Master of Odds

Nej bara för att chansen för att förlora 12 gånger i rad är 1 på 4096 (ser bort ifrån de gröna rutorna) betyder INTE det att det är större än 50% chans att man förlorar innan spel 2048. Chansen för att man förlorat innan dess är 1-(4095/4096)^2048 = 39,4% chans Men detta spelar ingen roll. Sen måste du komma ihåga att skilja på att vinna och att tjäna... Sen måste jag får lov att påpeka att det verkar som även du inte helt tänker rätt logiskt nu när du uttalar att du menar att det hade fungerat om man haft obegränsat kapital och att du får dubbla precis hur många gånger som helst. Man har alltid en förväntat nettoförlust i roulette och det finns inga garantier för att man kommer hamna i positiv varians även om man så tar bort de gröna rutorna!!!

Gjorde ett program som spelar enligt St Petersburgprincipen nu. Den spelar ungefär 2 miljoner omgångar (med omgång menas tills man förlorar) per sekund på en AMD Athlon 64 4000+ överklockad til 2,72mHz, 10000rpm S-ATA2 Raptor hårddisk osv... Man vet ju att Average Win ska gå mot oändligheten men det kommer naturligtvis att med oändligt hög sannolikhet att ta oändligt med tid. Programmet är gjort så att efter varje 10 miljonte spel så kommer uppdaterad info om hur mycket pengar man spelat in (baserat på att det är gratis att spela), Hur mycket man vunnit i snitt per spel och vad rekordvinsten är så här långt. Sen är modelleringen visserligen inte klockren eftersom jag bara behandlar tal upp till 3,4E+38 men chansen att man ska vinna så mycket i en omgång är ju just 1 på talet ifråga vilket antagligen inte kommer hända, men då bryter jag ju iofs just mot St Petersburgs-principer... Men men ska låta den stå på och köra 50 miljarder gånger... så den slutar lagom till frukost i morgon... För mig borde den således gå mot log2 till FLOAT'Last som blir ungefär 127... men det kommer ta larvigt lång tid för att få ett representativ urval (med larvig menar jag universiums ålder flera biljoner gånger om typ) =) Men en rolig grej i allafall. Utskriften ser ut t.e.x. så här: Microsoft Windows XP [Version 5.1.2600] © Copyright 1985-2001 Microsoft Corporation C:\Documents and Settings\Hejdaniel>peter Cash: 122865184.0 Games played: 0010000000 Average win: 12.287 Biggest win: 8388608.0 (in this session): 8388608.0 Cash: 233163776.0 Games played: 0020000000 Average win: 11.658 Biggest win: 16777216.0 (in this session): 16777216.0 Cash: 360200704.0 Games played: 0030000000 Average win: 12.007 Biggest win: 16777216.0 (in this session): 16777216.0 Cash: 462845312.0 Games played: 0040000000 Average win: 11.571 Biggest win: 16777216.0 (in this session): 8388608.0 Cash: 562373312.0 Games played: 0050000000 Average win: 11.247 Biggest win: 16777216.0 (in this session): 8388608.0 Cash: 675037056.0 Games played: 0060000000 Average win: 11.251 Biggest win: 16777216.0 (in this session): 16777216.0 Cash: 788672128.0 Games played: 0070000000 Average win: 11.267 Biggest win: 16777216.0 (in this session): 16777216.0 Cash: 1170314624.0 Games played: 0080000000 Average win: 14.629 Biggest win: 268435456.0 (in this session): 268435456.0 Cash: 1246909440.0 Games played: 0090000000 Average win: 13.855 Biggest win: 268435456.0 (in this session): 4194304.0 Cash: 1363634688.0 Games played: 0100000000 Average win: 13.636 Biggest win: 268435456.0 (in this session): 8388608.0 OSV.... och så vidare Cash: 4795476992.0 Games played: 0400000000 Average win: 11.989 Biggest win: 536870912.0 (in this session): 67108864.0 Cash: 4982164480.0 Games played: 0410000000 Average win: 12.152 Biggest win: 536870912.0 (in this session): 67108864.0 Cash: 5081508352.0 Games played: 0420000000 Average win: 12.099 Biggest win: 536870912.0 (in this session): 16777216.0 Sen när detta handlar om en loop som utförs så snabbt och så många gånger och man är beroende av slumpen så är det mycket möjligt att slumpgeneratorns beroende av processorklockan gör den för dålig på att generera bra nog slump... Jaja bara en liten rolig grej, ska se om jag kan vidareutveckla programmet sen =) Oj precis när jag skrev nu så råkade den vinna 4.294.967.296 (typ 2^32) på en omgång vilket höjde snittet nu till 12,630... Det är just det som är grejen, dessa otroligt ovanliga händelserna vill på sikt dra upp snittet (gällde inte samma simuleringen som talen över var hämtad från dock)

Ja vad gör spelaren om han aldrig vinner? (även om sannolikheten går mot 0 för att det ska hända, så kommer den ju aldrig bli 0...). Det finns alltid en kombination av utfall som gör att spelaren inte vinner... Vad är det för sida du har förresten, hade varit intressant att läsa.

