# Roulette %'s

#### Pfeif0

##### New Member
HI,
I am trying to calculate probabilities of a frequency of occurance; what I'm looking for is probably best described by roulette: Say you are playing based on the first 3rd that has a 12/38 chance every time you play. If you use a specific betting strategy 5,10,15,20,30,45,70 etc what is the overall % chances for each; obviously it is 12/38 for the first try, but the next try you win if you hit the first or second time b/c of the betting etc...
Where my problem lies is every time I try to replicate (F9) and count failures or successes I can't figure out how to keep continually adding successes every time a diffferent random number generates. I'm sure there's a simple way to do that but I am hoping ya'll can help me out.
Thanks,
Keith

### Excel Facts

Why are there 1,048,576 rows in Excel?
The Excel team increased the size of the grid in 2007. There are 2^20 rows and 2^14 columns for a total of 17 billion cells.

#### mortgageman

##### Well-known Member
I'm confused here. I don't know much about roulette, but I'm pretty sure that (unlike blackjack) each roll is brand new - independent of the previous roll. Is your game different?

Gene, "The Mortgage Man", Klein

#### Pfeif0

##### New Member
The difference is the amount you bet...if you only bet the same amount it would be the same chance each time...however, if you increase your bet so you still win overall each time you have that many more cahnces to win

#### mortgageman

##### Well-known Member
The difference is the amount you bet...if you only bet the same amount it would be the same chance each time...however, if you increase your bet so you still win overall each time you have that many more cahnces to win

Getting way off topic here, but that's just silly. The casino will have a cap on how much you can bet. Increasing your bet sounds like a variation of doubling your money until you win. It won't work because of the ceiling.

Gene, "The Mortgage Man", Klein

#### West Man

##### Well-known Member

The chances of winning or losing are the same regardless of the bet. Increasing your bet only gives you a chance to lose a larger amount.

It sounds like you are attempting to test a betting strategy where after a win, you revert to a 1 unit bet and after a loss, your bet is larger than your most recent string of losses (for example, double your bet after each loss). You will soon find the error in the strategy. Your bet may excced the table limit or your available cash.

#### Pfeif0

##### New Member
I totally understand what each of ya'll have suggested, but the issue is not that eventually you can't exceed the table limit but what are the % chances for each level you go up on the way to the limit. I'm trying to figure out how to calculate what my chance is for the 3rd, 4th, 5th try etc totally understanding you'd run out of money or hit the cap limit. It's not a 31.58% chance if you only need to hit once out of 5 times with that %. Imagine you had infinate cash and there was no table limit - is there a probability formula you can use to calculate this type of scenario or is there a way in excel to continuously count random number generation each time you hit F9 (or if there's a was to make a cell equal to a variable that would also help)
Thanks,
Keith

#### Joe Was

##### MrExcel MVP

OK, I built you an application to test your theory.

Add this code to a Standard Module, like: Module1.

Then in Row two, one number to a column add the numbers you will be betting on. Note: the code automatically uses both 0 and 00 as possible numbers on the wheel. The application will ask you the number of slots on the wheel, your bet and the total number of spins you will be testing!

To re-run the code you must delete the printed data from row 3 or 4 to the bottom, you can keep your bet-on-numbers.

Sub myRoulette()
'Standard module, like: Module1.
Dim mySpin%, maxNum%, numSpins%, spins%, myNum%, myEnd%, myBetC%
Dim myWinings&, MyLosses&, myWiner&, myLose&, myBet&
Dim myFlagW As Boolean, myFlagL As Boolean
Dim myRng As Range
Dim winNum\$

myEnd = ActiveSheet.Range("IV2").End(xlToLeft).Column

Set myRng = ActiveSheet.Range(Cells(2, 1), Cells(2, myEnd))

If myRng.Count = 0 Then _
MsgBox "In Row 2, one value to a Column, add the numbers you wish to bet on, starting in Column ""A!"""

