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Say you need a d6 dice for something, but you only have five coins. If you started with 1, flipped all the coins and counted each head as a 1, and tails as a zero, then added them up, would the change of getting any said number be the same as a dice?

No. The odds of rolling a 1 are 1 in 6. The odds of flipping five coins and their all coming up tails (the outcome you would need to simulate a roll of 1) is 1/32.

As there are multiple ways to get each possible outcome, some with more ways than others, the probability of getting any given number of heads by flipping 5 coins creates a curve. Getting a 3 or a 4 using the coins is far more likely than getting a 1 or a 5.

Let's look at the different permutations between getting a 1 and a 2.

First, we'll do 1. X is heads, O is tails

OOOOO

Only the one configuration can get you a 2. Now let's see how many configurations can get you a 1:

XOOOO
OXOOO
OOXOO
OOOXO
OOOOX

There's 5 different configurations that can get you a 2, and yes, those are distinct configurations. Therefore, getting a 2 is five times more likely than getting a 1. Clearly, this is not a flat probability.

What you could do to simulate the probability of a d6 is flip all of the coins as a set, keeping track of their order, until you get a configuration that would give you a 1, 2, 5 or 6 in your original setup. Instead of scoring it the same way, however, you take the position of the odd coin out and use that as your result. If it's all heads or all tails, then it's a 6.

(sorry if this is a bit confusing )

_{Dinnanid}Edit: that was my 42nd post.

Let's look at the different permutations between getting a 1 and a 2.

First, we'll do 1. X is heads, O is tails

Only the one configuration can get you a 2. Now let's see how many configurations can get you a 1:

There's 5 different configurations that can get you a 2, and yes, those are distinct configurations. Therefore, getting a 2 is five times more likely than getting a 1. Clearly, this is not a flat probability.

What you could do to simulate the probability of a d6 is flip all of the coins as a set, keeping track of their order, until you get a configuration that would give you a 1, 2, 5 or 6 in your original setup. Instead of scoring it the same way, however, you take the position of the odd coin out and use that as your result. If it's all heads or all tails, then it's a 6.

Permutations along with the scored result:

That's a flat probability curve.