmɔs tɛm i fɔ apin sɔmsay insay wan kasino we gɛt 20 tebul, ɛn ɛni wan de spin 40 tɛm pan awa, de ɛn nɛt?
Sho di ansa
Ansa Wan nɔmba we yu dɔn nem, fayv tɛm wan afta di ɔda: 1 insay 69 milyɔn. Ɛni nɔmba we kam fɔ tɛm mɔ afta i fɔs kam: 1 insay 1.87 milyɔn. Da kasino de spin lɛk 7 milyɔn tɛm pan ia, so i fɔ si strik fɔ fayv tri ɔ fɔ tɛm pan ia.
Nɔmba we yu dɔn nem gɛt chans 1/37 fɔ kam pan ɛni spin, so fayv wan afta di ɔda gɛt chans (1/37)⁵ = 1 insay 69,343,957. Bɔt nɔbɔdi nɔ de nem di nɔmba bifo. Ɛni nɔmba we fɔs kam, di nɛks fɔ spin fɔ ripit am: (1/37)⁴ = 1 insay 1,874,161.
20 tebul × 40 spin × 24 awa × 365 de = 7,008,000 spin pan ia. Ɛni spin kin bigin strik, so di kasino fɔ ɛkspɛkt 7,008,000/1,874,161 ≈ 3.7 strik fɔ fayv pan ia.
Nɔ ɔfishal rɛkɔd fɔ dis kayn tin nɔ de, ɛn wi nɔ nid am: tin we nɔ kin apin pan wan tebul na nɔmal tin we yu kɔnt ɔl di kasino, ɛn di stori dɛn de tɔk bɔt di tebul usay i apin. Di stori, insay Goldman (2007), apin pan wil wit dɔbul ziro, usay di nɔmba dɛn na 1 insay 79 milyɔn ɛn 1 insay 2.09 milyɔn.
Smɔl jok fɔ ɛz di maynd
Lɔng strik na aw rakpa tin de luk.
Usay wi gɛt am frɔm
- 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.