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Roulette Wheel

The Math Behind a Roulette Wheel

A Roulette Wheel Has 38 Numbers, 18 Of These Numbers Are Red 18 Of These Numbers Are Black, And Two Of The Numbers Zero And Double Zero Are Green, By The Way, This Description Is Of The American Roulette The European Version Has Just One Green Number. The Most Straightforward Bet In Roulette Is To Bet On One Of The Primary Colours Let’s Say Red Okay So If You Are Going To Bet $1 On Red It’s An Even-Money Bet Which Means That If You Bet $1, Then You’Ll Either Win Or Lose $1 Depending On Whether Or Not a Red Number Appears Here Let’s Say That The Number Appearing On The Wheel Is Red 27. You Know What Your Chances Of Winning Since There Are 38 Numbers Each Of Which Has The Same Chance Of Occurring And 18 Of These Numbers Are Red Are Then The Probability That You Win Is 18 Over 38 Which Is a Little Less Than 50%, You Have a Disadvantage At This Game We Can Quantify This Disadvantage Using The Fundamental Concept Of Expected Value

Expect Value

Expected Value

The Expected Value Of a Bet Is a Weighted Average Of How Much You Can Win Or Lose When You Bet On Red In Roulette You’Ll Either Win $1 With Probability 18 Over 38 Or You’Ll Lose $1, Or You Could Say Win Negative $1 With Probability 20 Over 38 Right Because There Are 18 Red Numbers And 20 Numbers That Aren’t Red Hence Your Expected Value Is One Times 18 Over 38 Plus Negative 1 Times 20 Over 38 That’s Negative Two Over 38 Negative .5 To 6 What This Means Is That On Average You’Ll Lose About 5.3 Cents For Every Dollar That You Bet Now In Roulette You Can Bet On Other Things Besides Colour, For Instance, You Can Bet That a Number Between 1 And 12 Shows Up Here. Let’s Say We Bet a Dollar That One Of The First Twelve Numbers Shows Up The Casino Pays Two-To-One Odds For This Bed Which Means That If You Bet a Dollar And You Win Then The Casino Pays You Two Dollars.


The Casino Pays 35 To 1 Odds Thus When You Make This Bet Then You Either Win $35 With Probability 1 Over 38 Just One Winning Number Out Of All 38 Or You Lose $1 With Probability 37 Over 38 So When You Calculate The Expected Value 35 Times 1 Over 38 Plus Negative 1 Times 37 Over 38 Once Again You Get Negative 2 Over 38 We Still Get Negative 5.3 Cents Interestingly When You Play Roulette Practically Every Bet Has The Exact Same Expected Value Of Negative 5.3 Cents Per Dollar Bet.