Skoj att du tycker det. Ja precis, man har så svårt att föreställa sig det, precis lika svårt som man har att föreställa sig hur enorm konsekvensen blir om det ändå skulle hända =) Men det känns dock som det finns väldigt många som fortfarande tror att man faktiskt kan hitta system som får spel med nettoförlust att bli vintgivande... det är synd för dem, hoppas en del lär sig snart innan det blir för sent =/

Det faktum att man får oändlig Expected Value med St Petersburg-paradoxet är överhuvudtaget vare sig relevant eller intressant inom Roulette. Detta eftersom man blir erbjudet ett oändligt bra erbjudande som man aldrig någonsin kommer att få på ett casino. Grejen som det faller på är ju att man inte förlorar nått om man råkar gå vidare en gång för mycket... man får bara det man hittils vunnit... Det är förvisso till en viss grad ganska intressant rent psykologiskt, men inget mer än det... Ungefär som att bli erbjuden dubbelchans i jeopardy på ja/nej-frågor om saker man har noll koll på och sedan i evighet få möjlighet att dubbla, utan att förlora om man svarade fel =) Det är ju faktiskt inga konstigheter alls med det. Om man har SUMMAN(x^n*Y^n) när n går från 0 till oändligt och x = 1/y så gäller ju det ALLTID att SUMMAN blir oändligt och funktionen blir konstant 1 för alla par X och Y sådana att de är inverter Finns ju hur många exepmler som helst på detta annars i anturen och matematiken.

OK ska erkänna att jag läste lite fel. Nu har jag insett vad idén går ut på, var lite diffust förklarat på wikipedia med tanke på hur jag förväntade mig att det skulle vara verklighetanknytet till just roulett, vilket det överhuvudtaget inte var. Trodde det menade att man satsade pengar in till potten före varje gång man flippade myntet. Men det gjorde man ju inte så ni kan se bort ifrån det jag har sagt om St Petersburg-paradoxet. Dock ska det sägas at St Petersburg-"paradoxet" överhuvudtaget inte är intressant vad gäller Roulette eftersom man inte satsar före varje rullning/myntkast Har personligen reflekterat över exakt samma paradox som det St. Petersburg Paradoxet är utan att veta att det hette just det. Tycker dock inte egentligen att det är ett paradox, men det har nog med att jag har så mycket med sådan matte att göra i vardagen att man ser för sig sånna saker som naturliga numera. Hm... vad ska man säga exponentutvecklingarna 2 och 0,5 är inverter till varandra så enkelt är det... därför blir ju produkten av P(n)*K(n) konstant = 1... Ser inte helt vad det har med roulette att göra...

OM det öht går att använda Martingale på ett positivt sätt så krävs det oändlig kredit, inget mindre duger. Fortfarande inte klarlagt huruvida det fungerar dock, skulle vara intressant med någon mattesajt som behandlar ämnet. Det enda jag hittat är casinosajter och de är ju svåra att lita på. Nej det går inte, tyvärr. Ja precis, Casionsajterna är ju intresserade av att folk tror att det finns sätt att lura oddsen... Har även sett dokumentärer på bl.a. Discovery Channel som handlar om hur casion slänger ut "fuskare". Detta är naturligtvis bara PR-trick från casionts sida för att få flera att fatta intressen för dessa "system" som itne funkar. På samma sätt som du uppmande mig och jag sedan beklagade att jag inte helt satt mig in i konceptet St Petersburg"Paradoxet" så ber jag även dig (fast höfligt) att nu kolla lite längre tilbaka i denna tråden vad jag har skrivit och förklarat om vissa casino"system" =)

