Rulɛt wil dɛn we nɔ kɔmɔn
Wil dɛn wit 18, 25, 26, 31, 40, 49, 62, 73 ɔ 105 pɔkit. Wan rul de sɛt di prayz fɔ ɔlmɔs ɔl dɛn: di pat pan di pɔkit dɛn we di pe dɛn nɔ kɔnt.
We dɛn sɛt di pe dɛn lɛk se di kasino pɔkit dɛn nɔ de, di kasino advantejmatematiksKasino advantejDi pat pan ɛni bɛt mɔni we di kasino de kip pan avrej: 2.70% na Yuropian rulɛt.Rid ɔl → na di kasino pɔkit dɛn we yu divayd bay ɔl di pɔkit dɛn, ɛni sayz di wil gɛt. Bɔku pan di wil dɛn we nɔ kɔmɔn de fala da rul de. Di wan dɛn we intrɛstin de brok am: pe we dɛn rawnd, bonɔs raund, ɔ bɛt we de stil de fɔ bɔku spin.
Wan rul fɔ ɛni wil
Yuropian rulɛtkayn rulɛtYuropian rulɛtWil wit wan ziro, 37 pɔkit, kasino advantej 2.70%. Na di main wil we dis sayt de yuz.Rid ɔl → de pe 35 to 1 lɛk se di wil gɛt 36 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl →. I gɛt 37, ɛn di pɔkit we nɔ de na di 2.70% ɛj. Di sem rul de wok pan ɛni wil: wit N nɔmba ɛn Z kasino pɔkit, bɛt pan n nɔmba we de pe (N − n)/n to 1 gɛt ɛj fɔ Z/(N + Z). Dɛn dɔn bil ɔ tink bɔt wil dɛn fɔ ɛni sayz pan dis rul, ɛn di tebul de put dɛn na ɔda bay prayz. In lain dɛn de gi bak di bezik tin dɛn fɔ aw fɔ ple Royal Roulette, di Ɔstrelia gem: in nɔmba dɛn na di kad dɛn frɔm 2 to king, in tu kasino pɔkit na di ace ɛn di joker, ɛn wan kad de pe 47 to 1.
Big wil kin chip mɔ
Pleya dɛn kin tink se wil wit 62 pɔkit tranga fɔ win pas, ɛn se di gem wɔs. Di ɛj dipen pan di pat fɔ kasino pɔkit nɔmɔ. Super 62 gɛt tu 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 →, lɛk di Amɛrikan wil, bɔt dɛn na 2 pan 62 pɔkit, nɔto 2 pan 38, so i kɔst 3.23% agens 5.26%. Roulette 73, wit 72 nɔmba ɛn wan ziro, go kɔst 1.37%, lɛk di sem as Frɛnch ivin mɔni. Di rul de wok di ɔda we pan smɔl wil. Bollman de sho wan ol wil wit 18 pɔkit, 1 to 16 plɔs 0 ɛn 00. Pan di rul, ɛni bɛt go kɔst 2/18, 11.11%: tu kasino pɔkit na big pat pan smɔl wil.
Usay di rul de brok: rawnd
PemɔniPeWetin bɛt we win de gi yu, dɛn de tɔk am as “X to 1” ɔn tɔp di bɛt mɔni we kam bak.Rid ɔl → fɔ bi chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl → mɔni we gɛt sɛns, ɛn we di rul gi frakshɔn, di kasino de rawnd am dɔŋ. 100 To 1 Roulette in Avenue bɛt de kɔba 15 pɔkit ɛn i fɔ pe 5⅔ to 1; i de pe 11 to 2, ɛn dat de rayz in ɛj frɔm 4.76% to 7.14%. Pan Super 62, sɛvin nɔmba gɛt di digit 6 (6, 16, 26, 36, 46, 56, 60) ɛn di bɛt pan da digit de pe 7 to 1, we mek am 9.68%, tri tɛm di rɛst pan di bɛt tebulikwipmɛntBɛt tebulDi bɛt grid we dɛn print pan di tebul. Dɛn kin kɔl am bak: tebul, felt, klɔt.Rid ɔl →. Riverboat Roulette in White bɛt de kɔba 8 nɔmba at 7 to 2; na tebul we nɔ gɛt 50-sɛnt chip, dɛn de pe pɔsin we win wit $5 $17, nɔto $17.50, ɛn dat de rayz di ɛj frɔm 5.26% to 7.37%. Di Amɛrikan bɛt pan fayv nɔmba, at 7.89%, na di kes we pipul dɛn sabi fɔ di sem tin.
