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Subject: Dice Statistics Question rss

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Willem Viljoen
Belgium
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Hey everyone.

In the game I am currently designing, when you attack you roll dice equal to your strength. My idea was to use dice like in Betrayal at House on the Hill (0/0/1/1/2/2). The maximum possible might that could be reached is 16. Is 16 dice too many? If yes then I was wondering can I substitute 2 of those dice for a (0/0/2/2/4/4) die, or would that change the odds of what is being thrown? Also note there will be an stat that allows you to rethrow some dice. Maybe someone has another idea for what I can do?

Thank you.
 
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Christopher Dearlove
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Vulcanite wrote:
Hey everyone.

In the game I am currently designing, when you attack you roll dice equal to your strength. My idea was to use dice like in Betrayal at House on the Hill (0/0/1/1/2/2). The maximum possible might that could be reached is 16. Is 16 dice too many? If yes then I was wondering can I substitute 2 of those dice for a (0/0/2/2/4/4) die, or would that change the odds of what is being thrown? Also note there will be an stat that allows you to rethrow some dice. Maybe someone has another idea for what I can do?

Thank you.


Changing dice (almost any case, certainly that one) will change odds. That particular one will make the distribution have a greater variance, so more chance of an unusually high or low value.

Is 16 dice too many? Depends on players and (most importantly) publisher's costs. It might actually be cheaper with more dice, but all the same.

What should you do? What are you attempting to achieve? (The more precisely you want an answer, the more precisely you need to know that.)
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Willem Viljoen
Belgium
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Dearlove wrote:
Changing dice (almost any case, certainly that one) will change odds. That particular one will make the distribution have a greater variance, so more chance of an unusually high or low value.

Is 16 dice too many? Depends on players and (most importantly) publisher's costs. It might actually be cheaper with more dice, but all the same.

What should you do? What are you attempting to achieve? (The more precisely you want an answer, the more precisely you need to know that.)


I want to try making a solo/co-op RPG turn based. With a final fantasy like feel but as a boardgame and with a different theme. I had the idea that if you roll all 0s then the attack would miss. I get what you mean with greater variation in distribution. What if it was a (0/0/1/2/3/4) dice? I have no idea even if 16 dice is a problem? I know some people like throwing hands full of dice but I don't want it to become a hasstle since it only determines the base damage of your attack.
I'm fairly new to boardgame creation but have spent many hours playing final fantasy and other RPGs so I thought I'd give it a try in the genre I enjoy the most.
 
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Jeremy Monts

Louisiana
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I'd say take what you think your average pool of dice would be, then roll that number of dice equivalent to what you think it will be rolled during a normal game. If you think rolling that many dice that many times is acceptable/fun/etc, then go for it.

There's a lot of math behind what numbers you want your dice to have, and it really depends on how often you want misses and what you want your base damage to average.

So if you want 10% of throws to miss, and you want your base damage to average 8, that will dictate a certain set of values for your dice. I, unfortunately, can't do that math. But I'm sure if you figure out those values, someone would be willing to help you with exact numbers.
 
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Christopher Dearlove
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monts wrote:
I'd say take what you think your average pool of dice would be, then roll that number of dice equivalent to what you think it will be rolled during a normal game. If you think rolling that many dice that many times is acceptable/fun/etc, then go for it.

There's a lot of math behind what numbers you want your dice to have, and it really depends on how often you want misses and what you want your base damage to average.

So if you want 10% of throws to miss, and you want your base damage to average 8, that will dictate a certain set of values for your dice. I, unfortunately, can't do that math. But I'm sure if you figure out those values, someone would be willing to help you with exact numbers.


It is of course easiest to answer the question "with these dice, what are X, Y and Z?" than "what dice produce X, Y and Z". Varying one parameter (e.g. How many dice, or try different patterns on all dice) is not hard. Varying more than one parameter is either harder or less precise (try various things, usually adjusting one thing at a time). But it can be done.
 
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Ian Parmenter
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16 dice with sides 0/0/1/1/2/2 will roll between 0 and 32, with an average of 16.

Substituting two of those dice for 0/0/2/2/4/4 would give you rolls from 0-36, with an average of 18.

Using dice of 0/0/1/2/3/4 will give you 0-64, with an average of about 26-27.
 
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Willem Viljoen
Belgium
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monts wrote:
I'd say take what you think your average pool of dice would be, then roll that number of dice equivalent to what you think it will be rolled during a normal game. If you think rolling that many dice that many times is acceptable/fun/etc, then go for it.

There's a lot of math behind what numbers you want your dice to have, and it really depends on how often you want misses and what you want your base damage to average.

So if you want 10% of throws to miss, and you want your base damage to average 8, that will dictate a certain set of values for your dice. I, unfortunately, can't do that math. But I'm sure if you figure out those values, someone would be willing to help you with exact numbers.