ActiveSheet.Range("A3").Value = "Spin"
ActiveSheet.Range("B3").Value = "This Bet"
ActiveSheet.Range("C3").Value = "Losses"
ActiveSheet.Range("D3").Value = "Wins"
ActiveSheet.Range("E3").Value = "This Win"
ActiveSheet.Range("F3").Value = "Winning Number"

'Get wheel!
maxNum = InputBox("What is the highest number on the wheel?" & vbLf & vbLf & _
"Note: The last two numbers will be converted to 0 and 00." & vbLf & _
"So, for 1 to 36 with 0 and 00, enter 38!", "Numbers to use!", 38)

'Get bet!
myBet = InputBox("What amount to add to the amount bet each spin?", "Enter bet pattern!", 5)
myBetC = myBet

'Get Number of spins/bets to make!
numSpins = InputBox("How many spins will you be making?", "Get Spin Cycles!", 100)

For spins = 1 To numSpins
'Initialize random-number generator.
Randomize
'Get random number for spin.
mySpin = Int((maxNum * Rnd) + 1)

'Get winning number!
If mySpin = maxNum - 1 Then
winNum = "0"
ElseIf mySpin = maxNum - 2 Then
winNum = "00"
Else
winNum = mySpin
End If

'Get win or loss!
For Each Cell In myRng
If mySpin = maxNum - 1 And Cell.Value = 0 Then
myWiner = (myBet * (((myRng.Count / maxNum) / 2) * 100)) - ((myRng.Count - 1) * myBet)
ActiveSheet.Range("D" & 4 + spins).Value = "Win"
ActiveSheet.Range("E" & 4 + spins).Value = myWiner
myFlag = True
ElseIf mySpin = maxNum - 2 And Cell.Value = "00" Then
myWiner = (myBet * (((myRng.Count / maxNum) / 2) * 100)) - ((myRng.Count - 1) * myBet)
ActiveSheet.Range("D" & 4 + spins).Value = "Win"
ActiveSheet.Range("E" & 4 + spins).Value = myWiner
myFlag = True
ElseIf mySpin = Cell.Value Then
myWiner = (myBet * (((myRng.Count / maxNum) / 2) * 100)) - ((myRng.Count - 1) * myBet)
ActiveSheet.Range("D" & 4 + spins).Value = "Win"
ActiveSheet.Range("E" & 4 + spins).Value = myWiner
myFlagW = True
Else
myLose = myLose + myBet
ActiveSheet.Range("C" & 4 + spins).Value = "Lose"
myFlagL = True
End If
Next Cell

ActiveSheet.Range("A" & 4 + spins).Value = spins
ActiveSheet.Range("B" & 4 + spins).Value = myBet
myBet = myBet + myBetC
If myFlagW = True Then myWinings = myWinings + myWiner
If myFlagL = True Then MyLosses = MyLosses + myBet
ActiveSheet.Range("F" & 4 + spins).Value = winNum

myFlagW = False
myFlagL = False
Next spins

MsgBox "You spent: \$" & MyLosses & vbLf & _
"You won: \$: " & myWinings & vbLf & _
"Your profit is: \$" & myWinings - MyLosses

End Sub

#### Pfeif0

##### New Member
great..thank you for all your work!

#### chicagodiceman

##### Active Member
A quick note on the theory that you are trying to prove. As Mortgageman stated, each roll is independent and not affected by the previous roll. Your theory is a variation of the Martingale theory proposed for gambling on table games. Although, a true Martingale requires you to double your bet each time (5, 10, 20, 40, 80, 160...). True to what Mortgageman said, you will eventually hit the table limit and cannot recover all of your wager.

The bet you are referring to (either column or "third" of the layout) pays 3 to 1. With this payout schedule, you are at a 5.3% disadvantage (or house advantage).

Your theory has been tested in millions of iterations and it is a guaranteed loser. As your betting schedule doesn't actually "double" your wager each time, it should be slightly worse in the long run.

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