Denja fɔ lɔs ɔl
Di prɔbabiliti se yu go lɔs ɔl yu gambul mɔni bifo yu rich yu tagɛt.
Fɔ ivin-mɔni bɛt, denja fɔ lɔs ɔl de fala di gambula in ruin fɔmula. Wit $500 gambul mɔni, $10 bɛt ɛn $600 tagɛt, yu de rich di tagɛt lɛk 57% fɔ di tɛm, ɛn yu de lɔs ɔl di ɔda tɛm.
Di kwɛstyɔn
Yu gɛt a 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 → fɔ gambul mɔnimɔniGambul mɔniƆl di mɔni we yu dɔn put asay fɔ ple. Fɔ manej yu gambul mɔni min fɔ disayd ɔmɔs pan am yu go risk fɔ ɛni bɛt ɛn fɔ ɛni sɛshɔn.Rid ɔl → ɛn yu want rich a + b yunit. Yu de bɛt wan yunit wan tɛm pan ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl → wit prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → fɔ win p = 18/37 ɛn prɔbabiliti fɔ lɔs q = 19/37. Wetin na di chans se yu go rich di tagɛt bifo yu rich ziro? Pascal, Fermat ɛn Huygens bin wok di ansa na di 1650 dɛn, ɛn i na wan pan di rizɔlt dɛn we ol pas ɔl na prɔbabiliti.
Di gambula in ruin fɔmula
P(rich tagɛt) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Denja fɔ lɔs ɔlmatematiksDenja fɔ lɔs ɔlDi prɔbabiliti fɔ lɔs ɔl yu gambul mɔni bifo yu rich yu tagɛt ɔ di nɔmba fɔ spin.Rid ɔl → na wan mayn dat. Wit q/p = 19/18 ≈ 1.0556, di rɛshio de gro ɛkspɔnɛnshal wit di nɔmba fɔ yunit, so di fɔmula de pɔnish smɔl yunit bad bad wan: di mɔ bɛt we yu nid fɔ rich di tagɛt, di mɔ tɛm yu de pe di 2.70% tol pan di rod.
Aw fɔ rid am
Smɔl yunit de mek yu wahala. Fɔ tray fɔ dɔbul $500 wit $10 bɛt de wok 6% fɔ di tɛm; wit wan $500 bɛt nɔmɔ i de wok 48.6% fɔ di tɛm. Fɔ ple wit bɔt at, wit lɛs bɛt we big pas, de gi yu di bɛst chans fɔ rich tagɛt na gem we gɛt nɛgativ ɛkspɛkteshɔn, bikɔs i de mek di advantej kam pan yu fyu tɛm. I de mek di variansmatematiksVariansWan mɛzhɔ fɔ aw di rizɔlt dɛn sprɛd rawnd di valyu we fɔ ɛkspɛkt. I ay fɔ bɛt pan wan nɔmba, i lɔ fɔ ivin-mɔni bɛt.Rid ɔl → fɔ wetin go apin to yu big pas ɔl bak, ɛn i de dɔn di ivintɛm kwik. Di tiorɛm nem “fɔ ple wit bɔt at na di bɛst”, ɛn Dubins ɛn Savage bin pruv am na 1965.
Usay di prɔblɛm bigin
Di kwɛstyɔn ol pas rulɛt. Na 1656, Pascal bin gi Fermat wan pazul: tu pleya de trowe tri dayz, ɛni wan bigin wit 12 kawnta; if di trowe na 11, wan kawnta de muv wan we, if na 14, i de muv di ɔda we. Di tu dɛn bin sɔlv am, ɛn Huygens, we bin yɛri bɔt am tru wan leta frɔm di matematishian Pierre de Carcavi, bin print am na 1657 lɛk di fayv prɔblɛm na di fɔs buk bɔt prɔbabiliti, wit di ansa bɔt nɔ pruf. Ilɛvin kin kam na 27 we ɛn fɔtin na 15 we nɔmɔ, so ɛni kawnta de muv go di fɔs pleya in say 9 tɛm na 14. Di fɔmula ɔp ya, wit 12 kawnta fɔ ɛni wan, de mek am gɛt lɛk 1,157 tɛm mɔ chans fɔ win ɔl pas fɔ lɔs ɔl. 2.70% advantej smɔl pas dat bad bad wan, bɔt di sem fɔmula de sho wetin i de du afta bɔku bɛt.
