Roulette maths · Inna practice · 7 minute

Di expected loss

Expected value times all wah yuh bet: wah di session cost yuh pon average.

Short ansa

Expected loss = all wah yuh bet × 1/37. Stake $10, 100 spin: $1,000 bet, $27 expected loss. Progression bet more, suh dem lose more.

fi evry $1 yuh bet
$0.027
$10 × 100 spin
$27
$10 × 50/hour
$13.50 a hour
fi a year, evry week
≈ $700

Turnover, nuh bankroll

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 → depend pon ow much money pass cross di table, nuh pon ow much yuh bring. A $100 bankrollmoney mattaBankrollAll di money yuh set aside fi play. Fi manage yuh bankroll mean yuh decide ow much a it yuh a go risk pon evry bet an evry session.Read di whole ting → weh yuh bet back nuff time can carry $2,000 a turnovermoney mattaTurnoverAll di money yuh bet ova a session or a period, countin di winnins yuh bet again (all di money yuh bet, roun afta roun). Nex name: handle, action.Read di whole ting → an $54 a expected loss; a $10,000 bankroll bet one time pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → carry $10,000 a turnover an $270. Di casino income a a toll pon traffic, an di traffic a evry 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 evry spin.

Di formula

E[loss] = Σ stake / 37. Fi a flat betta dat a stake × spin / 37. Fi a progressionstrategy demProgressionAny rule weh change di stake based pon di result dem weh pass. Negative progression raise it afta loss, positive progression afta win.Read di whole ting → it a di average stake × spin / 37, an di average stake higher dan di base, cause di stake dem climb wen yuh a lose. Martingalestrategy demMartingaleProgression weh double di bet afta evry loss. Look inna di Strategy section fi see wah it do an wah it nuh do.Read di whole ting → fram a $10 base at a $500 limit average bout $28 a spin ova a long session, suh it lose nearly tree time as much as flat $10 bettin, an it nuh change di odds a no single bet.

ow yuh playaverage stakebet ova 100 spinexpected loss
Flat bettin, $10$10$1,000$27
D’Alembert, $10 base≈ $14≈ $1,400≈ $38
Fibonacci, $10 base≈ $17≈ $1,700≈ $45
Martingale, $10 base, $500 limit≈ $28≈ $2,800≈ $75
Flat bettin, $10, pon a la partage table$10$1,000$13.50
Simulated average. Di edge fi evry dollar a 2.70% pon evry row, only nuh di las one.

Flat bettin strategy fi roulette

Speed

Live table run 40–60 spin a hour, casino floor 30–50, speed table 90 or more, RNG table as fast as yuh click. At di same stake, speed a di bigges single lever pon expected loss a hour: fi move fram a slow floor table to a RNG table weh yuh play at 200 spin a hour multiply di cost a di evenin by four, an di odds nuh change.

Expected loss a hour at $10 a spin$ a hour
Casino floor · 40/hour
$10.81
Live table · 55/hour
$14.86
Speed live · 100/hour
$27.03
RNG · 200/hour
$54.05
$ a hour
027.03$54.05
stake × spin a hour / 37. Speed a di bigges lever pon wah a hour cost.

Live roulette versus RNG roulette

Ova a year

A regula weh play two hour a week at $10 pon a 50-spin live table turn ova $52,000 a year an pay bout $1,400 inna expected loss pon a European wheel, $700 pon a French one, $2,700 pon a American one. Di arithmetic dull but di conclusion nuh dull: di choice a wheel an table worth more dan any system by a factor a infinity, cause system worth exactly 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 →.

Expected loss fi a year: 2 hour/week, $10 a spin, 50 spin/hour$
French (even money)
$702
European
$1,405
American
$2,737
Speed table, European, 100/hour
$2,811
$
01405.50$2,811

A game weh worth more dan any bank

Di St. Petersburg game, weh Nicolaus Bernoulli set inna 1713, toss a coin till it land heads an pay $2 if dat tek one toss, $4 if it tek two, $8 if it tek tree, doublin evry time. Evry possible length add $1 to di 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 →, suh pon paper di game worth a amount weh nuh have no end. No bank cyaan pay prize weh nuh have no end, an once yuh cap di prize dem at wah di bank hold, di value drop dung: wid a bank a $1 million di game worth bout $21, wid $1 billion bout $31. Di Martingale a di same game, see fram di odda side. It win one 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 → nearly evry cycle an lose evryting pon a rare long run; widout a limit, di long run dem woulda pay off by bigga an bigga win, an wid one dem nuh pay off, an a dat mek di table limitpon di tableTable limitDi minimum an maximum bet dem allow. Di maximum a weh stop progression weh double up.Read di whole ting → decide ow a Martingale fail, but nuh if it fail.

di bank can pay up tofair price a di game
$100$7.56
$10,000$14.22
$1 million$20.91
$1 billion$30.86
Di fair price a di expected payout wen any prize ova di bank get pay as di whole bank.
Di St. Petersburg game: pon paper it worth a amount weh nuh have no end, but bout $21 once di bank hold $1 million.

Di table limit dem inna roulette

Expected loss nuh di result

Any single session wi different fram it expected loss, nuff time by more dan di expected loss itself. Ova 100 even-money spin at $10, di standard deviationmathsStandard deviationDi square root a variance; ow far a result usually deh fram di expected value.Read di whole ting → a $100 gainst a expected −$27; a winnin session a nutten special. Di expected loss a di price; di 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 → a di packagin; di result pon any one night a a sample a one.

Formula

E[loss] = Σ stake / 37
E[loss a hour] = stake × spin a hour / 37

Question dem

Di casino tek 2.70% a mi buy-in?

No. 2.70% a evryting yuh bet. If yuh bet back yuh winnins, yuh a bet dem again.

A smalla stake always cheaper?

Fi evry hour, yes, at di same speed. Fi evry target yuh reach, no: see risk a ruinmathsRisk a ruinDi probability fi lose di whole bankroll bifo yuh reach a target or a spin count.Read di whole ting →.

Ow comp work?

Casino estimate yuh expected loss fram yuh average bet an di time yuh play, an give back a piece a it as comp. Dem a give back part a di price, dem nuh a give yuh a edge.

Sumting fi laugh

Turnover × 1/37. Di clock deh inna di formula.

Turnover × 1/37. Di clock deh inna di formula.

Source dem

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapter 13, pon roulette.
  2. Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
  3. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
wi check it 2026-09-28model: European wheel, single zeroow wi work it out ↗source dem ↗