Ja det är fullt möjligt. Det är extremt osannolikt.. Det som dock är ännu mer extramt är konsekvensen av om man ändå inte skulle vinna... tyvärr, läs vad jag har skrivit

quote="sulla" Med "flatbets" stämmer detta, då man regelbundet har samma insats, men enligt metoden att hela tiden ta igen sin tidigare förlust med en dubbel instats gör att man då man vinner, tar igen den förlust man gjort. Folk måste förstå att ingen i denna tråd har sagt att metoden går att tillämpa i verkligheten, men med de hypotetiska omständigheterna som nämnts gör att det går att plussa på det. Prata inte EV hit o dit. Enkla fakta är följande Du tar igen tidigare förlust om du dubblar insatsen hela tiden? Alla med? Om du kan sluta när du vill kan du sluta så fort du vunnit 2 i rad ( en för att ta igen förlusten och en för att vinna ett ursprungsbet.) Vadär svårt att fatta med detta? det spelar alltså ingen roll om du bestämt dig för att köra rött och det kommer 400 svarta i rad, för när det sedan kommer 2 röda i rad ligger du plus./quote men köra sulla, exakt när hade du tänkt att du med 100.000000% säkerhet kan fastställa att du kommer att vinna? Efter 14 dubbleringar, 1684351 dubbleringar eller rent av 65465465465465124 dubbleringar? Det är det det hela faller på, ni pratar hela tiden om: "NÄR man sen vinner" precis som om man garanterat nånsin kommer att vinna... =) Jag coh en del andra har ju redan på femtio-elva olika sätt bevisat varför man aldrig kan vara helt säker på att vinna, så jag orkar inte ta ett bevis till utan hänvisar till tidigare inlägg jag har gjort. Ber alla som tänker skriva något ytterligare i tråden att först läsa vad folk har skrivit före de skriver felaktiga saker som detta. Hoppas några av mina förklaringar gör att du förstår exakt på vilket sätt du ressonerar fel sulla mch Daniel Pedersen

Nej det gör det inte. Det de kallar "naive decision theory" ÄR just Expected Value, inte någon variant av det (läs noga!). Deras sätt att "lösa" paradoxen är att introducera avklingande marginalnytta. Det har inget alls att göra med att det "för eller senare måste komma en krona", ett sådant påstående sänker ju snarast EV. Var snäll och redovisa din beräkning.

Som senare sagt så baserar sig allt detta på min tidigare uppfattning av att man skulle dubbla sin insats efter varje slant, men nu när jag blev mer införstådd med vad St Petersburg-"paradoxet" var så kan det jag nyss skrev däremot bevisa varför man går exakt EV +-0 om man satsar på rött hela tiden på ett roulettbord utan grön ruta och dubblar hela tiden... St Petersburg"paradoxet" har lite eller inget med roulette att göra. Hehe det är hur lätt som helst att bevisa att att EV blir +-0 för den taktiken. EV räknas ju ut genom att ta (Konsekvens av vinst * Sannolikhet för vinst) - (Konsekvens av förlust - Sannolikhet för förlust) OK ta t.e.x. exemplet som de själva har angett i wikipedia: Här har vi förs konsekvens och sannolikhet av vinst i de 4 olika leden: Vinna med en gång: Chans 0,50 Konsekvens +1 ((2*1)-1) Produkt (Chans*konsekvens) = 0,50 Vinna efter två gånger: Chans 0,25 Konsekvens +1 ((2*2)-2-1) Produkt (Chans*konsekvens) = 0,25 Vinna efter tre gånger: Chans 0,125 Konsekvens +1 ((4*2)-4-2-1) Produkt (Chans*konsekvens) = 0,125 Vinna efter fyra gånger: Chans 0,0625 Konsekvens +1 ((8*2)-8-4-2-1) Produkt (Chans*konsekvens) = 0,0625 Summan av de fyra ledernas nettovinst blir såldeds 0,5+0,25+0,125+0,625 = 0,9375 Sen var det dags för minuenden, nämligen (Konsekvens av förlust - Sannolikhet för förlust) Konsekvensen av att man inte vinner de 4 första gångerna är ju naturligtvis att man förlorar allt man satsat, nämligen 1+2+4+8 = 15 Sannolikheten för detta är ju (1/2)^4 = 0,0625 Produkt (Chans*konsekvens) = 15*0,0625 = 0,9375 Nettoresultat blir 0,5+0,25+0,125+0,0625-0,9375 = 0 ALLTSÅ man har ingen förväntad vinst. Sen kan man med induktionsbevis visa att detta gäller för alla n, där n är hur många gånger man väljer att dubbla före man ger sig. Detta är enkel matte. Det är inte ens universitetsnivå ju! =) Som senare sagt så baserar sig allt detta på min tidigare uppfattning av att man skulle dubbla sin insats efter varje slant, men nu när jag blev mer införstådd med vad St Petersburg-"paradoxet" var så kan det jag nyss skrev däremot bevisa varför man går exakt EV +-0 om man satsar på rött hela tiden på ett roulettbord utan grön ruta och dubblar hela tiden... St Petersburg"paradoxet" har lite eller inget med roulette att göra.