Ah thanks I think you made me understand how to better ask this question. So when rolling the 1st mentioned die I was talking about (0/0/1/1/2/2) statistically you should average out at about 1 damage per die this is what it want. You have 33% chance to miss with one die, 16.67% with two dice, 9.26% with 3 dice. This way I see that the probability to miss goes down the more dice you have, with a 0.01% chance to miss with 16 dice, this maybe makes it better to use different dice rather than just adding more and more dice.

So let's say your dice look the following:
Str 1: 0/0/1/1/2/2
Str 2: 0/0/1/2/3/4
Str 3: 0/0/1/2/3/4/5/6
Str 4: 0/0/1/2/3/4/5/6/7/8
A 33.33% chance to miss with 1 die
Str 5: Str 4 Die + Str 1 die
Str 6: Str 4 Die + Str 2 die
Str 7: Str 4 Die + Str 3 die
Str 8: 2 x Str 4 Die
A 16.67% chance to miss with 2 Dice
Str 9: 2 x Str 4 Die + Str 1
Str 10: 2 x Str 4 Die + Str 2
Str 11: 2 x Str 4 Die + Str 3
Str 12: 3 x Str 4 Die
A 9.26% chance to miss with 3 Dice
Str 13: 3 x Str 4 Die + Str 1
Str 14: 3 x Str 4 Die + Str 2
Str 15: 3 x Str 4 Die + Str 3
Str 16: 4 x Str 4
A 5.4% chance to miss with 4 Dice

Could anyone confirm for me that this will statistically average out on about 1 Damage per Strength? As well is if my Miss percentage is in the right ballpark? Note that I rounded up before adding some numbers together so it might not be precise.
 
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Willem Viljoen
Belgium
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Just as I posted my previous post, I realised my math will be off.

Str 1 die will average at 1
Str 2 die will average at 1.67
Str 3 die will average at 2.625
Str 4 die will average at 3.6

Although this is not too bad the average for the rest will then be the previously mentioned averages added together of the dice you use divided by the number of dice you used. Can someone confirm this for me please though.

Edit: Nevermind I also just realised that the chance to miss decreases with the dice with more sides as well. Back to the drawing board with the maths for me.
 
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Willem Viljoen
Belgium
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This I think should be the correct numbers for my above mentioned Dice solution.

Str 1: 0/0/1/1/2/2 Avg 1 Miss 33.33%
Str 2: 0/0/1/2/3/4 Avg 1.67 Miss 33.33%
Str 3: 0/0/1/2/3/4/5/6 Avg 2.625 Miss 25%
Str 4: 0/0/1/2/3/4/5/6/7/8 Avg 3.6 Miss 20%
Str 5: Str 4 Die + Str 1 die Ave 4.6 Miss 8.33%
Str 6: Str 4 Die + Str 2 die Ave 5.27 Miss 8.33%
Str 7: Str 4 Die + Str 3 die Ave 6.2255 Miss 5%
Str 8: 2 x Str 4 Die Ave 7.2 Miss 4%
...
Str 16: 4 X Str 4 Die Ave 14.4 Miss 0.16 %

The average damage of this Dice idea is not too bad.
My ideal is though Average of 1 Damage per Strength and miss chance decreasing but not too drastically I would still prefer if people had a chance above 1% to miss at 16 Strength. Any suggestions?
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Jade Knight
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Easy way to figure out what changing your dice will do to your numbers:

http://anydice.com/
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Jeremy Lennert
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Descent uses a system where you roll several different kinds of dice to determine your damage, but you always roll one die with an X on one side, and if you roll that X then your attack misses regardless of your other dice. This allows them to make higher-damage attacks by adding more dice without affecting the chance of a miss.

Lots of games use one roll (or system) to determine whether you hit or miss, and a separate roll (or system) to determine how much damage you do.

Lots of other games give the target a "defense" or "armor" score that is subtracted from your damage, and so your odds of doing no damage depend on your target. A powerful attacker might have a guaranteed hit against a weak target but still have a chance of "missing" against a stronger target.


I notice, though, that you're creating a fairly complex set of dice to satisfy a fairly nebulous set of goals. You may end up creating a lot of work for yourself prototyping the dice and calculating the odds and balancing your game around a complex non-linear progression. What's the upside to all of that, if you haven't even figured out what you want?

Maybe start with something simple using one or two dice. Like:

Side 1: Miss
Side 2: 1/2 Str (round up)
Side 3: Str - 1
Side 4: Str
Side 5: Str + 1
Side 6: 2x Str

That gives an average damage almost equal to your strength, but you only need one die for everyone. Depending on your strength, it gives results of:

Str 1: 0/1/0/1/2/2 (mean = 1)
Str 2: 0/1/1/2/3/4
Str 3: 0/2/2/3/4/6
Str 4: 0/2/3/4/5/8
Str 5: 0/3/4/5/6/10
Str 6: 0/3/5/6/7/12
...
Str 16: 0/8/15/16/17/32 (mean = 14.67)
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Willem Viljoen
Belgium
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Thank you Jeremy I was thinking way too complicated. I love your 1st dice idea. Guess I got so caught up in my own idea that I couldn't see the easier solution.
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