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Roll results for d6: Deciding on a dice system.

Using a set of my own plain, cornered, white dice, I rolled out a bunch of test rolls for 7d6. I even went to a website and got some automated, electronic rolls.
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After about 100 rolls I've found that the most common numbers rolled were 22, 27, 24, 25, 21. I didn't make an exact tally, but in that order, those were the most frequent. The lowest number I rolled frequently was 18. The highest number I rolled frequently was 31.

On an equal playing field of a pool of 7 6-sided dice, you can expect to see a damage output of 3-5 on average rolls. In my opinion, it's more likely to see 7 damage dealt.

I decided to move on to 6d6. The numbers varied a lot more than I expected. Nonetheless, I saw common numbers. 20, 22, 19, 18, 23, 17. 15 was a common low. 26 was a common high. Comparing to a 7d6 attack, unaided or modified, I can expect to receive 5-8 damage.

What does this mean for the game? Nothing really. A LOT of work has to be done. Abilities need to be added, modifiers for terrain advantage and disadvantage. Stuff like, "this character can remove 1 die from his opponent when defending" or "this character receives a -2 modifier when defending".

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Out of boredom and curiosity, I decided to test roll the second choice for my game with a droid app. (I don't have d4s and such anymore. I need to buy some. For this test, I used 1d4, 1d6, and 1d8. After a bunch of electronic rolls, I saw a LOT of 9s and 12s. A lot of 1s were rolled. On 3 dice, the odds sway a LOT. When you're allowed only 1 roll, this sucker makes or breaks you. As you may have read before, Glory can raise the tier of a die. Coupled with modifiers and abilities, I'm thinking of going with this one. I still have to do proper physical rolls for it though.

Comments

Probability

Have you ever studied probability in school? If not, I have a few pointers that might help you:

When you roll one dice, on average, you should expect to the midpoint of the dice. This can be calculated by adding all of the dice faces together, and dividing by the number of faces (so, for a d4, it is (1+2+3+4)/4 = 2.5). If you roll several dice, on average, their sum will be equal to the sum of their averages (so, if I roll 3d4, it will be 2.5+2.5+2.5 = 7.5). So, for a d6, you expect to get 3.5 on average. For 7d6, you'd expect 24.5 (if I've done my calculations right).

The other thing you mention is the amount of variation in dice rolls. When you roll only 1 dice, you have an equal chance of everything. However, as you sum more and more dice, your results start to look like a Bell curve. There are then 2 things that start to happen: first, you get more variation in an absolute sense (i.e. for d6, the difference between a common high and a common low is 5,;whereas with 7d6, it is 11), but you get less variation relative to the size of the numbers (i.e. with 1d6, the common high is 6 times as big as the common low; with 7d6, it was less than double). This means that a +1 benefit will be more helpful the fewer dice are rolled, but also that your results will be more predictable the more dice are rolled.

You've heard of a standard deviation, right? The basic idea is that, generally, about 2/3rds of all rolls will be within 1 standard deviation of the average, and about 19/20 should be within 2. If I've done my calculations right, if you roll N dice, then one standard deviation should be about 1.7 x N^(1/4). So, for 7 dice, your most common rolls should be 24 and 25, with 2/3rds of your rolls between about 21 and 28, and very few of your rolls above 18 or below 31.

I hope that helps!

Simon

P.S. As someone who has worked on wargames before, I feel I should add one other note: having multiple dice rolls does make things more predictable, but it comes at a cost of gameplay. The more numbers you ask people to add together, the more things will be slowed down. I'm a math person myself, and the idea of needing to add 7 numbers together each time I wanted to attack worries me. If you want predictable results, another way you could handle this is just having the player roll 7 dice, and see how many times they get above a 5 (or something like that). It's a lot easier for people to do, and will still give fairly regular results if you have enough dice (although, if you are going to hive lots of benefits, it might be worth switching to d8s or something).

Thanks for the info!

I have an easy time adding up multiples of single digits, so I kind of enjoyed it and didn't see a problem. As you have stated, it could be a problem.

I really don't want to use the warhammer style of "anything above this number, hits". Mainly, because each success will count as 1 hit. If you want to roll more damage, you have to roll more dice. I thank you for your insight!

anydice

You might also want to check out the www.anydice.com for dice calculations...

For example, if you say "output 7d6" you will see the probabilities for each of the outcomes. It can also calculate the chance to have at least X, or at most Y... and lots of other possibilities... Check it out...

kornelijepetak wrote:You

kornelijepetak wrote:
You might also want to check out the www.anydice.com for dice calculations...

For example, if you say "output 7d6" you will see the probabilities for each of the outcomes. It can also calculate the chance to have at least X, or at most Y... and lots of other possibilities... Check it out...

You..... are the GREATEST! Charts ! Percentages ! Everything !

THANK YOU SO MUCH!!

Evil ColSanders

Evil ColSanders wrote:
kornelijepetak wrote:
You might also want to check out the www.anydice.com for dice calculations...

For example, if you say "output 7d6" you will see the probabilities for each of the outcomes. It can also calculate the chance to have at least X, or at most Y... and lots of other possibilities... Check it out...

You..... are the GREATEST! Charts ! Percentages ! Everything !

THANK YOU SO MUCH!!

Nope. God is the greatest :)

However, it is advisable to study the documentation on anydice.com because it can do really complex stuff...

For example (which is still a basic example) you can do this:

set "position order" to "lowest first"
output 2@4d20 > 3@4d20+5

This reads: "Chance that the second lowest (which is the third highest) of 4 dice will be greater than the third lowest (second highest) increased by 5".

That's as much as I go... :D

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