Lay-lay tɔk: rulɛt stratɛji we de win ɔltɛm
“A gɛt sistɛm we de win 80% pan di tɛm.” Sɔntɛm yu gɛt am. I stil de lɔs mɔni.
Sistɛm kin mek sɛshɔn we win kam bɔku tɛm. I nɔ go ebul mek di valyu we fɔ ɛkspɛkt pozitiv, bikɔs ɛni bɛt we i put na −1/37 pan in bɛt mɔni, ɛn valyu dɛn we fɔ ɛkspɛkt de ad. Di sistɛm dɛn we de win mɔs tɛm de lɔs pas ɔl we dɛn lɔs.
Wetin dɛn se
Di bilif: sɔmsay, rulɛt stratɛji de we de win ɔltɛm, sistɛm fɔ chenj bɛt mɔni we fala di rizɔlt dɛn we dɔn pas, we de tɔn rulɛt to gem we yu de win. Di pruf we dɛn gi: sɛshɔn dɛn we win wan afta di ɔda, vidio bɔt aw fɔ win na rulɛt ɛnitɛm, pɔsin we tɔk se i wok, sprɛdshit fɔ wan wik we gɛt lɔk. Bɔku tɛm di pɔsin nɔ de lay; i bilif am bikɔs i bin de wok.
Wetin mek i rɔng, insay wan lain
Valyu dɛn we fɔ ɛkspɛktmatematiksValyu we fɔ ɛkspɛktDi avrej rizɔlt fɔ ɛni bɛt if yu ple lɔng tɛm. −1/37 fɔ di bɛt mɔni fɔ ɛni nɔmal Yuropian bɛt.Rid ɔl → de ad. If ɛni bɛt gɛt EV = −1/37 pan in bɛt mɔni, ɛni sikwɛns fɔ bɛt gɛt EV = −1/37 pan ɔl di mɔni we yu bɛt, ɛni rul we pik di bɛt mɔni. Sistɛm na rul fɔ pik bɛt mɔni. So ɛni sistɛm gɛt EV = −1/37 pan ɔl di mɔni we yu bɛtmɔniƆl di bɛt mɔniƆl di mɔni we yu bɛt na wan sɛshɔn ɔ wan tɛm, wit di win mɔni we yu bɛt bak. Dɛn kin kɔl am bak: handle, action.Rid ɔl →. Dis na tiɔrɛm (Doob ɛn Halmos pruv am na di 1930 dɛn; Thorp 1969 se di kɔndishɔn dɛn), ɛn i nɔ gɛt ɛksɛpshɔn fɔ rul we sabi. Di wan kɔndishɔn we fayn fɔ no na smɔl limit fɔ bɛt: Thorp in ɛgzampul bɛt $1,000 pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →, dɔn 90 sɛnt, dɔn 9 sɛnt ɛn so so, i de smɔl go ɔltɛm. Wit chans 18/37, di fɔs bɛt win ɛn di pleya de ɔp fɔ ɔltɛm, pan ɔl we di rizɔlt we fɔ ɛkspɛkt stil na −1/37 pan ɔl wetin dɛn bɛt. Rial tebul in smɔl limit de stɔp dat, ɛn wit am ɛni op fɔ de ɔp if yu ple lɔng tɛm.
Wetin de apin if yu ple lɔng tɛm: di lɔ fɔ big nɔmba na rulɛt
Wetin mek i de luk lɛk se i de wok
Nɛgativ 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 → de mek sɛshɔn we win kam bɔku tɛm. MartingalestratɛjiMartingalePrɔgrɛshɔn we de dɔbul di bɛt afta ɛni lɔs. Luk di Stratɛji pat fɔ si wetin i de du ɛn wetin i nɔ de du.Rid ɔl → frɔm $10 wit $500 limit de ɛnd lɛk 80% pan sɛshɔn fɔ 100 spin wit sɔm yunitmɔniYunitDi bes bɛt mɔni we sistɛm ɔ pleya de wok wit. Dɛn de ɛksplen prɔgrɛshɔn wit yunit so dat i go wok na ɛni tebul.Rid ɔl → ɔp. Pleya we rɔn am fɔ twɛnti sɛshɔn de win sikstin pan dɛn ɛn i mɛmba dat. Ɛni wan pan di fɔ sɛshɔn we lɔs de lɔs pas wetin tɛn sɛshɔn we win de mek, ɛn di kalkulashɔn pan twɛnti sɛshɔn na lɔs. Di sistɛm nɔ chenj di avrej; i jɔs muf di lɔs dɛn go insay smɔl sɛshɔn we big pas, usay i izi fɔ kɔl am bad lɔk.