Nej tyvärr, Martingale fungerar inte =(

Jag förstår inte vad du vill säga med det du nu skriver... Kan du inte vara vänlig att pröva förklara lite mer konkret?

quote="sulla"quote="Nickefik"quote="sulla"]Kan jag med logikens hjälp inte se hur vi kan missa att hamna en plus./quote Precis. Men som Gdaily sa, det är ju ointressant om både vi och casinot har oändligt med pengar, för då har vi ju redan så pass mycket pengar att vinst eller förlust gör varken till eller från. Först när man inför möjligheten till att ha en oändlig kredit blir det intressant. Sant, men det går att presentera en faktisk summa som skulle göra risken att torska allt så obefintligt liten att ingen människa på denna jord underhela sin livstid skulle ens behöva vara orolig att det utfallet skulle drabba dem. Men då snackar vi sjukt stora summor. Ja det är det som är problemet. Vi pratar om sjuk stora summor. Problemet med de sjukt stora summorna är INTE först och främst det praktiska faktum att man inte kan ha så mycket pengar... Nej nej, det kan vi se bort ifrån... låt oss säga att vi faktiskt hade oändligt med pengar. Även då är det ett problem att vi pratar om så sjukt stora summor eftersom summan blir så stor att den växer snabbare mot oändligt än vad chansen för att inte vunnit går mot 0 omvänt proportionellt... Det är det som är problemet med den sjukt stora summan, huruvida man har oändligt med pengar och tid ändrar inte på det faktum. PUNKT =) mvh Daniel Pedersen

Detta spelar dock ingen roll eftersom: (Konsekvensen av att vinna * Chansen för att Vinna) << (Konsekvensen av att förlora * Chansen för att förlora) med << menas mycket mindre än ty 1*(1-(19/37)^219000) << (((2^219000)-1)*((19/37)^219000)) ty 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Precis. Men som Gdaily sa, det är ju ointressant om både vi och casinot har oändligt med pengar, för då har vi ju redan så pass mycket pengar att vinst eller förlust gör varken till eller från. Först när man inför möjligheten till att ha en oändlig kredit blir det intressant. Nej anledningen till att det är ointressant hur mycet pegar ni har, är att jag utfyllande redan bevisat i denna råden varför en sådan vinstgaranti aldrig kan komma (även om man dubblar i oändigheten). Tänk dig en gräshoppa som sitter på en två meter lång tumstock. Först sitter han vid 0cm (2 meter från målet som är när tumstocken slutar). Sen säger gräshoppan så här: "Nu kom jag på en rolig lek, jag ska hoppa halva avståndet som jag har kvar av tumstocken och sen hoppa hälften av det avståndet jag ahr kvar då osv.... Även om gräshoppan hoppar oändligt många gånger, så kommer han ju aldrig att komma fram de 2 meterna... Men visst han kommer att komma jääälvigt nära =) men det spelar ingen roll, han kommer ALDRIG att komma fram. Det är exakt samma princip med utvecklingen av chansen för att inte ha fått händelsen P med sannolikheten P(P) om man upprepar den N gånger. Så länge P(P) är ett tal större än 0 men mindre än 1, kommer P(P)^n där n går mot oändligt alltid GÅ mot 0, precis som gräshoppan hoppar mot 2 meter, men precis som gräshoppan så kommer utvecklingen aldrig att faktiskt nå 0, med andra kommer vi aldrig vara helt säkra på att ha vunnit... 1 hopp 1,000000000 Meter 2 hopp 1,500000000 Meter 3 hopp 1,750000000 Meter 4 hopp 1,875000000 Meter 5 hopp 1,937500000 Meter 6 hopp 1,968750000 Meter 7 hopp 1,984375000 Meter 8 hopp 1,992187500 Meter 9 hopp 1,996093750 Meter 10 hopp 1,998046875 Meter 11 hopp 1,999023438 Meter 12 hopp 1,999511719 Meter 13 hopp 1,999755859 Meter 14 hopp 1,999877930 Meter 15 hopp 1,999938965 Meter 16 hopp 1,999969482 Meter 17 hopp 1,999984741 Meter 18 hopp 1,999992371 Meter 19 hopp 1,999996185 Meter 20 hopp 1,999998093 Meter 21 hopp 1,999999046 Meter 22 hopp 1,999999523 Meter 23 hopp 1,999999762 Meter 24 hopp 1,999999881 Meter 25 hopp 1,999999940 Meter 26 hopp 1,999999970 Meter 27 hopp 1,999999985 Meter 28 hopp 1,999999993 Meter 29 hopp 1,999999996 Meter 30 hopp 1,999999998 Meter

