Chance of outcome....

[motilulla]

Using Excel 2010

Hello experts, today I have a question about chance of outcome “black in %” after losing in n times (for example 5 times continuously) bet on red, within 36 amount of times betting.

I do not have any idea, please guide with an example. Thank you all in advance.

Regards,
Moti

 

[StephenCrump]

Your question isn't clear, so I am only guessing this is what you mean?

(Assuming a roulette wheel with 18 black, 18 red and one zero, hence 18/37 probability of a win betting on black/red)

	A	B	C	D	E
1	p	48.65%
2
3	Spins (N)	Probability lose N-1 times, win on Nth spin
4	1	48.65%
5	2	24.98%
6	3	12.83%
7	4	6.59%
8	5	3.38%
9	6	1.74%
10	7	0.89%
11	8	0.46%
12	9	0.24%
13	10	0.12%
14	11	0.06%
15	12	0.03%
16	13	0.02%
17	14	0.01%
18	15	0.00%
19	16	0.00%
20	17	0.00%
21	18	0.00%
22	19	0.00%
23	20	0.00%
24
25		99.9998%
Sheet1

Cell Formulas
Range	Formula
B1	B1	=18/37
B4:B23	B4	=(1-p)^(A4-1)*p
B25	B25	=SUM(B4:B23)

Named Ranges
Name	Refers To	Cells
p	=Sheet3!$B$1	B4:B23

 

[motilulla]

Your question isn't clear, so I am only guessing this is what you mean?

(Assuming a roulette wheel with 18 black, 18 red and one zero, hence 18/37 probability of a win betting on black/red)

StephenCrump, your guess is correct, I was question about roulette also true there is 37 possibility of including zero.

If I understand you mean to say (hence 18/37 probability of a win betting on black/red) if the black come in the row within (N) spin there will be the chance for red to outcome in % as shown or vice versa. Is it correct?

Thank you for your guidance with example. Have a blessed day

Kind Regards,
Moti

 

[StephenCrump]

Sorry, I still don't understand your question. Can you give an example of an outcome where you want to calculate the probability?

My table shows, for example, that there are probabilities of:

- 48.65% of getting a red on the first spin (or vice versa - getting a black on the first spin)
- 24.98% of not getting a red (i.e. getting black or zero) on the first spin, followed by getting a red on the second spin (or vice versa)
- 12.83% of not getting a red (i.e. getting black or zero) on the first two spins, followed by getting a red on the third spin (or vice versa)
- etc

So it can provide the answer to the question: If I keep betting on red, how many spins do I expect it to take until I win?

 

[motilulla]

Sorry, I still don't understand your question. Can you give an example of an outcome where you want to calculate the probability?
So it can provide the answer to the question: If I keep betting on red, how many spins do I expect it to take until I win?

StephenCrump, thanks to you for taking a time and answering of my question.

Sorry for replaying late, just wakeup…for example if within 24 spin results are as following outcomes…what would be the chance of 25th outcome, red or black?

StephenCrump Chance of outcome.xlsm
	A	B	C	D	E
1
2
3
4
5		24-Spins	Results	% Chance
6		1	Red	??
7		2	Red	??
8		3	Black	??
9		4	Red	??
10		5	Red	??
11		6	Red	??
12		7	Black	??
13		8	Red	??
14		9	Black	??
15		10	Black	??
16		11	Black	??
17		12	Black	??
18		13	Black	??
19		14	Red	??
20		15	Red	??
21		16	Black	??
22		17	Red	??
23		18	Red	??
24		19	Red	??
25		20	Black	??
26		21	Red	??
27		21	Red	??
28		23	Red	??
29		24	Black	??
30		25	????	??
31
Sheet1

Kind Regards,
Moti

 

[StephenCrump]

If the winning numbers in successive spins are independent and equally likely (which you can assume to be the case in any "reputable" casino) then the probability of a red or a black in any one spin is 18/37, regardless of what the previous results have been.

In these circumstances, believing that previous results affect the chances of the next result is called the gambler's fallacy, i.e. it's incorrect.

 

[motilulla]

StephenCrump, thanks, perfect got it. What about in case of football teams example if team “Seattle Sounders” paly matches at home or away from home with different teams and the results are following what will be the chance of winning or losing (W-L) in the next 47th game??...as per the previous (W-L) results are shown in the column G.

