I'm embarrassed to have to ask this.

T

thefondrens

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Can you please provide me with a formula to calculate the most likely outcome of rolling three 6-sided dice one time.
 
It would help if you provide some context, such as whether you are taking a class, or are just curious, or what. We like to know what you understand and what help you need, in order to answer in the most useful way.

But a quick answer would be to use the symmetry of the dice to see that the distribution of sums will be symmetrical, so that it is at least reasonable that the most likely outcome (the peak of the histogram) would be exactly in the middle -- the average of the lowest and highest possible sums. What is that?
 
I'm playing a board game where I can place a bonus spot on any space I want on the board. If I land on it, I automatically roll 3 dice. I want that dice roll to move me to the most high-paying space on the board. I need to know how many spaces away from the high-paying space I should place the bonus spot. I've been placing it 9 spaces away in hopes the total of the three dice would be nine, but I'm not sure if 9 is one of the most likely totals of the 3 dice.
 
Isn't the lowest outcome 1,1,1 which obviously sums to 3, or do you perhaps have custom dice for your game with different numbers marked on?
 
thefondrens said:
Seems like it would be anything between 9 and 12?
Click to expand...

Sorry, I initially thought this was a response to finding the lowest and highest possible sums (which Dr. Peterson advised you to find). But my commonsense has just kicked in, and I think you're just guessing at the final answer. Why not follow Dr. Peterson's advice...

For standard dice the lowest possible sum is 3. The highest is ??. The average of these two numbers is ??
 
One die: average = (1+2+3+4+5+6)/6 = 21/6 = 7/2 = 3.5. Why was that so hard?
 
Wow, Jomo - You are MEAN! I wonder what happened to you to make you that way. Hope things get better for you!
 
thefondrens said:
I'm playing a board game where I can place a bonus spot on any space I want on the board. If I land on it, I automatically roll 3 dice. I want that dice roll to move me to the most high-paying space on the board. I need to know how many spaces away from the high-paying space I should place the bonus spot. I've been placing it 9 spaces away in hopes the total of the three dice would be nine, but I'm not sure if 9 is one of the most likely totals of the 3 dice.
Click to expand...
Look at this expansion.
In that expansion the term \(25x^9\) tells us that if we roll three dice there are twenty-five ways to get a sum of nine.
Every term \(Wx^S\) tells us there are \(\bf{W}\) ways to get a sum of \(\bf{S}\).
 
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