Du påstår här att man ALLTID förr eller senare kommer at vina. Då är min fråga, om det finns en sådan garanti, måste det även finnas ett ta n, sådant att n antal födubblingar garanterar vinst Hur många gånger menarduman måste fördubba för att vara 100% säker?

Vilken serie är mer trolig? R= Röd S= Svart SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSS Eller samma antal spinn men där det finns minst ett R någonstans. Håller du inte med om att jag kommer att gå vinnande från sessionen om jag får spela enligt de förutsättningar jag satte upp i mitt scenario? Svara på exakt den frågan. Hej Nickefik. Ja det är mycket mer troligt att det finns mitt ett R någonstans (pga permutationsutvecklingen). Det är jag helt enig med dig i. Sen till den andra frågan, som jag ska svara exakt på: Nej, du kommer inte nödvändigtvis gå vinnande från sessionen eftersom det inte finns något tal n, där n är antal fördubblingar man gör, som 100% garanterar att man kommer att ha vunnit. Visst är de löjligt sannolikt att du kommer att vinna, men detta spelar ingen roll eftersom det faktum av att konsekvensen av att om du ändå inte skulle vinna växer snabbare omvänt proportionellt. Sen kan du säga, ja men då dubblar jag ju bara vidare tills jag vinner... men då säger ja: Ja men det ändrar inte på det faktum som jag nyss skrev... tyvärr =)

Jag har inte påstått någonting sådant, det enda jag har sagt att det finns processer som inte går mot sitt EV när man kör dem oändlig tid, d.v.s. icke-väntevärdesriktiga processer. Om detta är en sådan process har jag inte någon aning och har förmodligen supit bort den kunskap som krävs för att bevisa/motbevisa det. Kan du gå med på att det finns sådana processer? Om det finns en sådan process så beror det på en enda sak: EV är felberäknad

Nja, han påstår att man alltid måste hamna på ett positivt utfall förr eller senare. Det är ju en helt annan sak än +EV. Ja förlåt jag skrev fel. Menade naturligtvis: Jo det är det, tyvärr. Du påstår att man ALLTID måste hamna på plus förr eller senare

Det ni tycks glömma är att det ni faktiskt måste kunna bevisa för att det ska vara relevant i detta sammanhang, är att man ALLTID kommer för eller senare att hamna på EV+... Lycka till! Ok, men det här behöver ju inte nödvändigtvis vara sant i så fall? Japp Jo det är det, tyvärr. Du påstår att man ALLTID måste hamna på EV+ förr eller senare

Det ni tycks glömma är att det ni faktiskt måste kunna bevisa för att det ska vara relevant i detta sammanhang, är att man ALLTID kommer för eller senare att hamna på EV+... Lycka till!

Ja men för att ditt påstående skall vara relevant i denna sammanhangen måste du kunna bevisa att man alltid kommer att hamna på plus. Lycka till, nobelpriset väntar om du klarar detta, samt att tusentals matematiker antagligen kommer att ta sitt eget liv om du klarar att bevisa det Jag är alldeles för matematiskt rostig för att ens göra ansatsen till ett bevis, men jag tror verkligen du blandar ihop begreppen här. Skulle jag visa att roulette gick att göra till ett +EV-spel, ja då skulle nog hela matematiken rasa samman. Men att påstå att man med ett oändligt antal möjliga försök förr eller senare pga varians alltid kommer att landa på plus oavsett om spelet är -EV, det är en HELT annan sak. Förstår inte helt exakt vad du menar nu, förtydliga gärna det sista avsnittet du nyss skrev

Jo, och det behövs ju inte ens det. Det räcker med att prova att sätta en gräns (säg 573 st svart, där är det stopp) och konstatera att det alltså skulle innebära att det ALLTID blev rött på det 574e försöket. Då tänjer man liksom lite på fysikens lagar om inte sannolikhetsteorins Det är ju just det du nyss skrev som är ett induktionsbevis (om än ett inverterat sådant) =) Men bra att vi är eniga i allafall =)