StephenCrump Chance of outcome.xlsm
	A	B	C	D	E	F	G	H
1
2
3		Game Played At Home			GamePlayed Away From home
4	Match	Seattle Sounders			Seattle Sounders	EM	Team Seattle Sounders
5	Match	Team	Goles	Goles	Team	EM	Win -Loss Result
6	1	Motagua	0	0	Seattle Sounders		L
7	2	Seattle Sounders	5	0	Motagua		L
8	3	Seattle Sounders	0	1	Nashville MLS		W
9	4	Real Salt Lake	1	0	Seattle Sounders		L
10	5	Seattle Sounders	3	0	León		L
11	6	Seattle Sounders	3	2	LA Galaxy		L
12	7	León	1	1	Seattle Sounders		L
13	8	Austin FC	1	1	Seattle Sounders		L
14	9	Minnesota United	1	2	Seattle Sounders		W
15	10	Seattle Sounders	3	1	New York City		L
16	11	New York City	1	1	Seattle Sounders		L
17	12	Seattle Sounders	0	1	Inter Miami CF		W
18	13	SJ Earthquakes	4	3	Seattle Sounders		L
19	14	Pumas UNAM	2	2	Seattle Sounders		L
20	15	Seattle Sounders	3	0	Pumas UNAM		L
21	16	Dallas	2	0	Seattle Sounders		L
22	17	Seattle Sounders	3	1	Minnesota United		L
23	18	Houston Dynamo	0	1	Seattle Sounders		W
24	19	Colorado Rapids	1	0	Seattle Sounders		L
25	20	Seattle Sounders	2	1	Charlotte		L
26	22	Seattle Sounders	4	0	Vancouver		L
27	23	Seattle Sounders	1	1	Los Angeles FC		L
28	24	Seattle Sounders	3	0	Sporting Kansas		L
29	25	Seattle Sounders	1	2	Montreal		W
30	26	Toronto	0	2	Seattle Sounders		W
31	27	Seattle Sounders	0	3	Portland		W
32	28	Nashville MLS	1	0	Seattle Sounders		L
33	29	Chicago Fire	1	0	Seattle Sounders		L
34	30	Seattle Sounders	2	1	Colorado Rapids		L
35	31	Los Angeles FC	2	1	Seattle Sounders		L
36	32	Seattle Sounders	1	0	Dallas		L
37	33	Atlanta	2	1	Seattle Sounders		L
38	34	Seattle Sounders	1	2	Real Salt Lake		W
39	35	LA Galaxy	3	3	Seattle Sounders		L
40	36	Portland	2	1	Seattle Sounders		L
41	37	Orlando	3	2	Seattle Sounders		L
42	38	Seattle Sounders	2	1	Houston Dynamo		L
43	40	Seattle Sounders	3	0	Austin FC		L
44	41	Vancouver	2	1	Seattle Sounders		L
45	42	Seattle Sounders	1	1	Cincinnati		L
46	44	Sporting Kansas	1	0	Seattle Sounders		L
47	45	Seattle Sounders	2	2	SJ Earthquakes		L
48	46	Seattle Sounders	0	1	Al Ahly		W
49
50	47	Austin FC			Seattle Sounders		??
51
52
Sheet2

Kind Regards,
Moti

 

[StephenCrump]

What about in case of football teams example if team “Seattle Sounders” paly matches at home or away from home with different teams and the results are following what will be the chance of winning or losing (W-L) in the next 47th game??...as per the previous (W-L) results are shown in the column G.

Ha ha, that's a little more complicated. I'm not sure an Excel forum is the right place to ask about forecasting football results?

 

[motilulla]

Ha ha, that's a little more complicated. I'm not sure an Excel forum is the right place to ask about forecasting football results?

StephenCrump, thanks, I think your answer is straight, asking about forecasting may my question is incorrect …may I ask what would be the probability % playing 47th game having historical data winning max 3 times and losing max 9 times in the row does this make sense?

Kind Regards,
Moti

 

[motilulla]

StephenCrump, ok if we take your example of post#2 insert column B where is sequence of outcome red/black as shown how will vary the % in column “C” I am not sure whether this would be the correct question or not please help.

StephenCrump Chance of outcome.xlsm
	A	B	C	D	E
1	p		48,65%
2
3	Spins (N)	out come	Probability lose/win N-1 times, win/loss on Nth spin	What would be chance of red/black
4	1	Red	%	<--Chance of Red/Black
5	2	Red	%	<--Chance of Red/Black
6	3	Red	%	<--Chance of Red/Black
7	4	Black	%	<--Chance of Red/Black
8	5	Black	%	<--Chance of Red/Black
9	6	Red	%	<--Chance of Red/Black
10	7	Black	%	<--Chance of Red/Black
11	8	Red	%	<--Chance of Red/Black
12	9	Black	%	<--Chance of Red/Black
13	10	Black	%	<--Chance of Red/Black
14	11	Black	%	<--Chance of Red/Black
15	12	Black	%	<--Chance of Red/Black
16	13	Black	%	<--Chance of Red/Black
17	14	Red	%	<--Chance of Red/Black
18	15	Black	%	<--Chance of Red/Black
19	16	Black	%	<--Chance of Red/Black
20	17	Red	%	<--Chance of Red/Black
21	18	Red	%	<--Chance of Red/Black
22	19	Red	%	<--Chance of Red/Black
23	20	Black	%	<--Chance of Red/Black
24
25			0,00%
26
27
Sheet3

Cell Formulas
Range	Formula
C1	C1	=18/37
C25	C25	=SUM(C4:C23)

Kind Regards,
Moti