Variance: ow far di result dem swing
Wah mek a straight up an a red bet wid di same 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 → feel like two different game.
Variance measure ow far di result dem spread out roun di expected value. Fi evry unit yuh stake, it a bout 34 fi a straight up an bout 1 fi red.
Di formula fi one bet
Fi a bet weh pay W to 1 wid probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → p, di result fi evry 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 → a +W wid probability p an −1 wid probability 1 − p. 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 → a pW − (1 − p) = −1/37. 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 E[X²] − EV² = pW² + (1 − p) − (1/37)². Fi a straight upbet demStraight upOne single numba, pay 35:1.Read di whole ting →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. Fi redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Wah it mean fi a session
Variance add up cross independent spinmathsIndependent spinEvry spin have di same probability dem, nuh matta wah happen bifo (one spin nuh know bout di nex one). Di base fi evry calculation pon dis site.Read di whole ting →, suh ova N spin at a fix stake, di variance a di total a N × stake² × σ², an di standard deviationmathsStandard deviationDi square root a variance; ow far a result usually deh fram di expected value.Read di whole ting → a σ × stake × √N. 100 spin at $10: di standard deviation a bout $584 fi straight up an $100 fi red, roun di same expected −$27. One playa see di result dem swing by hundreds; di odda one see a soft drift. Both a pay di same price.
Variance an system
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 → nuh change di EV fi evry unit yuh bet, but it change both ow much yuh bet an di shape a di distribution. 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 → bring dung di variance a most session (nuff likkle win) an add a fat tail (di rare big loss); di total variance cross all session higher dan fi flat bettinstrategy demFlat bettinFi bet di same amount evry spin. Di baseline weh dem compare evry progression gainst.Read di whole ting → cause a dat tail. Parolistrategy demParoliPositive progression: double afta a win, start ova afta a loss or afta tree win straight. Nex name: reverse Martingale.Read di whole ting → do di opposite. Fi pick a system a fi pick a variance profile; di average nuh deh pon di menu.
- p10 −$500
- p25 −$500
- median −$500
- p75 +$40
- p90 +$1,120
Flat bettin strategy fi rouletteParoli strategy fi roulette (reverse Martingale)
Wah mek it matta to a playa
A variance mek short session hard fi predict an long one easy fi predict. Wid σ = $100 an EV = −$27 ova 100 spin, di edge a one quarter a di noise an a winnin session a normal ting. Ova 10,000 spin di EV a −$2,700 an σ a $1,000; now di edge nearly tree time di noise an a winnin run a tree-sigma event. Variance a di playa fren inna di short run an di house fren inna di long run.
Variance a a mix a bet
Fi nuff bet pon di same spin, di result dem link up (a hit pon 17 a also a hit pon blackbet demBlackEven-money bet pon di 18 black numba. Inna French: noir.Read di whole ting → an di second dozenbet demDozen1–12, 13–24 or 25–36, pay 2:1.Read di whole ting →), suh yuh cyaan jus add up di variance dem. Di Bet Builder tool work out di exact distribution fi any set 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 → by goin tru all 37 result, an dat a di only correct way fi do it.
Formula
Question dem
No. Evry bet have di same expected value. Higher variance mean bigger swing roun it.
Even-money betbet demEven-money betRed/black, odd/even, high/low. 18 numba, pay 1:1.Read di whole ting →, at σ ≈ 1 fi evry unit. Even lower wid la partagerule demLa partageFrench rule: wen zero hit, half a di even-money stake come back. It cut di house edge pon dem bet deh inna half, to 1.35%.Read di whole ting →, weh mek di average betta too.
Di expected profit a di same fi evry dollar; variance only change ow lumpy di casino income come, an a casino have tousands a playa fi smooth it out.
Fun wid maths
Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.
Two playa each bet $1 a spin fi 100 spin pon a European wheel, one always pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting →, di odda one always pon 17. Who more likely fi deh ahead at di end?
Show di ansa
Ansa Di playa pon 17: 50.9%, gainst 35.5% fi red. Both a dem lose $2.70 pon average.
Red: di playa deh ahead wid 51 or more win outta 100, each one wid probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → 18/37. Di binomial distribution give 35.5%, an exactly 50 win, weh break even, anodda 7.7%.
Numba 17: each win return $36, suh two win (−$28) nuh enough an tree (+$8) enough. Di chance a tree or more hit inna 100 spin at 1/37 a 50.9%.
Di straight-up playa deh ahead more often, but di result dem lumpier: one hit more or less move di result by $36, an di playa dem weh deh behind usually deh furtha behind. Bollman (2024) give di American figure dem, 26.5% an 49.2%.
Sumting fi laugh
Same expected loss. One a dem tell yuh bout it loud.
Source dem
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.