Di tɛst we ɛnibɔdi kin rɔn
Di Stratɛji Simulɛta pan dis sayt de rɔn 10,000 sɛshɔn fɔ ɛni sistɛm, ɔ yu yon kod, insay wan sɛkɔn. Sɛt am to di sistɛm we yu bilif ɛn rid di avrej. If di avrej bin pozitiv fɔ ɛni sɛtin, dis pej go se so. Ɛni sɛtin, ɛni sistɛm, ɛni tebul limittebulTebul limitDi smɔl ɛn di big bɛt we dɛn alaw. Na di big limit de stɔp prɔgrɛshɔn dɛn we de dɔbul.Rid ɔl → de gi avrej fɔ −2.70% pan ɔl di bɛt mɔni plɔs nɔys. Wetin pɔsin tɔk na sampul fɔ wan; di simulɛta na sampul fɔ tɛn tawzin.
Sistɛm we nɔ go ebul lɔs
Na 1997, di poka rayta Mike Caro put rulɛt sistɛm ɔnlayn fɔ jok, ɛn Gambling Times pablish am bak na 2001. Na list fɔ bɛt we yu fɔ avɔyd: nɔ ɛva rɛd ɔ blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, ɔd ɔ ivin, ɔ 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; nɔ rɛd nɔmba we ɔd ɛn nɔ blak nɔmba we ivin; ɛn natin pan 30, ɔ pan di lɔng lain fɔ pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → frɔm 11 we yu go di we klɔk de tɔn rawnd to 14 pan di Amɛrikan wil. Put di rul dɛn togɛda ɛn nɔ nɔmba nɔ lɛf. Di wan pɔkit dɛn we de na do da lain de na 0, 28, 9, 26, 30 ɛn 2; dɛn ban 30 bay in nem, ɛn di res na ziro, ivin ɛn blak, ɔ ɔd ɛn rɛd. Pleya we fala di sistɛm nɔ de ɛva bɛt ɛn i nɔ de ɛva lɔs. In ɛj na ziro, ɛn na di wan rulɛt sistɛm we tɔk tru bɔt aw i de rich de.
Sistɛm dɛn we gɛt nem, wan lain fɔ ɛni wan
Sistɛm dɛn we dɛn sɛl wit nem, ɔ as rulɛt fɔmula fɔ win, nɔ difrɛn. Ɛni wan na sɛt fɔ bɛt, ɛn ɛni bɛt de pe di wil in 2.70%. Bollman (2024) wok tru sɔm pan dɛn fɔ Amɛrikan wil, usay ɛni wan de kɔst 5.26%; ya, wi gɛt dɛn pan Yuropian wil.
Di vashɔn we tɔk tru
Sistɛm dɛn de chenj di shep fɔ sɛshɔn: ɔmɔs tɛm yu de win, aw di win dɛn big, aw di wɔs tin bad. Dɛn na rial chɔys, ɛn pleya kin lɛk wan shep pas di ɔda. Wetin sistɛm dɛn nɔ de chenj na di prays, we na 2.70% pan ɔl wetin yu bɛt, ɛn bikɔs prɔgrɛshɔn dɛn de bɛt pas fɔ bɛt di sem mɔni ɔltɛmstratɛjiBɛt di sem mɔni ɔltɛmFɔ bɛt di sem mɔni ɛni spin. Na dis ɛni prɔgrɛshɔn de kɔmpia wit.Rid ɔl →, dɛn de pe mɔ pan am.
Kwɛstyɔn dɛn
Siks mɔnt fɔ sɛshɔn ɛni wik na lɛk 25 sɛshɔn. Martingale de win 80% pan dɛn. Di sɛshɔn dɛn we lɔs de kam, ɛn dɛn big pas.
Di rul fɔ stɔp de mek ɔl di mɔni we yu bɛt smɔl, so i de mek di lɔs we fɔ ɛkspɛktmatematiksLɔs we fɔ ɛkspɛktValyu we fɔ ɛkspɛkt tɛm ɔl di mɔni we yu bɛt; di avrej mɔni we yu de lɔs insay wan sɛshɔn ɔ wan tɛm.Rid ɔl → smɔl. I nɔ de mek am pozitiv.