Rial bɛt wit bɔt at
Na Epril 2004, Ashley Revell, wan yɔŋ Inglish man, bin sɛl ɔlmɔs ɔl wetin i gɛt, ivin in klos, ɛn i tek $135,300 go na di Plaza na Las Vegas. Afta sɔm smɔl bɛt, i put di ɔl mɔni pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →, wan tɛm. Di bɔlikwipmɛntBɔlDi smɔl bɔl we dɛn trowe na di rod agens di rotɔ. Di nyu bɔl dɛn na ivorine ɔ Teflon, 18–21 mm.Rid ɔl → fɔdɔm pan rɛd 7 ɛn i kɔmɔt wit $270,600. Pan dɔbul-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 → wil, da wan spin de bin na 47.37% chans ɛn i bin kɔst am $7,121 pan avrej, di 5.26% advantej pan wan bɛt. If i bin sheb am pan $10 bɛt, di sem tagɛt fɔ ɔlmɔs nɔ gɛt op. Fɔ ple wit bɔt at nɔ de mek di bɛt gud; i de mek am shɔt as i kin bi.
Denja fɔ lɔs ɔl we yu nɔ gɛt tagɛt
If yu jɔs ple te yu lɔs ɔl ɔ yu stɔp afta N spin, di kwɛstyɔn tɔn to “wetin na di chans se mi gambul mɔni go tɔch ziro insay N spin?”. Fɔmula we klos nɔ de fɔ ɛni N, bɔt di simulɛta dɛn pan dis sayt de kalkul am: $500 gambul mɔni wit $10 pan rɛd ɔlmɔs nɔ de lɔs ɔl na 100 spin (ɔnda 1%), i de lɔs ɔl lɛk 9% fɔ di tɛm na 500 spin, ɛn lɛk 95% fɔ di tɛm na 5,000. If yu nɔ gɛt rul fɔ stɔp, di prɔbabiliti de go to 100%. Dat na di kasino advantejmatematiksKasino advantejDi pat pan ɛni bɛt mɔni we di kasino de kip pan avrej: 2.70% na Yuropian rulɛt.Rid ɔl → if yu ple lɔng tɛm.
- p10 −$500
- p25 −$500
- midul valyu −$500
- p75 +$0
- p90 +$350
Wetin de apin if yu ple lɔng tɛm: di lɔ fɔ big nɔmba na rulɛt
Aw lɔng, ɛn aw fa yu kin go bifo
Tu ɔda ol rizɔlt de ansa kwɛstyɔn we pleya rili de aks. If yu nɔ gɛt tagɛt, ivin-mɔni bɛt wit di sem mɔni ɔltɛm de las pan avrej 37 spin fɔ ɛni yunit fɔ gambul mɔni pan Yuropian wil ɛn 19 pan Amɛrikan wil, bikɔs ɛni spin de tek 1/37 fɔ yunit pan avrej (1/19 pan Amɛrikan wil): 100 yunit de las 3,700 spin pan avrej, pan ɔl we af fɔ dɛn sɛshɔn ya de dɔn insay 3,134 (luk “Aw di sɛshɔn lɔng ɛn ɔmɔs i de kɔst”). Ɛn ilɛk aw di gambul mɔni big, di chans pan Yuropian wil fɔ ɛva de k yunit bifo na (18/19)ᵏ. Dat na 95% fɔ wan yunit ɛn 58% fɔ tɛn, bɔt nɔ gambul mɔni, ilɛk aw i dip, nɔ de gi fifti-fifti chans fɔ ɛva de 13 yunit bifo; pan Amɛrikan wil di chans na (9/10)ᵏ ɛn i de go ɔnda af na 7 yunit.
Aw di sɛshɔn lɔng ɛn ɔmɔs i de kɔstAmɛrikan rulɛt wil ɛn rul dɛn
Gambul mɔni fɔ fifti-fifti chans
Tɔn di kwɛstyɔn rawnd: ɔmɔs yu fɔ kam wit fɔ gɛt fifti-fifti chans ɔ mɔ fɔ win wan mɔni bifo yu lɔs ɔl? Fɔ smɔl win, nɔto bɔku. Fɔ big wan, di gambul mɔni we yu nid de go ɔp kwik kwik, ɛn afta wan pɔynt nɔ gambul mɔni nɔ de nɔf, bikɔs ivin wan we nɔ de dɔn de gi lɛs pas fifti-fifti chans fɔ ɛva go so fa bifo. Taylor (2021) de tɔk am ɔda we: pan Amɛrikan wil, fɔ gɛt fifti-fifti chans fɔ rich 100 yunit, yu fɔ bigin wit 94, ɛn yu de put 94 na denja fɔ win 6. Pan Yuropian wil yu go nid 88.
