Te Hītori o ngā Pūnaha Rūreti
E rua rautau o te tangata e tuhi ana i ngā ture mō te panoni i tana moni peti.

Nō te rautau 18 te Martingale; i tapaina te D’Alembert ki tētahi tohunga pāngarau kāore i pai ki taua pūnaha; ko te Labouchère he mahi ngahau nā tētahi kaitōrangapū o te wā o Wikitōria. Kāore tētahi i whai hua i taua wā anō.
Martingale
Nō te kupu ā-waha petipeti o Provence te ingoa (à la martegalo, “pērā i te iwi o Martigues”, he iwi e rongonui ana mō te kūware) mō tētahi peti whakarearua, ā, kua tuhia ki ngā papakupu Wīwī mai i ngā tau 1760. Ko Thorp (1984), e whai ana i te American Heritage Dictionary, ka hoatu he whakamārama ā-iwi tuarua: i tāwaitia te iwi o Martigues mō ō rātou tikanga rerekē, tae atu ki te here i ō rātou tarau ki muri, nō reira i noho te kīanga hei tikanga mō “i tētahi āhua wairangi”. He kōrero whakatūpato kē i Pārihi i te rautau 18: e whakaahua ana a Casanova i tana ngaronga o tētahi taonga nui i a ia e whakarearua ana i te faro i Venice i ngā tau 1750. Ko te pāngarau o te take e rahua ai, ko te tepe tēputēpuTepe tēpuTe peti iti rawa me te peti nui rawa ka whakaaetia. Ko te tepe nui te mea e aukati ana i ngā kauneke whakarua.Pānuitia katoatia → me te pūtea tākaromoniPūtea tākaroTe katoa o te moni kua wehea mō te tākaro. Ko te whakahaere pūtea tākaro te whakatau i te nui e tūraru ai i ia peti, i ia wā tākaro.Pānuitia katoatia → whai tepe, i mōhiotia i ngā tau 1770. I te ariā tūponotangapāngarauTūponotangaTe tūpono o tētahi putanga, mai i te 0 ki te 1, mai i te 0% ki te 100% rānei. Tau kotahi: 1/37 = 2.70%.Pānuitia katoatia →, i noho a “martingalerautakiMartingaleHe kauneke e whakarua ana i te peti i muri i ia hinga. Tirohia te wāhanga Rautaki mō ōna mahi me ngā mea kāore e mahia e ia.Pānuitia katoatia →” hei kupu hangarau i ngā tau 1930 mō tētahi kēmu tōkekepāngarauKēmu tōkekeHe kēmu kāore he painga ki tētahi taha: he kore te uara tūmanako o ia peti.Pānuitia katoatia →, koinei anō te mea kotahi ehara i te Martingale rūreti.

D’Alembert
I tohe a Jean le Rond d’Alembert i te Encyclopédie (1754) i muri i te raupapa o ngā upoko, ka nui ake te tūpono o te hiku, he kōrero tōmua o te pōhēhē a te kaipetipeti nā tētahi tohunga pāngarau rongonui. Ko te pūnaha peti e tāpiri ana i tētahi waemoniWaeTe moni peti taketake e mahi ai tētahi pūnaha, tētahi kaitākaro rānei. Ka whakaahuatia ngā kauneke ki ngā wae kia hāngai ai ki ia tēpu.Pānuitia katoatia → i muri i te hinga, e tango ana i tētahi i muri i te toa, i tapaina ki tōna ingoa e ngā kaipetipeti o muri mai i whai i taua whakapono. Ehara nāna i tono, ā, i ōna rā pai ake, kua whakakāhoretia e ia.
Labouchère
Ko Henry LabouchèrerautakiLabouchèreHe pūnaha whakakore: tuhia he rārangi tau, petihia te tapeke o ngā pito e rua, whakakorea i muri i te toa, tāpiritia te moni peti kua ngaro i muri i te hinga.Pānuitia katoatia → (1831–1912), he kairīpoata, he rangatira whare tapere, he mema Pāremata Rīpera, nāna i whakarongonui te pūnaha whakakore i te pāpori o Rānana i ngā tau 1870, ā, e ai ki ngā kōrero i whakamahia e ia i Monte Carlo. Ko te tikanga, te tuhi i tētahi rārangi tau me te peti i te tapeke o ngā pito, he tawhito ake i a ia. I mau tōna ingoa nā te mea i rongonui ia mō ētahi atu mea, ā, nā te mea he āhuatanga onge tō te pūnaha, ko te nuinga o te wā ka whai hua, ā, nā tērā i noho ai hei kaupapa kōrero i te tēpu kai.
Ka hinga a Casanova i a ia e whakarearua ana i te faro. He tawhito kē te Martingale.
Ka whakaputaina e D’Alembert te pōhēhē ka mau i tōna ingoa hei pūnaha i muri mai.
Ka uru te “Martingale” ki ngā papakupu Wīwī hei kupu ā-waha petipeti.
Ka whakarongonuitia e Labouchère te whakakore i Rānana.
Ka puta ngā kauneke Fibonacci me Paroli i ngā pukapuka petipeti.
Ka hokona mā te mēra ngā pūnaha “wāhanga” e hāngai ana ki te tahora o te wīra.
Ka whakamatuatia e Halmos, he ākonga a Doob, e kore tētahi pūnaha peti e taea te huri i tētahi kēmu kino hei kēmu pai.
Ka whaihangatia e ngā rorohiko ia pūnaha. Ka whakaatu katoa i te −1/37 o te tapeke peti.
Ko aua pūnaha anō e hokona ana ā-ipurangi me ngā hua ōrite, ka whaihangatia i roto i te pūtirotiro i tēnei pae.
Te rautau 20
I uru te FibonaccirautakiFibonacciHe kauneke e whai ana i te raupapa 1, 1, 2, 3, 5, 8, 13…: kotahi te hīkoi whakamua i muri i te hinga, e rua ngā hīkoi whakamuri i muri i te toa.Pānuitia katoatia → me te ParolirautakiParoliHe kauneke whakarunga i te toa: whakaruatia i muri i te toa, tīmata anō i muri i te hinga, i muri rānei i ngā toa e toru i te raupapa kotahi. Arā anō: Martingale kōaro.Pānuitia katoatia → ki ngā pukapuka petipeti i te takiwā o 1900. I te waenganui o te rautau ka puta ngā pūnaha i hokona mā te mēra, he kōrero whakamihi tō ia mea me te kī taurangi ka whakahokia te moni, me ngā whaihanga rorohiko tuatahi, i whakaatu i te mea kua kīia kē e te pāngarau. Kua kitea kē te whakamatuatanga e kore tētahi pūnaha e whai hua: i whakaatu a Joseph Doob (1936) rāua ko Paul Halmos (1939) e kore tētahi ture mō te kōwhiri āhea, ā, e hia te nui o te peti e panoni i te hua tūmanako o tētahi kēmu tōkeke, kino rānei, ā, i whakatakotoria e te arotake a Thorp i 1969 ngā āhuatanga i te āhua e tūtaki ai ngā kaipetipeti. Mai i tērā wā kāore anō ngā pūnaha kia panoni; kua nuku te whakatairanga mai i ngā pukapuka iti ki te ataata.

