Roulette Maths Help Please

Hi all

I am sure someone can help me with maths for this.

Say I play 6 numbers on a single zero roulette wheel.

What is the calculation that one of the six numbers will hit within 10 spins and 20 spins

Thanks in advance

Quote: Pando

Hi all

I am sure someone can help me with maths for this.

Say I play 6 numbers on a single zero roulette wheel.

What is the calculation that one of the six numbers will hit within 10 spins and 20 spins

Thanks in advance

There is a nice table already populated with data in Nope27's Blog. It shows probabilities for "at least 1" hit.
The top of the last table has the formulas
Table 3 Nope27 Blog
Answers:
at least 1 hit in 10 spins: 82.955%
at least 1 hit in 20 spins: 97.095%
Or if you are looking for exactly 1 hit and not at least 1
exactly 1 hit in 10 spins: 32.991%
exactly 1 hit in 20 spins: 11.247%

I would say this is a binomial distribution.

One can also use the BINOMDIST() function in Excel

Exact probability:
=BINOMDIST(1,10,6/37,0) 10 spins
=BINOMDIST(1,20,6/37,0) 20 spins
At least 1 probability:
=1-BINOMDIST(0,10,6/37,0) 10 spins
=1-BINOMDIST(0,20,6/37,0) 20 spins
Hope this helps

This sort of thing is easier to figure out from the other direction.

I.E. What's the odds that any of the other 31 numbers are the numbers that come up in each of the next 10 spins. Then subtract that from 1.

( 31 / 37 ) ^ spins :

Spins		31/37 Odds	1 in …		6/37 Odds	1 in …
1		83.78%	1.19		16.22%	6.17
2		70.20%	1.42		29.80%	3.36
3		58.81%	1.70		41.19%	2.43
4		49.28%	2.03		50.72%	1.97
5		41.29%	2.42		58.71%	1.70
6		34.59%	2.89		65.41%	1.53
7		28.98%	3.45		71.02%	1.41
8		24.28%	4.12		75.72%	1.32
9		20.34%	4.92		79.66%	1.26
10		17.05%	5.87		82.95%	1.21
15		7.037%	14.21		92.96%	1.08
20		2.905%	34.42		97.09%	1.03
25		1.199%	83.37		98.80%	1.01
30		0.495%	201.93		99.50%	1.00
35		0.204%	489.10		99.80%	1.00
40		0.084%	1,184.68		99.92%	1.00
45		0.035%	2,869.47		99.97%	1.00
50		0.014%	6,950.27		99.99%	1.00
55		0.006%	16,834.56		99.99%	1.00
60		0.002%	40,775.74		100.00%	1.00
65		0.001%	98,764.75		100.00%	1.00
70		0.000%	239,222.55		100.00%	1.00
80		0.000%	1,403,467.69		100.00%	1.00
90		0.000%	8,233,845.64		100.00%	1.00
100		0.000%	48,306,216.48		100.00%	1.00

The 31/37 Odds columns show the odds of never hitting one of your six numbers in that many spins.
The 6/37 Odds columns show the odds of having hit it at least once in that many spins. It's just 1 minus the 31/37 odds.

Note that the items in bold are rounding errors. The odds will never equal 0% or 100%.

Thank you 7craps

Thats a great help

Pando

Thanks DJTeddyBear

Thats a different but useful way to look at it

Pando