Usay di rul de brok: bonɔs
Fast Action Roulette, we dɛn bigin na Marina Bay Sands na 2020, de yuz rial wil wit fɔ ziro, we bay insɛf go kɔst 10%. Tɛn Bonus nɔmba de layt ɛni kayn we ɛni spin. Bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → de pe 35 to 1, 40 to 1 if in nɔmba na Bonus nɔmba, ɛn 80 to 1 if in ol lain fɔ fɔ na Bonus, ɛn dat de briŋ am to 6.65%. Di gem in ɔda tri bɛt kɔst mɔ fa. IGT in Double Bonus Spin de ad yɛlo Bonus pɔkit, wan pɔkit ɛn af wayd, to Amɛrikan wil; we 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 → lan de, ɛni bɛt de gɛt tu fri spin. Bay wi kalkul, dat de lɔ di ɛj to bitwin 1.94% (bɛt pan wan nɔmba) ɛn 2.73% (ivin mɔni), ɔnda di plen Amɛrikan wil. Bollman (2021) de print 3% to 16% fɔ dis gem; in simpul fɔmula gɛt mistek na di aljibra, ɛn fɔ ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl → i de se di fri spin dɛn de lɔs mɔ pas di bɛt mɔni, we nɔ pɔsibul.
Usay di rul de brok: bɛt we de stil de
Riverboat Roulette (2012) gi 32 nɔmba pan Amɛrikan wil sɛkɔn kɔla. White de mak di fɔ pɔkit dɛn rawnd ɛni ziro (1, 2, 9, 10, 13, 14, 27, 28). Bɛt pan kɔla grup de win if wan pan in nɔmba dɛn kam bifo wan pan di et White nɔmba. White nɔmba na “White Out” we de klin ɛni kɔla bɛt. Ɛni ɔda nɔmba na nɔ win nɔ lɔs: di bɛt de stil de, ɛn bitwin spin dɛn yu kin pul am ɔ rayz am. Teal de kɔba tri nɔmba ɛn i de pe 2 to 1. Pan ɛni bɛt we dɔn sɛtul, i de lɔs 2/11 pan di bɛt mɔni, 18.18%. Pan ɛni spin i de lɔs 2/38, di 5.26% we pipul dɛn sabi, bikɔs di avrej bɛt de stil de 38/11, lɛk 3.5 spin.
Wil we Thorp bin ebul si bifo: Big Six
Di Big Six, ɔ wil fɔ lɔk, na big wil we tinap ɔp wit 54 slɔt: 24 de pe 1 to 1, 15 de pe 2 to 1, sɛvin 5 to 1, fɔ 10 to 1, tu 20 to 1, ɛn tu logo slɔt de pe 40 to 1. Ziro nɔ de; di kasino de tek in pat bay we i de pe smɔl, ɛn di ɛj de frɔm 11.1% pan di slɔt dɛn we de pe 1 to 1 to 24.1% pan di logo dɛn. Na 1961, Thorp bil wan mashin fɔ si bifo we sayz lɛk matches bɔks fɔ am, we yu de wok wit swich na yu fut, ɛn na 1981, we i tɛm wan tɔn pan kasino wil wit in an wach, i fɛn se bɔku tɛm i kin nem di ples we i go stɔp insay fayv slɔt. If yu bɛt pan di slɔt dɛn we de pe ay nia di prɛdikshɔn nɔmɔ, i go gi bak lɛk +211%, if dɛn bin de tek bɛt afta di wil dɔn spin. Dɛn nɔ de tek am, ɛn di wil de tɔn slo wan ɛn ɔlman de si am, so bɛt we lɛt go klia; Thorp rayt se di gem nɔ bin gɛt bɔku akshɔn fɔ ayd wan.
