On average, how many trials will it take to see a streak of...? 8 Qs for fun

I have been asked and have heard these type of questions for the games I play, mainly, Baccarat, Roulette and Craps.
Seems that most gamblers want to know "how many spins" or "how many dice rolls" or "how many hands" until a losing streak or a winning streak is seen on average.
I would rather show the theoretical distribution but that goes over most people's heads.

So, averages here we come.

So, for now, here are some tables to the questions below.
Later I will add the formulas, they are already in another thread see On average how many trials will it take to lose 2 in a row on a 50/50 game of chance?, and some good Wizard links.
mean recurrence time formula
((p^-n)-1)/(1-p) or =(1/(p^n)-1)/(1-p)
p = prob
n = run length
All data in each table is in the form of 1 in X (1/p)

American Double Zero Roulette

First question.
1. On average how many spins will it take (or the average wait time) to lose 6 in a row betting "red" in American Double Zero Roulette?

hint: the correct answer is NOT 1/(20/38)^6 or 1 in 47.04

Why not?
because that is the answer for this question:
What is the probability of losing 6 in a row in 6 spins betting "red" in American Double Zero Roulette?
We are looking for the average number of spins it can take to lose 6 in a row.

2. On average how many spins will it take (or the average wait time) to win 4 in a row betting "black" in American Double Zero Roulette?
That would make a nice parlay!

streak	50/50	20/38	18/38	26/38	12/38	18/37	19/37
1	2.00	1.90	2.11	1.46	3.17	2.06	1.95
2	6.00	5.51	6.57	3.60	13.19	6.28	5.74
3	14.00	12.37	15.98	6.72	44.95	14.97	13.12
4	30.00	25.40	35.84	11.28	145.51	32.82	27.51
5	62.00	50.16	77.77	17.95	463.93	69.52	55.51
6	126.00	97.21	166.30	27.70	1,472.29	144.95	110.05
7	254.00	186.60	353.18	41.94	4,665.42	300.01	216.25
8	510.00	356.43	747.72	62.76	14,776.99	618.75	423.07
9	1,022.00	679.12	1,580.64	93.19	46,796.98	1,273.94	825.81
10	2,046.00	1,292.23	3,339.01	137.67	148,193.61	2,620.70	1,610.11
11	4,094.00	2,457.13	7,051.13	202.67	469,282.92	5,389.06	3,137.43
12	8,190.00	4,670.44	14,887.83	297.67	1,486,065.76	11,079.56	6,111.68
13	16,382.00	8,875.74	31,431.97	436.51	4,705,878.08	22,776.70	11,903.64
14	32,766.00	16,865.81	66,358.48	639.44	14,901,950.42	46,820.83	23,182.72
15	65,534.00	32,046.93	140,092.24	936.03	47,189,512.82	96,244.88	45,147.25
16	131,070.00	60,891.08	295,752.40	1,369.50	149,433,460.42	197,838.75	87,920.27
17	262,142.00	115,694.94	624,368.29	2,003.04	473,205,961.17	406,670.59	171,215.11
18	524,286.00	219,822.30	1,318,112.94	2,928.99	1,498,485,546.89	835,936.05	333,420.85
19	1,048,574.00	417,664.26	2,782,684.98	4,282.29	4,745,204,234.97	1,718,315.04	649,295.19
20	2,097,150.00	793,564.00	5,874,559.28	6,260.19	15,026,480,080.59	3,532,094.08	1,264,418.89

Craps
can you find the correct answer?
3. On average, how many pass line bets will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps?

4. On average, how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps? This one is a challenge.
added: see 7Craps post below for the solution

5. On average, how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "the Field" in Craps?

6. On average, how many dice rolls will it take (or the average wait time) to win 3 in a row betting "the Field" in Craps?

