Step-by-step · Step-by-step · 6 minute

Step-by-step: di two-dozen strategy fi roulette

Ten dolla pon each a two dozen, 24 numba cover, fi fifty spin. Di roulette two dozens strategy a di coverage bet weh win two spin inna tree an still cost 2.70%.

Short ansa

A simulate session a 50 spin wid $10 pon di fus an second dozen. Thirty-one win a $10, nineteen loss a $20 (third dozen or zero). Net −$70, afta wi did up $90. Di bet weh feel safe cause it win often, an it price exactly like evry odda one.

evry spin
$20 pon 1–12 an 13–24
cover
24 outta 37
p(win)
64.9%
expected evry spin
−$0.54

Di plan: di roulette two dozens strategy

$10 pon di fus dozenbet demDozen1–12, 13–24 or 25–36, pay 2:1.Read di whole ting → an $10 pon di second. A numba fram 1 to 24 pay one dozen $20 an lose di odda $10: +$10. A numba fram 25 to 36, or zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting →, lose both: −$20. Expected valuemathsExpected valueDi average result pon evry bet inna di long run. −1/37 a di stake fi evry standard European bet.Read di whole ting →: (24 × 10 − 13 × 20)/37 = −20/37 = −$0.54 evry spin, an dat a 2.70% a $20. Win rate 64.9%, an a dat figure sell di bet.

Spin 1–25

Eighteen win, seven loss: +$180 − $140 = +$40. Di seven loss include zero one time an a run a tree third-dozen numba at spin 11–13 weh cost $60 back to back an feel like di exception. It did jus a di 35.1% a come inna a bunch, an bunch a wah dem do.

spininna 1–24inna 25–36 or 0netbalance
1–1073+$10+$10
11–1303−$60−$50
14–25111+$90+$40
Tree numba inna a row fram di dozen weh nuh cover cost $60: di 35% a come inna a bunch.

Spin 26–50

Thirteen win, twelve loss: +$130 − $240 = −$110. Twelve loss inna 25 spin a a 20% ting, nuh rare. Final −$70; top +$90 at spin 31. Di bet neva gi a big swing nuh way, cause di win a $10 an di loss $20; it jus grind.

Dis session an nine more like itresult versus di start
+$530$0−$500+$190−$2500125250375500spinresult
1,000 session × 500 spin · violet p10/p25/p75/p90, light blue median, 82 faint sample · move ova di chart fi see di quantile dem at a spin
  • p10 −$500
  • p25 −$500
  • median −$280
  • p75 −$40
  • p90 +$170
1,000 session × 500 spin · y-axis cut to di 1st–99th percentile (di extreme dem: −$500 to +$980) · 500 spin · $20 base · two dozen
Two dozen at $20 total: +$10 two spin inna tree, −$20 one spin inna tree. Low variance; di average line slope at −$0.54 a spin, di same slope as $20 pon red.

Di account

Total bet $1,000 ova 50 spin. Expected lossmathsExpected lossExpected value times all di money yuh bet; di average amount yuh lose ova a session or a period (di loss yuh fi expec pon average).Read di whole ting → $27; actual −$70, bout one standard deviationmathsStandard deviationDi square root a variance; ow far a result usually deh fram di expected value.Read di whole ting → below (σ evry spin a bout $14, suh bout $100 ova 50 spin). Di same $20 pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → woulda have di same expectation an a bigger σ, bout $140 ova di session: two dozen a a lower-variancemathsVarianceA measure a ow wide di result dem spread roun di expected value. High fi straight up, low fi even-money bet.Read di whole ting → way fi lose di same amount.

Wah di session show

Fi cover 24 numba mek roulette feel like a game yuh usually win, an yuh do: 64.9% a di spin dem. Di payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting → set suh dat di 35.1% weh yuh lose cost twice wah di win dem pay, an di betting layoutgearBetting layoutDi bettin grid weh print pon di table. Nex name: table, felt, cloth.Read di whole ting → tune di ratio to −1/37 a di total stake. Put a chipmoney mattaChipA token weh stand fi a fix amount, weh yuh put pon di betting layout fi mek a bet. Nex name: check.Read di whole ting → pon zero fi “insurance” an di blended edge still a 2.70%, cause di insurance price at 2.70% too. Di page “Problem: Two Dozens and a Chip” work it tru.

Question dem

Two dozen or two column?

Same arithmetic: 24 numba, +1 unitmoney mattaUnitDi base stake weh a system or a playa work wid. Dem describe progression inna unit suh dem work at any table.Read di whole ting → pon a hit, −2 pon a miss. Columnbet demColumnTwelve numba inna one column weh go up an dung pon di betting layout, pay 2:1.Read di whole ting → spread di numba weh cover all ova di wheel; dozen bunch dem up pon di layout. None a dat matter.

Wah bout a chip pon zero?

It cover 25 numba; zero now net +$15 instead a −$20, an it cost $1 evry spin. Di expected value a −$0.57 pon $21, still 2.70%.

64.9% nuh a “most a di time”?

A suh, an di payout size fi match it. Most a di time yuh win $10. Some a di time yuh lose $20. Di average a di house edgemathsHouse edgeDi part a evry stake weh di casino keep pon average: 2.70% inna European roulette.Read di whole ting →.

Sumting fi laugh

Win two spin inna tree. Lose twice as much pon di third. Wah come out a 2.70%.

Win two spin inna tree. Lose twice as much pon di third. Wah come out a 2.70%.

Source dem

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapter 13, roulette.
wi check it 2026-09-28model: European wheel, single zeroow wi work it out ↗source dem ↗