Wetin mek pipul nɔ de tek bɔku pan dɛn
Wil fɔ kasino kɔst tawzin tawzin dɔla, ɛn wil wit nɔmba fɔ pɔkit we nɔ kɔmɔn, dɛn fɔ mek am spɛshal. So bɔku nyu rulɛt gem de kip di nɔmal wil ɛn ad bɛt, ɛn na dat mek di pej fɔ sayd bɛt lɔng pas dis wan. Di igul wil wit 31 pɔkit we bin de na Amɛrika na di 19 sɛnchri, at 12.90% pan wan nɔmba ɛn 9.68% pan ɔl ɔda tin, day bikɔs ɔf in yon prayz. Di aydia fɔ tɔd kasino pɔkit kam bak na 2016 pan wil wit 39 pɔkit, usay i kɔst 7.69%.
Kwɛstyɔn dɛn
Nɔto bay insɛf. Di ɛj na di pat fɔ kasino pɔkit: 1 insay 73 chip pas 1 insay 37.
Roulette 73, at 1.37%, bɔt na dizayn we dɛn pablish, nɔto tebul we yu go fɛn izi. Pan di wil dɛn we dɛn dɔn gi pleya dɛn, Super 62 at 3.23% de kam nɛks afta Yuropian ɛn Frɛnch.
Pɔsin fɔ pe fɔ bonɔs, bɔku tɛm bay we dɛn kɔt di bes pe ɔ bay sɛpret bɛt wit ay ɛj.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Royal Roulette, we dɛn mek na Ɔstrelia, gɛt 50 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl →: di 48 kad frɔm 2 to kin, plus wan ays ɛn wan joka. Wan kad de pe 47 to 1, tu kad 23 to 1, tri 15 to 1, fɔ 11 to 1, siks 7 to 1, et 5 to 1, twɛlv 3 to 1, sikstin 2 to 1 ɛn twɛnti-fɔ 1 to 1. Wetin na di rul we mek dɛn pemɔniPeWetin bɛt we win de gi yu, dɛn de tɔk am as “X to 1” ɔn tɔp di bɛt mɔni we kam bak.Rid ɔl → ya, ɛn ɔmɔs ɛni bɛt de kɔst?
Sho di ansa
Ansa Ɛni bɛt pan n kad de pe (48 − n)/n to 1, so ɛni bɛt de kɔst 2/50 = 4%.
Tray di rul pan sɔm bɛt: 47/1 = 47, 36/12 = 3, 32/16 = 2, 24/24 = 1. I fit ɔl di nayn. Di rul de prays di wil lɛk se i gɛt 48 pɔkit, so di ays ɛn di joka na di tu kasino pɔkit, jɔs lɛk aw 0 ɛn 00 de pan Amɛrikan wil.
Tu kasino pɔkit pan 50 de gi advantej fɔ 4%. Wan “Yuropian” vɛshɔn de pul di joka ɛn kip di pe dɛn: wan kasino pɔkit pan 49, advantej fɔ 2.04%.
Super 62 gɛt wan bɛt se wan dijit we yu pik go de insay di nɔmba we kam. Mek di sem bɛt fɔ nɔmal Amɛrikan wil. Ɔmɔs pan di nɔmba 1 to 36 gɛt ɛni dijit, ɛn wetin na di pe dɛn we go kip di yuzhual 5.26%?
Sho di ansa
Ansa Na jɔs di dijit dɛn we de insay 3 ɔ 4 nɔmba gɛt klin pe (11 to 1 ɛn 8 to 1). Dɛn nɔ fit pe di dijit 1, 2 ɛn 3 fɛr wit ful chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl →.
Kɔnt di nɔmba dɛn. Dijit 1 de insay 1, 10 to 19, 21 ɛn 31: 13 nɔmba. Dijit 2 de bak insay 13 nɔmba ɛn dijit 3 insay 10. Di dijit 4, 5 ɛn 6 de insay fɔ nɔmba ɛni wan (4, 14, 24, 34), ɛn 7, 8 ɛn 9 insay tri ɛni wan.
Bɛt pan n nɔmba de kip di Amɛrikan advantej if i pe (36 − n)/n to 1. Dat de gi 8 to 1 fɔ fɔ nɔmba ɛn 11 to 1 fɔ tri, ɛn dɛn tu na ful nɔmba. Fɔ 13 nɔmba i de gi 23/13, lɛk 1.77 to 1, ɛn fɔ 10 nɔmba 2.6 to 1. If yu raund 1.77 dɔŋ to 7 to 4, di bɛt de kɔst 5.92%; if yu raund am ɔp to 2 to 1, di pleya gɛt 2.63% advantej. If yu raund 2.6 dɔŋ to 5 to 2, i de kɔst 7.89%.