Di lɛsin fɔ yuz
Disayd wetin yu de tray fɔ du. If di gol na wan patikula win, bɛt big ɛn fyu. If di gol na lɔng ivintɛm, bɛt smɔl ɛn gri se di advantej go tek in 2.70% frɔm bɔku 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 →. If di gol na di tu, wan go gi we, ɛn bɔku tɛm na di tagɛt.
Fɔmula
Kwɛstyɔn dɛn
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 → de mek am smɔl fɔ shɔt sɛshɔn ɛn i de mek am big bad bad wan fɔ lɔng wan. 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 → wit big yunit na di ɔnɛs we fɔ mek am smɔl.
Di fɔmula ɔp ya na fɔ ivin-mɔni. Fɔ bɛt we gɛt ay varians, fɔ lɔs ɔl de apin mɔ wit smɔl bɛt mɔni, ɛn yu de rich di tagɛt wit big big jɔmp; yuz di kalkuleta.
Ɛni stɛp go to di tagɛt gɛt smɔl lɛs chans pas ɛni stɛp go to lɔs ɔl; di rɛshio de mɔltipay pan ɔl di stɛp dɛn.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Yu gɛt $100 ɛn yu want $1,000, ɛn yu de bɛt ɔnli pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →. Plan wan: bɛt $1 ɛni tɛm. Plan tu: bɛt ɔl wetin yu gɛt te yu pas $500, dɔn bɛt jɔs wetin yu nid fɔ rich $1,000. Wish plan bɛtɛ, ɛn bay ɔmɔs?
Sho di ansa
Ansa Plan tu, fa fa. I de rich $1,000 lɛk 9.0% pan di tɛm, nia di fɛr 10%. Plan wan de wok lɛk 7 tɛm insay 10²².
Insay fɛr gemmatematiksFɛr gemGem usay nɔbɔdi nɔ gɛt advantej: ɛni bɛt gɛt valyu we fɔ ɛkspɛkt we na ziro.Rid ɔl → yu go rich $1,000 frɔm $100 wan tɛm insay tɛn, ilɛk wetin yu du, bikɔs di avrej valyu fɔ yu mɔni de stay na $100.
Di advantej de tek 2.70% pan ɛni bɛt, so di smɔl we yu bɛt pan ɔl, na di nia yu de stay to wan insay tɛn. Plan tu de dɔn di tin insay smɔl bɛt: $100 tɔn $200, $400, $800, ɛn dɔn $200 dɔn du. I de wok lɛk 9.0% pan di tɛm. Plan wan de tek tawzin tawzin bɛt bifo di waka dɔn, ɛn di advantej, we smɔl pan ɛni wan, de ad ɔp te i nia fɔ shɔ se yu go lɔs ɔl.
Dis na di Dubins–Savage rizɔlt in we we izi pas (Epstein, 2013): insay gem we de fayv di kasino, bɛt ɔmɔs yu nid, bɔt fiu tɛm as yu ebul.
Yu gɛt $500 ɛn yu want $1,000, ɛn yu go stɔp jɔs we yu gɛt am. Yu pik wan kayn bɛt ɛn yu ripit am te i win wan tɛm ɔ di mɔni dɔn. Wish kayn de gi di bɛst chans?
Sho di ansa
Ansa Wan $500 bɛt pan rɛd: 48.6%. Ɛni plan we de sprɛd di mɔni pan smɔl bɛt de du wɔs.
Pik ɛni bɛt mɔni so dat wan win dɔn du: $30 pan bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → de win $1,050, $60 pan splitbɛtSplitTu nɔmba we de nia wan ɔda, i de pe 17:1.Rid ɔl → de win $1,020, ɛn so so. Dɔn kɔnt di chans we wan bɛt go win bifo di mɔni dɔn. Di chans we sikstin bɛt fɔ $30 pan wan nɔmba ɔl go mis na (36/37)¹⁶ = 64.5%, so dɛn de rich $1,000 35.5% pan di tɛm.
Di tebul de sho ɛni bɛt. Rɛd de du bɛst bikɔs i de rich de wit wan bɛt, so yu de pe di advantej wan tɛm, pan $500. Di siks lainbɛtSiks lainSiks nɔmba na tu rɔw we de nia wan ɔda, i de pe 5:1. Na Frɛnch: sixain.Rid ɔl → de kam sɛkɔn bikɔs i nid ɔnli tri. Wan dɔzinbɛtDɔzin1–12, 13–24 ɔ 25–36, i de pe 2:1.Rid ɔl → bɛt na di wɔs, chans 12/37; ilɛk yu ple am wit $250 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 → te yu gɛt $1,000 ɔ mɔ, di dɔzin de rich de ɔnli 46.4% pan di tɛm.