Pakiwaitara: He Rautaki Rūreti e Toa Ana i ngā Wā KatoaTe Rautaki Rūreti Fibonacci
He aha i ora tonu ai
Ka hoatu e tētahi pūnaha he mahi mā te kaitākaro me tētahi kōrero hei kōrero. Ko te nuinga o ngā wā tākaro i raro i te nuinga o ngā pūnaha ka mutu ki tētahi toa iti, he kōrero pai ake i te tātai. He onge ake ngā wā tākaro hinga, ā, ka maumaharatia hei waimarie kino. Kāore te whakatairanga e hiahia ana kia teka mō ngā tūpono; me whakaatu noa i tētahi wā tākaro toa, ā, he maha ērā. Ko te tohenga whakahē, ko te 2.70% o te tapeke petimoniTapeke petiTe tapeke o te moni kua petihia i roto i te wā tākaro, i tētahi wā rānei, tae atu ki ngā moni toa kua petihia anō. Arā anō: handle, action.Pānuitia katoatia →, kua wātea mai i 1843, ā, kāore anō kia rite tōna kaha whakapono ki tētahi pō waimarie.
Ngā pūnaha hei hoko
I tāpirihia e te hokohoko o te rautau 20 ōna ake kaupapa, he whakaritenga hou ia mea o aua peti tōraro anō. I hokona te Phase One mō te $25 me te 10% o ngā moni toa a te kaihoko, me te kī taurangi o tētahi Phase Two ina utua te $500, me tētahi “Inner Circle” i te $5,000. Kāore tētahi e panoni i te tātai: ko te uara tūmanakopāngarauUara tūmanakoTe hua toharite mō ia peti i te wā roa. −1/37 o te moni peti mō ia peti Ūropi paerewa.Pānuitia katoatia → o tētahi raupapa peti, ko te tapeke o ō rātou uara tūmanako.
Te mea ehara i te pūnaha
Ngā ture mutu: te whakatau i mua e hia te nui ka ngaro, ka toa rānei, kātahi ka wehe. He maha ngā wā ka hokona hei wāhanga o tētahi pūnaha, ā, ko te wāhanga anake tēnei e whai pānga ana, nā te mea ka whakaiti i te tapeke peti. Kāore he tangata i tapaina ai, ā, e tika ana tērā.
Ngā pātai
Ko te Martingale, kotahi rautau, nui ake rānei. Ko te whakarearua i muri i te hinga te whakaaro tuatahi a te katoa.
Ko D’Alembert te mea i tata rawa, mā te pōhēhē noa. I whakamārama katoa a Pascal, a Fermat, a Huygens, a Bernoulli me Laplace he aha i rahua ai.
Nā te mea ka toa te nuinga o ngā wā tākaro, ā, he iti te utu ki te hanga i tētahi ataata o tētahi wā tākaro toa.
He katakata iti

E rua rautau o ngā ingoa. Kotahi te tau.
Ngā Puna
- 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.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.