streak	pass line bet(244/495)	any pass line point(201/495)	16/36	20/36	6/36	30/36
1	2.03	2.46	2.25	1.80	6.00	1.20
2	6.14	8.53	7.31	5.04	42.00	2.64
3	14.49	23.46	18.70	10.87	258.00	4.37
4	31.43	60.25	44.33	21.37	1,554.00	6.44
5	65.79	150.83	102.00	40.27	9,330.00	8.93
6	135.50	373.91	231.74	74.28	55,986.00	11.92
7	276.92	923.27	523.67	135.50	335,922.00	15.50
8	563.82	2,276.20	1,180.51	245.70	2,015,538.00	19.80
9	1,145.84	5,608.02	2,658.41	444.06	12,093,234.00	24.96
10	2,326.58	13,813.27	5,983.66	801.11	72,559,410.00	31.15
11	4,721.93	34,020.21	13,465.49	1,443.79	435,356,466.00	38.58
12	9,581.35	83,783.57	30,299.60	2,600.62	2,612,138,802.00	47.50
13	19,439.60	206,335.12	68,176.35	4,682.92	15,672,832,818.00	58.20
14	39,438.92	508,141.20	153,399.05	8,431.05	94,036,996,914.00	71.04
15	80,011.31	1,251,394.98	345,150.11	15,177.69	564,221,981,490.00	86.44
16	162,320.05	3,081,796.06	776,589.99	27,321.64	3,385,331,888,946.00	104.93
17	329,298.85	7,589,500.22	1,747,329.73	49,180.76	20,311,991,333,682.00	127.12
18	668,046.82	18,690,562.71	3,931,494.14	88,527.17	121,871,948,002,098.00	153.74
19	1,355,260.95	46,029,000.17	8,845,864.06	159,350.70	731,231,688,012,594.00	185.69
20	2,749,404.37	113,355,002.89	19,903,196.38	286,833.06	4,387,390,128,075,570.00	224.03

8 Deck Baccarat
can you find the correct answer?
7. On average how many hands will it take (or the average wait time) to win 8 in a row betting "Banker" in Baccarat with an 8 deck shoe?

8. On average how many hands will it take (or the average wait time) to lose 6 in a row betting "Banker" in Baccarat with an 8 deck shoe?

streak	Banker 8 Deck 0.50682483	Player 8 Deck 0.49317517
1	1.97	2.03
2	5.87	6.14
3	13.55	14.48
4	28.70	31.38
5	58.61	65.66
6	117.61	135.16
7	234.02	276.08
8	463.70	561.84
9	916.89	1141.25
10	1,811.06	2316.12
11	3,575.32	4698.38
12	7,056.31	9528.83
13	13,924.56	19323.42
14	27,476.06	39183.69
15	54,214.10	79453.93
16	106,970.06	161109.00
17	211,061.14	326679.17
18	416,439.88	662402.13
19	821,666.01	1343140.12
20	1,621,204.58	2723457.43

Sally

I have to admit I didn't think that Loss followed by a Win question through very carefully.
In a string of 2 you have 1 case where you have a Loss-Loss, and one case where you have a Loss-Win (out of 4 cases)
In a string of 3 you have 3 cases where you have a Loss-Loss, and 3 cases where you have a Loss-Win (out of 8 cases)

I really jumped the gun, and thought that they would continue to match, but they start to diverge quickly.
In a string of 4 you have 8 cases where you have a Loss-Loss, and 11 cases where you have a Loss-Win (out of 16 cases)

So the average number of trials to see a Loss-Win is 4, while the average number of trials to see a Loss-Loss is 6.

I had to go back and really read your .pdf files.
Thank you for enlightening me.

Quote: mustangsally

Craps
4. On average how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps? This one is a challenge.

I will give this one a try.
The others look like the answers may be in your tables but not this one.

251/495 would be the probability of a pass line loss.
using this formula from your other thread
((p^-n)-1)/(1-p)=
58.4876662 average number of pass line bets.

Now you asked for how many dice rolls.

The expected number of rolls per decision is
557/165

The solution by the Wizard
In one of your answers you state that the average number of rolls for a shooter in craps is 8.522551. How is that number obtained?

"So the expected number of throws per round is 1+(2/3)*((3/12)*4 + (4/12)*3.6 + (5/12)*(36/11)) = 3.375758"

58.4876662 * 3.375758 =
197.4 dice rolls on average to see a pass line losing streak of 5.

I could verify this with a sim but will wait for other answers.
Every 2 hours or so? Seems low.
Looks like ~64% probability. OK. That is my final answer.

Most of your questions look to be around the length of a Martingale.
Pacomartin had some info, I would have to look it up, on length of losses for those attempting Martys in different games. Maybe another day.