Dijit 0 na chɔys: 10, 20 ɛn 30 nɔmɔ de pe 11 to 1 wit 5.26%; ad 0 ɛn 00 ɛn i tɔn bɛt pan fayv nɔmba, 6 to 1 wit 7.89%, lɛk di baskitbɛtBaskitPan wil wit wan ziro: 0, 1, 2, 3 wit wan chip, i de pe 8:1. Dɛn kin kɔl am bak: fɔs fɔ, quatre premiers.Rid ɔl →.
dijitnɔmbadi rul sei fit pekasino advantej1, 2131.77 to 17 to 45.92%3102.6 to 15 to 27.89%4, 5, 648 to 18 to 15.26%7, 8, 9311 to 111 to 15.26%100 To 1 Roulette de pe (100 − n)/n to 1 pan mɔs bɛt, pan wil we gɛt 100 nɔmba ɛn 5 kasino sayn. Di bɛt dɛn de kɔba 1, 2, 3, 4, 5, 10, 15, 20 ɔ 50 pɔkit ɛn pe 100, 49, 32, 24, 19, 9, 11 to 2, 4 ɛn 1 to 1. Di bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → ɛn di Avenue we kɔba 15 pɔkit nɔ fala di rul. Wish ɔda bɛt nɔ fala am, ɛn ɔmɔs i de kɔst?
Sho di ansa
Ansa Di bɛt pan tri pɔkit: di rul se 32⅓ to 1, i de pe 32 to 1, ɛn i de kɔst 5.71%, nɔto 4.76%.
Chɛk ɛni pe wit di rul: 98/2 = 49, 96/4 = 24, 95/5 = 19, 90/10 = 9, 80/20 = 4 ɛn 50/50 = 1 ɔl fit. Fɔ tri pɔkit di rul de gi 97/3 = 32⅓, ɛn nɔ chip nɔ fit pe dat, so dɛn raund am dɔŋ to 32.
Di bɛt de win 3 tɛm pan 105 spin ɛn i de gi 33 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 → bak, wit di bɛt mɔni: 3 × 33 = 99 yunit kam bak fɔ ɛni 105 we yu bɛt, lɔs fɔ 6/105 = 5.71%.
Roulette 73, wan dizayn we dɛn dɔn pablish, gɛt 72 nɔmba ɛn wan 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 →, ɛn ɛni bɛt de pe (72 − n)/n to 1. Yu fit kɔba in 24 gre nɔmba wit 14 chip: 4 bɛt pan wan nɔmba ɛn 10 splitbɛtSplitTu nɔmba we de nia wan ɔda, i de pe 17:1.Rid ɔl →. Ɔmɔs da bɛt wit 14 chip de kɔst?
Sho di ansa
Ansa 1.37% pan di 14 chip, lɛk ɛni ɔda bɛt pan da wil de.
Di lɔng we: bɛt pan wan nɔmba de pe 71 to 1 ɛn split de pe 35 to 1. If wan pan di 4 nɔmba we yu bɛt wan-wan kam, yu win 71 ɛn lɔs di ɔda 13 chip: +58. If wan pan di 20 split nɔmba kam: +35 − 13 = +22. Pan di ɔda 49 pɔkit yu lɔs ɔl 14. Pan avrej pan 73 spin: 4 × 58 + 20 × 22 − 49 × 14 = 232 + 440 − 686 = −14 yunit, we na 1/73 pan ɛni chip.
Di shɔt we: 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 → de ad. Ɛni chip na nɔmal bɛt we de lɔs 1/73 pan insɛf, so 14 chip de lɔs 14/73. If yu jɔyn bɛt dɛn, i de chenj aw di rizɔlt dɛn de sprɛd, bɔt i nɔ de chenj wetin dɛn kɔst.
Super 62 gɛt 60 nɔmba, 0 ɛn 00, ɛn i de pe (60 − n)/n to 1. Di wan dɛn we dizayn am bin drɔ am bak wit wan, tri ɛn fɔ kasino pɔkit. Alphabetic Roulette de pe (24 − n)/n to 1 pan 25 pɔkit, ɛn i gɛt wan vɛshɔn we Y ɛn Z gɛt dɛn yon pɔkit. Prays ɔl di fayv.
Sho di ansa
Ansa Wit wan to fɔ ziro: 1.64%, 3.23%, 4.76% ɛn 6.25%. Alphabetic we Y ɛn Z de sɛpret: 7.69%.
