Step by Step: One Paroli Run
Ten dollars on black, double am afta every win, and keep am afta three wins one afta di oda. Di reverse Martingale, spin by spin.
One Paroli session wey we simulate for 80 spins. Thirteen losses for di first spin, twenty-four runs wey break, and three triples wey complete and pay $70 each. Net −$160 afta e don go up reach $50. Di system wey dey lose often and win once in a while, for di exact shape wey di arithmetic predict.
Waka through di system
Win dey move one step forward. Loss, or di third win, dey go back to di start.
Stakes and results dey in units of di base bet.
Di Plan
Bet $10 on blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin →. Afta one win, leave di $20 make e ride. Afta di second win, leave di $40 make e ride. Afta di third win, carry di $80 comot and start again with $10. If you lose for anywhere, start again with $10. Every attempt dey risk $10 of our own moni and e go win $70 if black show three times one afta di oda, and dat one dey happen (18/37)³ = 11.5% of di time. We expect about one run wey complete for every nine attempts.
Spins 1–25
R B B R R B R B B R B B R R B R 0 B B B B R B B R. Twelve attempts: four lose for di first spin (−$10 each, one of dem to zerowheelZeroDi one green pocket wey no even-money, dozen or column bet dey cover; na im be di source of di house edge. Dem also dey call am: single zero, 0.Read di whole tin →), three lose for di second spin (−$10 each, becos di $20 na di house moni plus our own), four lose for di third spin (−$10 each, di same way), and one triple complete for spins 18–20 (+$70). Net −$40. Di run wey complete be like proof. Di eleven failures be like notin, and na dat one be di point of di design.
Spins 26–55
Two more triples, for spins 28–30 and 37–39, each one inside run of four blacks wey we cash afta three: di fourth black win di fresh $10 and di next redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → carry di $20. Fifteen attempts, di net for dis stretch na +$10; di running total na −$30; di highest na +$50 for spin 39. Three triples for 27 attempts na di 3.1 wey we expect; for di highest point di session dey $50 up and e be like method.
- p10 −$780
- p25 −$510
- median −$210
- p75 +$90
- p90 +$370
Spins 56–80
Thirteen losing attempts one afta di oda, nine of dem for di second or third spin, where di ride end one or two blacks short. Net −$130 for dis stretch; di final na −$160. Dis streak of failures get probabilitymathsProbabilityDi chance of one outcome, from 0 to 1 or from 0% to 100%. One number: 1/37 = 2.70%.Read di whole tin → of about 20%, and dat one mean sey e go happen to ParolistrategyParoliPositive progression: double afta you win, start again afta you lose or afta three wins one afta di oda. Dem also dey call am: reverse Martingale.Read di whole tin → player about every fifth session of dis length.
Di Accounts
Di total wey we bet na $1,460 for 80 spins, compared to $800 for person wey dey bet flat $10: di rides dey add turnovermoniTurnoverDi total moni wey you bet for one session or one period, including winnings wey you bet again. Dem also dey call am: handle, action.Read di whole tin →. Expected lossmathsExpected lossExpected value times di total moni wey you bet; di average amount wey you go lose for one session or one period.Read di whole tin → on $1,460 na $39; wetin happen, −$160, dey small pass one standard deviationmathsStandard deviationSquare root of variance; di normal distance between one result and di expected value.Read di whole tin → below, notin strange. Di person wey dey bet flat for our side get di same expectation for every dollar and result wey swing about half as much.
Wetin Di Session Show
Paroli na MartingalestrategyMartingaleProgression wey dey double di bet afta every loss. Check di Strategy section to see wetin e dey do and wetin e no dey do.Read di whole tin → wey dem turn upside down: e dey lose one unitmoniUnitDi base stake wey system or player dey work with. Dem dey describe progressions in units so dat dem go fit work for any table.Read di whole tin → most of di time and win seven units once in a while, instead of to win one unit most of di time and lose sixty-three once in a while. Di distribution no dangerous like dat becos di big number na win, no be loss, and di stake never pass $40, wey only $10 of am na our own. Di expected loss for every dollar no change. Na di better system for player wey want variancemathsVarianceOne measure of how wide di results dey spread around di expected value. E high for straight up, e low for even-money bets.Read di whole tin → without cliff, and e still dey cost 2.70% of turnover.
Questions wey pipo dey ask
Four one afta di oda na 5.6% and e dey pay $150. Di target na just to taste; di edge na di same for every target.
No. Afta one win, di $20 wey dey di table na your own. Paroli dey feel cheap becos when you lose ride, e no be like sey you lose your own moni. But na your own moni.
Di same expectation, smaller maximum stake, no table-limit cliff. E better for every way except di one wey matter, and dat one no change.
Small laugh
Lose small often, win big once in a while. Di reverse of Martingale, and di same price.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.