Nɔto pan fɛr wil. Pan wil we gɛt bayaslabWil we gɛt bayasWil we gɛt pɔblɛm na in bɔdi we mek sɔm pɔkit kin kam pas 1/37. I nɔ kɔmɔn, ɛn yu kin fɛn am nɔmɔ wit tawzin tawzin spin we yu dɔn rayt dɔn.Rid ɔl →, we na fizyks prɔblɛm, nɔto sistɛm.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Mike Caro in jok sistɛm fɔ di Amɛrikan wil na 1997 de ban rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → ɛn blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, ɔd ɛn ivin, ɛn 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; ɔd rɛd nɔmba ɛn ivin blak wan dɛn; di nɔmba 30; ɛn ɛni pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → na di pat frɔm 11, di we klɔk de tɔn, raund to 14. Yuz di rul dɛn wan bay wan. Wish nɔmba dɛn lɛf fɔ bɛt?
Sho di ansa
Ansa Natin nɔ lɛf. Di sistɛm nɔ ɛva bɛt, so in advantej na ɛgzakt ziro.
If yu ban rɛd, blak, ɔd, ivin ɛn di ziro dɛn, na jɔs wan-wan nɔmba ɛn smɔl grup dɛn pan 1 to 36 lɛf.
Nɔ ɔd rɛd ɛn nɔ ivin blak de lɛf di ivin rɛd dɛn (12, 14, 16, 18, 30, 32, 34, 36) ɛn di ɔd blak dɛn (11, 13, 15, 17, 29, 31, 33, 35): sikstin nɔmba. If yu ban 30, fiftin lɛf.
Pan di Amɛrikan wil, di pat frɔm 11, di we klɔk de tɔn, to 14 de kɔba 32 pan di 38 pɔkit. Di siks we de atsay am na 0, 28, 9, 26, 30 ɛn 2. Ɔl di fiftin we lɛf de insay di pat, so di las rul de pul dɛn bak. Sistɛm we nɔ ɛva bɛt na di wangren wan we nɔ ɛva lɔs, ɛn na dat Caro bin want sho.
Kryptos de rɔn tri MartingalestratɛjiMartingalePrɔgrɛshɔn we de dɔbul di bɛt afta ɛni lɔs. Luk di Stratɛji pat fɔ si wetin i de du ɛn wetin i nɔ de du.Rid ɔl → di sem tɛm, wan pan ɛni pia fɔ ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl → (ay ɔ lɔ, ɔd ɔ ivin, rɛd ɔ blak), wit bɛt mɔni 1, 2, 4, 8, 16, 32 ɛn stɔp afta siks lɔs. Tek wan pan di tri pan Yuropian wil. Ɔmɔs tɛm i de lɔs ɔl siks bɛt, wetin wan saykul de mek pan avrej, ɛn wetin na dat pan di mɔni we yu bɛt?
Sho di ansa
Ansa I de lɔs ɔl siks lɛk wan tɛm pan 55 saykul, 1.83% pan di tɛm, ɛn dat de kɔst 63 yunitmɔniYunitDi bes bɛt mɔni we sistɛm ɔ pleya de wok wit. Dɛn de ɛksplen prɔgrɛshɔn wit yunit so dat i go wok na ɛni tebul.Rid ɔl →. Pan avrej wan saykul de lɔs lɛk 0.17 yunit pan 6.42 yunit we yu bɛt: 2.70%, di prays fɔ ɛni bɛt pan di wil.
Bɛt de lɔs wit chans 19/37, wit di ziro insay. Siks wan afta di ɔda: (19/37)⁶ = 0.0183, lɛk 1 pan 55, ɛn dɔn di bɛt mɔni 1 + 2 + 4 + 8 + 16 + 32 = 63 dɔn go. If nɔto dat, di saykul de ɛnd wit win ɛn +1 yunit.
Avrej: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = −0.17 yunit.
Mɔni we yu bɛt: yu ɔltɛm put di fɔs bɛt, di sɛkɔn wan jɔs afta lɔs, ɛn so so: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = 6.42 yunit. Ɛn −0.17/6.42 = −2.70%.
Di siks spin we dɛn rayt jɔs de disayd wish sayd ɛni bɛt de, ɛn di wil nɔ fit no dɛn. If yu rɔn ɔl tri, di mɔni we yu bɛt de tɔn tri tɛm, ɛn di avrej lɔs de tɔn tri tɛm bak. Bollman (2024) wok di sistɛm pan Amɛrikan wil, usay ɛni wan pan dɛn de lɔs siks wan afta di ɔda 2.1% pan di tɛm.
Smɔl jok fɔ ɛz di maynd
Fɔ win bɔku tɛm ɛn fɔ win mɔni na difrɛn nɔmba.
Usay wi gɛt am frɔm
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.