• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Can one predict an outcome over (n) spins?

  • Thread starter RoundWheel
  • Start date
I’m interested in following statistical question regarding the random chance of a Roulette Wheel:

Suppose I were to place a single bet on the first column of numbers (1, 4, 7,10,13,16, 19, 22, 25, 28, 31, 34), which pays 2-1, what is the probability that I will hit at least one of these numbers in the column in any one of 3 consecutive spins of the wheel; 6 consecutive spins; 9 consecutive spins; 12 consecutive spins and 15 consecutive spins.

Given the statistical laws of distribution, at what point (spin :rofl: # (n)) would one expect the first occurrence of one of these selected numbers appearing?

Please show probability separately for each group of spins as to clearly show the mathematical differences and how they affect the outcome.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,845
17
What have you done so far?
 
Lacking the use of an actual Roulette wheel, I instead used a Die trial with numbers 1 & 2 to represent column 1, 3 & 4 as column2 and 4 & 5 as cloumn 3. After 200 throws found that the maximum numbers of throws (spins) before a 1 or 2 came out was 10. However, this does not take into consideration the affect of "0" and "00" has on this event.
 
1,056
0
In this case, we have 38 outcomes, 2 of which are 0 or 00. Let p=12/38=6/19. Then the possibility of not hitting a number is 13/19. In three turns of the wheel we consider the Bernoulli trials: (p+q)^3. The number of no hits is q^3, so the probability of at least one hit is 1-q^3. Similarly the probabilities are 1-q^6, and 1-q^9. That is: 68%, 90%, 97% chance of at least one hit.
 

Related Threads for: Can one predict an outcome over (n) spins?

Replies
1
Views
1K
  • Posted
Replies
1
Views
1K
Replies
4
Views
2K
Replies
1
Views
383
Replies
4
Views
2K
  • Posted
Replies
5
Views
2K
Replies
24
Views
13K
Replies
4
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top