Tastratijit Martingale
Tastratijit Martingale n rulit tessnernay rrehn s snat deffir yal lexsara u tettuɣal ɣer rrehn n tazwara deffir rrbeḥ. Yal rrbeḥ yerra-d akk lexsarat yezrin d yiwen n uferdis n tazwara. Asebter-a yesskan-d acu i yettxeddim waya i ugerruj, d acuɣer ur yezmir ara ad ibeddel lexsara yettwaṛǧan.
Amek yeddu unagraw Martingale n rulit?
Texsrem, snernit s snat. Terbḥem, uɣalet ɣer rrehn n tazwara. D wa i d anagraw meṛṛa. S rrehn n tazwara n $10 d talast n ṭṭabla n $500 amyizwer yekfa deffir sḍis n lexsarat. Tagejdit taneggarut d taprubabilit n uwaḍ ɣer tseddart-nni s rrehn s lexlaṣ imsawi, anda yal lexsara tesɛa taprubabilit 19/37.
Rrehn n tazwara $10, talast n ṭṭabla $500. Deffir sḍis n lexsarat, rrehn d-iteddun d $640, nnig talast: anagraw yerreẓ s lexsara n $630. Taprubabilit n sḍis n lexsarat ṭṭafarent ɣef uzeggaɣ d (19/37)^6 = 1,83%, qrib yiwet n tikkelt deg 55 n yiɛraḍen.
Ḍfer anagraw
Lexsara tessnernay rrehn s snat. Rrbeḥ yettuɣal ɣer tazwara.
Rrhun d yigmaḍ s yiferdisen n rrehn n tazwara.
Amek i d-tettban teɣimit?
Tiseddarin timecṭuḥin ɣer d asawen, syin tawwurt n wakal. Deg Martingale n rulit, yal azrar n usnerni s snat i yekfan yerna yiwen n rrehn n tazwara, ihi ajerriḍ yettali s leɛqel. Azrar i yewwḍen ɣer talast n $500 yettekkes $630 deg yiwet n tikkelt: 63 seg tseddarin-nni.
- p10 −$1 000
- p25 −$1 000
- azal n tlemmast −$1 000
- p75 +$930
- p90 +$1 830
Asimulatur
Yal aɣewwar yesselkam 2 000 n tɣimiyin n rrhun s lexlaṣ imsawi seg ugerruj n $1 000. Igmaḍ ttbeddilen imir kan.
Tuget n tɣimiyin kfant s rrbeḥ amecṭuḥ (40,8%), d ayagi i yesseḥmalen. Alemmas ddaw n yilem (−$66,44) acku tiɣimiyin s lexsara meqqrit: anagraw n usnerni yewweḍ ɣer talast n ṭṭabla deg 59,3% n tɣimiyin. Amurar yettrehnen $10 ur nettbeddil deg tuzzyiwin-nni yiwet yettwaṛǧu ad yexser qrib $27.
Acḥal n tikkal i d-yettas uzrar n lexsara
Rrehn s lexlaṣ imsawi ɣef uḍebsi s yiwen yilem yettexsar 19 n tuzzyiwin seg 37. Yal ajerriḍ d taprubabilit ara xesrent akk tuzzyiwin n yiwen uzrar, d wayen yexser ar tura umurar n Martingale, i yessnernayen rrehn s snat deffir yal lexsara.
| lexsarat ṭṭafarent | taprubabilit | qrib 1 seg | lexsara ar tura | rrehn d-iteddun |
|---|---|---|---|---|
| 1 | 51,4% | 2 | $1 | $2 |
| 2 | 26,4% | 4 | $3 | $4 |
| 3 | 13,5% | 7 | $7 | $8 |
| 4 | 7,0% | 14 | $15 | $16 |
| 5 | 3,6% | 28 | $31 | $32 |
| 6 | 1,8% | 55 | $63 | $64 |
| 7 | 0,94% | 106 | $127 | $128 |
| 8 | 0,48% | 207 | $255 | $256 |
| 9 | 0,25% | 403 | $511 | $512 |
| 10 | 0,13% | 784 | $1 023 | $1 024 |
| 11 | 0,065% | 1527 | $2 047 | $2 048 |
| 12 | 0,034% | 2974 | $4 095 | $4 096 |
| 13 | 0,017% | 5792 | $8 191 | $8 192 |
| 14 | 0,0089% | 11279 | $16 383 | $16 384 |
| 15 | 0,0046% | 21965 | $32 767 | $32 768 |
Taprubabilit d 19/37 yettwasgeten s yiman-is yiwet n tikkelt i yal lexsara, seg yiwet n tuzzya yettwafernen. Taɣimit taɣezfant tesɛa aṭas n tuzzyiwin anda yezmer ad yebdu wazrar am wa, ihi deg yiwet n tmeddit taprubabilit-is tugar aṭas ayen i d-yesskan yiwen ujerriḍ.
Azrar n xmesṭac n lexsarat yettas-d qrib yiwet n tikkelt deg 22 000 n yiɛraḍen. Yettban ulac lxeṭṛ. Mačči akka, s sin n ssebbat. Yal tuzzya tebda aɛraḍ amaynut, u tameddit tesɛa timiḍiyin n tuzzyiwin. U ulac win ara yawḍen ɣer xmesṭac: seg rrehn n tazwara n $10, talast n $500 tḥebbes asnerni s snat deffir sḍis n lexsarat, i d-yettasen qrib yiwet n tikkelt deg 55 n yiɛraḍen.
Acuɣer ur yezmir ara ad ibeddel tiprubabiliyin?
Azal yettwaṛǧan yettemrennu. Ma yella yal rrehn iman-is yesɛa ayen yettwaṛǧan n −2,70% n wadrim-is, ihi yal amyizwer n rrhun, akken yebɣu yili ufran n rrhun, yesɛa ayen yettwaṛǧan n −2,70% n umatu yettwarehnen. Afran n rrehn yezmer ad yebnu ɣef yigmaḍ yezrin; ur yezmir ara ad yebnu ɣef win d-iteddun.
bᵢ yettwafren qbel tuzzya i; Xᵢ = ±1 d amanay ɣef bᵢ
Tikta yettwassnen ur nṣeḥḥa ara
Taḍsa i usgunfu
Aṭas n rrbeḥ amecṭuḥ, yiwet n lexsara tameqqrant tura d tura. U d kunwi i yettxelliṣen.