Quote: mustangsally

I'm almost 22 and in my short gambling career, I have been asked and have heard these type of questions for the games I play, mainly, Baccarat, Roulette and Craps.
Seems that most gamblers want to know "how many spins" or "how many dice rolls" or "how many hands" until a losing streak or a winning streak is seen on average.
I would rather show the theoretical distribution but that goes over most people's heads.

So, averages here we come.

So, for now, here are some tables to the questions below.
Later I will add the formulas, they are already in another thread see On average how many trials will it take to lose 2 in a row on a 50/50 game of chance?, and some good Wizard links.

All data in each table is in the form of 1 in X (1/p)

American Double Zero Roulette

First question.
1. On average how many spins will it take (or the average wait time) to lose 6 in a row betting "red" in American Double Zero Roulette?

hint: the correct answer is NOT 1/(20/38)^6 or 1 in 47.04

Why not?
because that is the answer for this question:
What is the probability of losing 6 in a row in 6 spins betting "red" in American Double Zero Roulette?
We are looking for the average number of spins it can take to lose 6 in a row.

2. On average how many spins will it take (or the average wait time) to win 4 in a row betting "black" in American Double Zero Roulette?

streak	50/50	20/38	18/38	26/38	12/38	18/37	19/37
1	2.00	1.90	2.11	1.46	3.17	2.06	1.95
2	6.00	5.51	6.57	3.60	13.19	6.28	5.74
3	14.00	12.37	15.98	6.72	44.95	14.97	13.12
4	30.00	25.40	35.84	11.28	145.51	32.82	27.51
5	62.00	50.16	77.77	17.95	463.93	69.52	55.51
6	126.00	97.21	166.30	27.70	1,472.29	144.95	110.05
7	254.00	186.60	353.18	41.94	4,665.42	300.01	216.25
8	510.00	356.43	747.72	62.76	14,776.99	618.75	423.07
9	1,022.00	679.12	1,580.64	93.19	46,796.98	1,273.94	825.81
10	2,046.00	1,292.23	3,339.01	137.67	148,193.61	2,620.70	1,610.11
11	4,094.00	2,457.13	7,051.13	202.67	469,282.92	5,389.06	3,137.43
12	8,190.00	4,670.44	14,887.83	297.67	1,486,065.76	11,079.56	6,111.68
13	16,382.00	8,875.74	31,431.97	436.51	4,705,878.08	22,776.70	11,903.64
14	32,766.00	16,865.81	66,358.48	639.44	14,901,950.42	46,820.83	23,182.72
15	65,534.00	32,046.93	140,092.24	936.03	47,189,512.82	96,244.88	45,147.25
16	131,070.00	60,891.08	295,752.40	1,369.50	149,433,460.42	197,838.75	87,920.27
17	262,142.00	115,694.94	624,368.29	2,003.04	473,205,961.17	406,670.59	171,215.11
18	524,286.00	219,822.30	1,318,112.94	2,928.99	1,498,485,546.89	835,936.05	333,420.85
19	1,048,574.00	417,664.26	2,782,684.98	4,282.29	4,745,204,234.97	1,718,315.04	649,295.19
20	2,097,150.00	793,564.00	5,874,559.28	6,260.19	15,026,480,080.59	3,532,094.08	1,264,418.89

Craps
can you find the correct answer?
3. On average how many pass line bets will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps?

4. On average how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps? This one is a challenge.

5. On average how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "the Field" in Craps?

6. On average how many dice rolls will it take (or the average wait time) to win 3 in a row betting "the Field" in Craps?