Bollman (2024) mek di sem tebul fɔ Amɛrikan wil. Mistek de na in dɔzin lain: i fɔ rid 12/38 = 31.6%.
bɛtbɛt mɔni × ɔmɔs bɛtchans fɔ rich $1,000Bɛt pan wan nɔmba$30 × 1635.5%Split$60 × 835.9%Strit$90 × 534.5%Kɔna$125 × 436.7%Siks lain$166, $166, $16841.2%Dɔzin$500 × 132.4%Rɛd$500 × 148.6%Yu bɛt wan yunit pan rɛd, spin afta spin, wit gambul mɔnimɔniGambul mɔniƆl di mɔni we yu dɔn put asay fɔ ple. Fɔ manej yu gambul mɔni min fɔ disayd ɔmɔs pan am yu go risk fɔ ɛni bɛt ɛn fɔ ɛni sɛshɔn.Rid ɔl → we nɔ ɛva de dɔn. Afta di fɔs spin yu de wan yunit ɔp ɔ wan yunit dɔŋ. Wetin na di chans we yu go ɛva kam ivin bak rayt rayt?
Sho di ansa
Ansa 36 insay 37, 97.3%. Pan Amɛrikan wil na 36 insay 38, 94.7%.
If di fɔs spin win (18 tɛm insay 37), yu de wan yunit ɔp, ɛn di advantej de drag ɛni sɛshɔn we nɔ de ɛnd go dɔŋ, so sɔntɛm ɔ ɔda tɛm yu go pas ivin bak: dat de shɔ. If i lɔs (19 tɛm insay 37), yu fɔ klem wan yunit, ɛn di chans fɔ ɛva de wan yunit ɔp na 18/19 (luk di tebul ɔp).
Togɛda: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
Jɛnɛral wan, di chans na 1 mayn di difrɛns bitwin di chans fɔ win ɛn fɔ lɔs wan spin: 1 − 1/37 pan Yuropian wil, 1 − 2/38 pan Amɛrikan wan. Insay gem we nɔ gɛt 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 → di difrɛns na natin ɛn di chans na 1: di skɔ ɔltɛm de kam bak to ivin. Epstein (2013) gi di jɛnɛral rul.
Pascal in pazul frɔm 1656: tu pleya de trowe tri dayz, ɛn ɛni wan bigin wit 12 kɔnta. Ɛni 11 de muf wan kɔnta go to di fɔs pleya, ɛni 14 de muf wan go to di sɛkɔn; di ɔda trowe nɔ de kɔnt. Aw di fɔs pleya gɛt chans fɔ win ɔl 24? Ɛn if yu bɛt 1 yunit pan rɛd ɛni spin wit padi we de ple bank, 12 yunit ɛni wan, wetin na yu chans fɔ win ɔl 24?
Sho di ansa
Ansa Di fɔs pleya de win lɛk 1,157 tɛm insay 1,158. Yu, pan rɛd, de win ɔl 24 yunit ɔnli lɛk 34% pan di tɛm.
Tri dayz de mek 11 insay 27 we ɛn 14 insay 15 we, so ɛni kɔnta we muf de go to di fɔs pleya 27 tɛm insay 42, 9 tɛm insay 14. If ɛni say bigin wit 12, di chans fɔ tek ɔl na 1/(1 + r¹²), usay r na di ɔda say in chans sheb bay yu yon.
Fɔ di fɔs pleya r = 5/9, ɛn (5/9)¹² ≈ 0.00086, so di chans na lɛk 0.99914: ɔds fɔ 9¹² to 5¹², ɔ 282,429,536,481 to 244,140,625, lɛk 1,157 to 1. Huygens print da sem nɔmba dɛn rayt rayt na 1657.
Pan rɛd, r = 19/18 bikɔs fɔ di ziro, ɛn (19/18)¹² ≈ 1.913: yu chans na 1/2.913 ≈ 34.3%. Kɔyn go gi 50%. Di 2.70% advantej pan ɛni bɛt de ad ɔp, oba di bɔku bɛt we i de tek, te i tɔn difrɛns fɔ 16 pɔynt.
Smɔl jok fɔ ɛz di maynd
Fɔ ple wit bɔt at na di bɛst. I de dɔn kwik bak.
Usay wi gɛt am frɔm
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.
- Carcavi, P. de. Leta to Huygens, 28 Sɛptɛmba 1656, bɔt di prɔblɛm we Pascal bin gi Fermat.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Reuters. “Briton bets it all on roulette spin, and wins.”
- Las Vegas Sun. “Man wagers life’s worth.”