Varians
Wetin mek bɛt pan wan nɔmba ɛn bɛt pan rɛd, we gɛt di sem 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 →, de fil lɛk tu difrɛn gem.
Varians de mɛzh aw fa di rizɔlt dɛn de sprɛd rawnd di valyu we fɔ ɛkspɛkt. Pan ɛni yunit we yu bɛt, i na lɛk 34 fɔ bɛt pan wan nɔmba ɛn lɛk 1 fɔ rɛd.
Di fɔmula fɔ wan bɛt
Fɔ bɛt we de pe W to 1 wit prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → p, di rizɔlt pan ɛni 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 → na +W wit prɔbabiliti p ɛn −1 wit prɔbabiliti 1 − p. Di valyu 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 → na pW − (1 − p) = −1/37. 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 → na E[X²] − EV² = pW² + (1 − p) − (1/37)². Fɔ bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. Fɔ rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Wetin i min fɔ wan sɛshɔn
Varians de ad pan spin we nɔ dipen pan ɔda wanmatematiksSpin we nɔ dipen pan wan ɔdaƐni spin gɛt di sem prɔbabiliti, ilɛksɛf wetin dɔn apin bifo. Na dis ɛni kalkulɛshɔn na dis sayt bil pan.Rid ɔl →, so fɔ N spin wit di sem bɛt mɔni, di varians fɔ di tɔtal na N × bɛt mɔni² × σ², ɛn di standad diviyeshɔnmatematiksStandad diviyeshɔnDi skwɛ rut fɔ varians; di nɔmal distans bitwin wan rizɔlt ɛn di valyu we fɔ ɛkspɛkt.Rid ɔl → na σ × bɛt mɔni × √N. 100 spin wit $10: di standad diviyeshɔn na lɛk $584 fɔ bɛt pan wan nɔmba ɛn $100 fɔ rɛd, rawnd di sem −$27 we fɔ ɛkspɛkt. Wan pleya de si di rizɔlt dɛn de swing bay ɔndrɛd ɔndrɛd dɔla; di ɔda wan de si i de muv smɔl smɔl. Di tu dɛn de pe di sem prays.
Varians ɛn sistɛm dɛn
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 → nɔ de chenj di EV pan ɛni yunit we yu bɛt, bɔt i de chenj di mɔni we yu bɛt ɛn di shep fɔ di distribyushɔn. 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 di varians smɔl fɔ bɔku sɛshɔn (bɔku smɔl win) ɛn i de ad fat tel (di big lɔs we nɔ kin apin bɔku). Di tɔtal varians fɔ ɔl di sɛshɔn dɛn ay pas bɛt di sem mɔni ɔltɛmstratɛjiBɛt di sem mɔni ɔltɛmFɔ bɛt di sem mɔni ɛni spin. Na dis ɛni prɔgrɛshɔn de kɔmpia wit.Rid ɔl → bikɔs fɔ da tel de. ParolistratɛjiParoliPɔzitiv prɔgrɛshɔn: dɔbul afta yu win, bigin bak afta yu lɔs ɔ afta tri win wan afta di ɔda. Dɛn kin kɔl am bak: Martingale we tɔn bak.Rid ɔl → de du di ɔda we. If yu pik sistɛm, yu de pik aw di varians go tan; di avrej nɔ de fɔ pik.
- p10 −$500
- p25 −$500
- midul valyu −$500
- p75 +$40
- p90 +$1,120
Rulɛt stratɛji: bɛt di sem mɔni ɔltɛmParoli rulɛt stratɛji (Martingale we tɔn bak)
Wetin mek i impɔtant fɔ pleya
Na varians de mek yu nɔ kin no wetin go apin na shɔt sɛshɔn, bɔt yu kin no fɔ lɔng wan. Wit σ = $100 ɛn EV = −$27 fɔ 100 spin, di advantej na wan kwata fɔ di nɔys, ɛn sɛshɔn we yu win na nɔmal tin. Fɔ 10,000 spin, di EV na −$2,700 ɛn σ na $1,000; naw di advantej ɔlmɔs tri tɛm big pas di nɔys, ɛn fɔ win na tin we nɔ kin apin pas tri sigma. Varians na di pleya in padi fɔ shɔt tɛm, ɛn di kasino in padi fɔ lɔng tɛm.
Varians fɔ bɛt dɛn we yu jɔyn
Fɔ bɔku bɛt pan di sem spin, di rizɔlt dɛn gɛt kɔnɛkshɔn (if 17 kam, i kam bak fɔ blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl → ɛn di sɛkɔn dɔzinbɛtDɔzin1–12, 13–24 ɔ 25–36, i de pe 2:1.Rid ɔl →), so di varians dɛn nɔ jɔs de ad. Di Bet Builder tul de kalkul di rial distribyushɔn fɔ ɛni sɛt chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl → bay we i de kɔnt ɔl di 37 rizɔlt. Na di wan we nɔmɔ kɔrɛkt fɔ du am.
Fɔmula
Kwɛstyɔn dɛn
Nɔ. Ɛni bɛt gɛt di sem valyu we fɔ ɛkspɛkt. Ay varians min se di swing rawnd am big pas.
Ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl →, wit σ ≈ 1 pan ɛni yunit. I lɔ pas dat wit La PartagerulLa partageFrɛnch rul: if ziro kam, af fɔ di ivin-mɔni bɛt mɔni de kam bak. I de kɔt di kasino advantej pan dɛn bɛt ya to af, 1.35%.Rid ɔl →, we de mek di avrej bɛtɛ bak.
Di prɔfit we fɔ ɛkspɛkt na di sem pan ɛni dɔla; varians de chenj jɔs aw di kasino in mɔni de kam, smɔl ɔ big big. Di kasino gɛt tawzin tawzin pleya fɔ mek am ivin.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Tu pleya de bɛt $1 ɛni spin fɔ 100 spin pan Yuropian wil, wan ɔltɛm pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →, di ɔda wan ɔltɛm pan 17. Udat gɛt mɔ chans fɔ de ɔp na di ɛnd?
Sho di ansa
Ansa Di pleya pan 17: 50.9%, ɛn 35.5% fɔ rɛd. Ɔl tu de lɔs $2.70 pan avrej.
Rɛd: di pleya de ɔp wit 51 win ɔ mɔ insay 100, ɛni wan wit prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → 18/37. Di binomial distribyushɔn de gi 35.5%, ɛn 50 win rayt rayt, we na nɔ win nɔ lɔs, ɔda 7.7%.
Nɔmba 17: ɛni win de gi bak $36, so tu win (−$28) nɔ du ɛn tri (+$8) du. Di chans fɔ tri ɔ mɔ insay 100 spin bay 1/37 na 50.9%.
Di pleya we de bɛt pan wan nɔmba de ɔp mɔ tɛm, bɔt di rizɔlt dɛn de kam wit big jomp: wan win mɔ ɔ lɛs de muf di rizɔlt bay $36, ɛn di pleya dɛn we de dɔŋ bɔku tɛm de dɔŋ pas. Bollman (2024) gi di Amɛrikan nɔmba dɛn, 26.5% ɛn 49.2%.
Smɔl jok fɔ ɛz di maynd
Di sem lɔs we fɔ ɛkspɛkt. Wan pan dɛn de tɛl yu bɔt am wit lawd vɔys.
Usay wi gɛt am frɔm
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.