In the board game monopoly, a player tosses two dices together and the sum of the two dices points is the number of steps he or she should go. For example a player gets a 2 and a 3, then he or she should go 5 steps forward. If the two dices give the same number (for example two 2), which is called a “double”, after moving forward (4 steps), the player gets another chance to toss and move forward again. However, if someone tosses 2 consecutive doubles, he or she will be sent to jail.
Consider that you are tossing two fair dices for many times. You won’t stop until you get 2 doubles. After you stop, take down the number of tosses you use. Use a loop to repeat this at least 1000 times. Calculate the average of the 1000 results, that is, how many tosses is needed on average, to be able to get three consecutive doubles.
To calculate the average number of tosses needed to get three consecutive doubles in the board game Monopoly, you can follow these steps:
1. Initialize a variable "totalTosses" to keep track of the sum of tosses required for 1000 iterations. Set it to 0 initially.
2. Set a loop to iterate 1000 times. In each iteration:
a. Initialize a variable "tosses" to keep track of the number of tosses required to get three consecutive doubles. Set it to 0 initially.
b. Initialize a variable "consecutiveDoubles" to keep track of the number of consecutive doubles obtained. Set it to 0 initially.
c. Start a nested loop that continues until "consecutiveDoubles" reaches 3.
d. In each iteration of the nested loop:
i. Simulate the toss of two dice and calculate their sum.
ii. If the two dice show the same number (double), increment "consecutiveDoubles" by 1. Otherwise, reset it to 0.
iii. Increment "tosses" by 1.
e. After coming out of the nested loop (i.e., when "consecutiveDoubles" reaches 3), add the value of "tosses" to "totalTosses".
3. Calculate the average by dividing "totalTosses" by 1000.
4. Print the average number of tosses required to get three consecutive doubles.
Here is a Python code snippet to implement the above steps:
```python
import random
totalTosses = 0
iterations = 1000
for _ in range(iterations):
tosses = 0
consecutiveDoubles = 0
while consecutiveDoubles < 3:
dice1 = random.randint(1, 6)
dice2 = random.randint(1, 6)
if dice1 == dice2:
consecutiveDoubles += 1
else:
consecutiveDoubles = 0
tosses += 1
totalTosses += tosses
averageTosses = totalTosses / iterations
print("Average number of tosses required to get three consecutive doubles:", averageTosses)
```
By running the above code, you will get the average number of tosses required to get three consecutive doubles in Monopoly by simulating the game 1000 times.