How to simulate a 10 sided die using a 6 sided die

Question

Accepted Answer

Simulate a 10-sided die using a 6-sided die.

Assign each number on the 6-sided die to two numbers on the 10-sided die.
Roll the 6-sided die twice and combine the results to get a number between 1 and 36.
If the result is between 1 and 30, divide it by 3 and take the ceiling to get a number between 1 and 10.
If the result is 31, 32, 33, 34, 35, or 36, re-roll.

Accepted Answer

Goal - Is to reach a probability of 1/10 for each number.

First, throw choose a multiplier. (1 or 2) 
1-3 gives multiplier 1 (P1(1) = 1/2) 
4-6 gives multiplier 2 (P1(2) = 1/2)

Throw the dice and multiply with the multiplier.

Second, obtain the digit.

Probability of each digit in step 2.

P2(1) = 1/6 + 1/36 + 1/216 ... = (1/6)/(1-1/6) = 1/5 
P2(2) = 1/5 
P2(3) = 1/5 
P2(4) = 1/5 
P2(5) = 1/5

Now to arrive at the total probability of each outcome just multiply and the outcomes will be 1*1, 1*2, 2*1, 2*2 ..... 5*1, 5*2.

P1*P2 = 1/10 for each

Accepted Answer

Roll the 6 sided twice. Now on the 3rd roll keep rolling until you get a 1,2,3,4,5 and reject/reroll a 6.

Accepted Answer

Simulating 10-Sided Die

How to simulate a 10 sided die using a 6 sided die

ChatGPT

Simulating a 10-sided die using a 6-sided die is possible by modifying the rolls and applying some basic math. Here's one method to simulate a 10-sided die using a 6-sided die:

Number the faces of the 6-sided die from 1 to 6.
Roll the die twice.
If the first roll results in a 1, 2, 3, or 4, use the value as is.
If the first roll results in a 5 or 6, ignore it and roll again.
If the second roll results in a 1 or 2, assign a value of 7 or 8, respectively.
If the second roll results in a 3 or 4, assign a value of 9 or 10, respectively.
If the second roll results in a 5 or 6, ignore it and repeat the process from step 2.

By following these steps, you'll obtain a random number between 1 and 10 with equal probability. Note that this method relies on the assumption of a fair 6-sided die and may require multiple rolls in some cases.

Accepted Answer

Simulate a 10-sided dice using a 6-sided dice - Faraz Gerrard Jamal - Medium

How to simulate a 10 sided die using a 6 sided die

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