streak	pass line bet	any pass line point	16/36	20/36	6/36	30/36
1	2.03	2.46	2.25	1.80	6.00	1.20
2	6.14	8.53	7.31	5.04	42.00	2.64
3	14.49	23.46	18.70	10.87	258.00	4.37
4	31.43	60.25	44.33	21.37	1,554.00	6.44
5	65.79	150.83	102.00	40.27	9,330.00	8.93
6	135.50	373.91	231.74	74.28	55,986.00	11.92
7	276.92	923.27	523.67	135.50	335,922.00	15.50
8	563.82	2,276.20	1,180.51	245.70	2,015,538.00	19.80
9	1,145.84	5,608.02	2,658.41	444.06	12,093,234.00	24.96
10	2,326.58	13,813.27	5,983.66	801.11	72,559,410.00	31.15
11	4,721.93	34,020.21	13,465.49	1,443.79	435,356,466.00	38.58
12	9,581.35	83,783.57	30,299.60	2,600.62	2,612,138,802.00	47.50
13	19,439.60	206,335.12	68,176.35	4,682.92	15,672,832,818.00	58.20
14	39,438.92	508,141.20	153,399.05	8,431.05	94,036,996,914.00	71.04
15	80,011.31	1,251,394.98	345,150.11	15,177.69	564,221,981,490.00	86.44
16	162,320.05	3,081,796.06	776,589.99	27,321.64	3,385,331,888,946.00	104.93
17	329,298.85	7,589,500.22	1,747,329.73	49,180.76	20,311,991,333,682.00	127.12
18	668,046.82	18,690,562.71	3,931,494.14	88,527.17	121,871,948,002,098.00	153.74
19	1,355,260.95	46,029,000.17	8,845,864.06	159,350.70	731,231,688,012,594.00	185.69
20	2,749,404.37	113,355,002.89	19,903,196.38	286,833.06	4,387,390,128,075,570.00	224.03

8 Deck Baccarat
can you find the correct answer?
7. On average how many hands will it take (or the average wait time) to win 8 in a row betting "Banker" in Baccarat with an 8 deck shoe?

8. On average how many hands will it take (or the average wait time) to lose 6 in a row betting "Banker" in Baccarat with an 8 deck shoe?

streak	Banker	Player
1	1.97	2.03
2	5.87	6.14
3	13.55	14.48
4	28.70	31.38
5	58.61	65.66
6	117.61	135.16
7	234.02	276.08
8	463.70	561.84
9	916.89	1141.25
10	1,811.06	2316.12
11	3,575.32	4698.38
12	7,056.31	9528.83
13	13,924.56	19323.42
14	27,476.06	39183.69
15	54,214.10	79453.93
16	106,970.06	161109.00
17	211,061.14	326679.17
18	416,439.88	662402.13
19	821,666.01	1343140.12
20	1,621,204.58	2723457.43

Answers coming soon
Sally

Nice questions Sally, so

1.
a) average spins to lose 6 in a row betting red on american roulette: probab of loss=20/38 then average= 97.21
b) average spins to win 4 in a row betting black on american roulette: probab. of win= 18/38 then average= 35.84

I'll skip the craps questions, dont know exatly the rules


3.
a) how many hands on average to win 8 in a row betting "banker": probability win= 1/1.97 then average= 463.70
b) how many hands on average to lose 6 in a row betting "banker": probability loss= 1- probab win= 1-1/1.97 or equals probab. 6 wins in a row player. Then average= 135.16


I hope i made no mistake :-))))))))))))))).


How about average hands to win/lose for the first time k in a row?

Quote: mustangsally

1. On average how many spins will it take (or the average wait time) to lose 6 in a row betting "red" in American Double Zero Roulette?
2. On average how many spins will it take (or the average wait time) to win 4 in a row betting "black" in American Double Zero Roulette?
3. On average how many pass line bets will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps?
4. On average how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "pass line" in Craps? This one is a challenge.
5. On average how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "the Field" in Craps?
6. On average how many dice rolls will it take (or the average wait time) to win 3 in a row betting "the Field" in Craps?
7. On average how many hands will it take (or the average wait time) to win 8 in a row betting "Banker" in Baccarat with an 8 deck shoe?
8. On average how many hands will it take (or the average wait time) to lose 6 in a row betting "Banker" in Baccarat with an 8 deck shoe?
Answers coming soon
Sally

1. 102
2. 34
3. 59
4. 201
5. 45
6. 16
7. 554 if you don't count ties, 607 if you do count ties
8. 119 if you don't count ties, 131 if you do count ties

Quote: pacomartin

Quote: mustangsally

5. On average how many dice rolls will it take (or the average wait time) to lose 5 in a row betting "the Field" in Craps?
6. On average how many dice rolls will it take (or the average wait time) to win 3 in a row betting "the Field" in Craps?

5. 52 (assuming either snake eyes or boxcars pays triple)
6. 15 (assuming either snake eyes or boxcars pays triple)

How does the amount of the payout (double vs. triple) affect the probability of encountering a particular series of wins or losses?

Quote: Doc

How does the amount of the payout (double vs. triple) affect the probability of encountering a particular series of wins or losses?

Sorry, brain dead answer. I was adding house edge instead of probability of winning. The correct answer should be 45 and 16,