Whats the probability of european roulette spin same colour between 1-20 times?

The above answers are correct only if you want to know the probability of getting specifically red or specifically black n times in a row.

Assuming you do not mind which colour you want to get 20 times in a row, then the probability of getting red or black n times in a row, out of n spins, is given by (36/37)*(18/37)^(n-1)

First spin there is a 36/37 chance of getting red or black.

after 2 spins there is a (36/37)(18/37) chance of getting the same colour both times.

=0.47

After 3 spins there is a (36/37)(18/37)^2 chance of getting the same colour every time.

1 spin: 0.973

2 spins: 0.47

3 spins: 0.23

4 spins: 0.11

5 spins: 0.055

6 spins: 0.026

7 spins:0.013

8 spins: 0.0063

9 spins:0.0031

10 spins: 0.0015

11 spins:0.00072

12 spins:0.00035

13 spins:0.00017

14 spins:0.000083

15 spins:0.000041

16 spins:0.000020

17 spins:0.0000096

18 spins:0.0000047

19 spins:0.0000023

20 spins:0.0000011

You can see that my figure of n spins is the same (to within a factor of 0.97) as martin's figure for n-1 spins (that is, my figure for 8 spins is the same as Martin's figure of 7 spins) As I said at the beginning, this is because I assumed it did not matter what the 1st spin was, as long as it wasn't 0 (neither red or black). The important thing is that all the following colours are the same.

The probability of one color in a row in percentages:

1 48,64864865%

2 23,66691015%

3 11,51363197%

4 5,601226362%

5 2,724920933%

6 1,325637211%

7 0,644904589%

8 0,313737368%

9 0,15262899%

10 0,074251941%

11 0,036122566%

12 0,01757314%

13 0,008549095%

14 0,004159019%

15 0,002023307%

16 0,000984311%

17 0,000478854%

18 0,000232956%

19 0,00011333%

20 0,0000551135%

(18/38)^13 You can do the math from there.

take a quarter,flip it 99 times, if it lands on heads 99 times, the 100th flip is still 50/50 that it will land on heads......excluding the zeros

1 time in a row 18/37

2 times in a row 18/37 * 18/37

3 times in a row 18/37 * 18/37 * 18/37

Etc...