Ɛni wan pan dɛn ya de kip in pe dɛn ɛn i de chenj jɔs ɔmɔs kasino pɔkit de, so di advantej na kasino pɔkit ÷ ɔl di pɔkit.
Wan ziro, 61 pɔkit: 1/61 = 1.64%. Tu, 62 pɔkit: 2/62 = 3.23%. Tri, 63 pɔkit: 3/63 = 4.76%. Fɔ, 64 pɔkit: 4/64 = 6.25%. Ɛni ziro we dɛn ad de kɔst lɛk wan pɔynt ɛn af.
Alphabetic de pe lɛk se i gɛt 24 lɛta. If Y ɛn Z de sheb wan pɔkit, di kasino gɛt 1 pan 25, 4%. If Y ɛn Z de sɛpret, i gɛt 2 pan 26, 7.69%, lɛk wil wit tripul ziro. We dɛn split wan pɔkit tu, di prays kam nia dɔbul.
wilpɔkitkasino pɔkitkasino advantej60 nɔmba, wan ziro6111.64%Super 626223.23%60 nɔmba, tri ziro6334.76%Super 646446.25%Alfabɛt2514.00%Alphabetic, Y ɛn Z sɛpret2627.69%Wan ol-ol wil gɛt 18 pɔkit: 1 to 16, 0 ɛn 00. Ɔd nɔmba ɛn 0 na rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl →, ivin nɔmba ɛn 00 na blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, ɛn di 16 nɔmba de pan bɛt tebulikwipmɛntBɛt tebulDi bɛt grid we dɛn print pan di tebul. Dɛn kin kɔl am bak: tebul, felt, klɔt.Rid ɔl → we na 4 bay 4. Mek wan pe tebulmɔniPe tebulDi list fɔ wetin ɛni bɛt ɔ rizɔlt de pe. Pan mashin ɛn sayd bɛt, na de dɛn de sɛt di kasino advantej.Rid ɔl → we go gi ɛni bɛt di sem advantej. Ɛn wetin mek 0 fɔ lɔs bɛt pan rɛd, pan ɔl we i rɛd?
Sho di ansa
Ansa Pe (16 − n)/n to 1: 15 to 1 pan wan nɔmba, 7 pan tu, 3 pan fɔ, 1 pan et. Ɛni bɛt de kɔst 11.11%. If 0 win di rɛd bɛt, rɛd go bi fɛr bɛt.
Prays di wil lɛk se 0 ɛn 00 nɔ de. Bɛt pan n nɔmba de win n tɛm pan 18 ɛn pe (16 − n)/n to 1, so i de bring 16 yunit bak, wit di bɛt mɔni, fɔ ɛni 18 we yu bɛt. Ɛni bɛt de kɔst 2/18, 11.11%.
Di nachral bɛt dɛn pan di bɛt tebul de kam ful: wan nɔmba 15 to 1, tu we de nia dɛnsɛf 7 to 1, wan lain ɔ wan kɔlɔmbɛtKɔlɔmTwɛlv nɔmba na wan kɔlɔm we tinap na di bɛt tebul, i de pe 2:1.Rid ɔl → fɔ fɔ nɔmba 3 to 1, ɛn tu lain, ɔ di et ɔd, ivin, lɔ ɔ ay nɔmba, 1 to 1. Bɛt pan tri nɔmba go nid 4⅓ to 1; if dɛn raund am dɔŋ to 4 to 1, i de kɔst 16.67%.
Rɛd de kɔba di et ɔd nɔmba. If 0, we rɛd, bin win di rɛd bɛt bak, rɛd go kɔba 9 pan di 18 pɔkit fɔ 1 to 1: fɛr gemmatematiksFɛr gemGem usay nɔbɔdi nɔ gɛt advantej: ɛni bɛt gɛt valyu we fɔ ɛkspɛkt we na ziro.Rid ɔl → we nɔ gɛt advantej atɔl. Di kasino pɔkit dɛn de gɛt dɛn advantej jɔs bay we dɛn de lɔs ɛni bɛt pas bɛt pan dɛnsɛf.
Smɔl jok fɔ ɛz di maynd
Kɔnt di kasino pɔkit dɛn, dɔn luk fɔ di rawnd.
Usay wi gɛt am frɔm
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”