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"Check my math, die success progression" Topic

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Stryderg07 May 2021 9:12 p.m. PST

While looking for a way to increase chances of successful die results on d6's, I came up with this:

Base chance: on 1d6, a 1 is successful
One step up: on 1d6, a 1 is successful, if a 2 is rolled then roll a second d6 and 1, 2 or 3 is successful
Two steps up: on 1d6, a 1 or 2 is successful
Three steps up: on 1d6, a 1 or 2 is successful, if a 3 is rolled then roll a second d6 and 1, 2 or 3 is successful
Four steps up: on 1d6, a 1, 2 or 3 is successful

I think each progression is an increase of 8.33%

1st question: Does that make sense?
2nd question: Is my math right?
3rd question: Is there a better way to describe that?

jwebster Supporting Member of TMP07 May 2021 9:47 p.m. PST

Note that Pr(1) is twice the others. Not sure whether this then gives 11 levels or 12, so 8.3% may be slightly off. Perhaps you could use a d12 instead

You could also roll both dice at once with the second a different colour.

The problem I have with this scheme is that you would always be having to look up on chart whether you need the second die or not


advocate Supporting Member of TMP08 May 2021 2:51 a.m. PST

Your figures look correct to me, though your base chance is obviously 16.66%.
For me, its too complicated, even with jwebster's good suggestion of two different dice.
You could use a D12 and count your base chance as 1-2 (has the added advantage that you could take your base down to 8.33%).
A D10 would approximate the effect with fewer increments.

Personal logo etotheipi Sponsoring Member of TMP08 May 2021 3:13 a.m. PST

It's not what you described.

The outcomes of the second die rolls are independent of the first: Each roll of the second die, halves the probability of a success from the probability of the first.

d0 d1 p
1 16.6%
1 1-3 8.33%
1-2 33.3%
1-3 1-3 16.6%
1-3 50%
1-3 1-3 25%
1-4 66.6%
1-4 1-3 33.3%
1-5 84.4%
1-5 1-6 41.6%
1-6 100%
1-6 1-6 50%

You can't come up with a table that replicates a d12 from 2d6. The 7, 8, and 11 rolls do not have common factors with {1, 2, 3, 4, 5, 6}.

You need a procedural solution:

8.3%: 1 on d1 and 1-3 on d2
16.6%: 1 on d1
25%: 1 on d1 or 1 on d1 and 1-3 on d2
33%: 2 on d1
41.6%: 1-2 on d1 or 3 on d1 and 1-3 on d2
and so on …

with this, the steps the way you describe them are out of order.

GildasFacit Sponsoring Member of TMP08 May 2021 3:26 a.m. PST

No etotheipi, you have misinterpreted the instructions.

The roll of the 2nd die is dependant on the 1st die being a certain number. It probability of success is not affected but it only counts if the first die is the appropriate number.

so …

Base – D1=1 > 16.7%
Step 1 – D1=16.7% + D1=2 AND D2=1,2 or3 > 16.7%/2
(for the 50% success rate of throwing 1-3 on the 2nd die after a 2 is thrown on the first)

and so on.

I'd second using a D12 or even a D20 if you want a linear ramp distribution with smaller increments than a D6 gives.

Stryderg08 May 2021 4:21 a.m. PST

Thanks guys. I thought it would be overly complicated, but was hoping I was on to something.

Dexter Ward08 May 2021 5:13 a.m. PST

Just use a D12, or if you want to stick to d6, roll 2 dice. If the second dice is 4,5,6, add 6 to the first dice. That will get the same effect with much less complication.

UshCha09 May 2021 12:04 a.m. PST

We long since addopted D20. I have to confess it was not my idea. My son is a dedicated RPG man and many of them long since abandoned D6 in favor of D20.

We did so on his recommndation and have never looked back. 5% seems to be a sweetspot. Most certainly modelling reality closer than 5% in a wargame is being a bit optermistic. However 5% lets you account sensibly for the key variables.

Slavishly sticking to a D6 when clearly inadequate seems to me to be a waste of time. Plus at times its possible for 1 D20 to do two jobs at once if the proabilities are compatible, this makes the game faster.

Wolfhag09 May 2021 4:20 a.m. PST

I use a D20 for almost everything in my game. You can get a 1% to 4% result using a re-roll on a "1" with a 1-4 = 1%, 5-8 = 2%, 9-12 = 3%, 13-16 = 4% and 17-20 = 5%.


Stryderg09 May 2021 7:08 a.m. PST

I agree that d20's are awesome, but I'm kicking around rules for a print and play game. And I figured that the great unwashed masses would have easier access to d6's.

Wolfhag09 May 2021 1:40 p.m. PST

You're probably right about the D6.


Personal logo etotheipi Sponsoring Member of TMP11 May 2021 12:39 p.m. PST

Just use a D12, or if you want to stick to d6, roll 2 dice. If the second dice is 4,5,6, add 6 to the first dice. That will get the same effect with much less complication.

I personally agree with you, however I have seen what I consider to be unaccountable shock in response to gaming concepts like "add six to a number".

For things like your recommendation, I often make a d2 from a d6. Take a black d6 with white pips. Use a black marker pen on the corner and side pips. Now you have a binary die that rolls {0,1}. Of you can do {1,2} about as easily.

The d3 is also useful for similar concepts, but it always looks a little wonky since you need four odd numbers (center pips) for {1,2,3,1,2,3} but only get three odd numbers in the standard pip layout for {1,2,3,4,5,6}.

bobm195929 Jun 2021 5:58 a.m. PST

Your maths is correct. Each additional step increases the success rate by 8.333%.
However if you're a fan of diminishing returns i.e. each step up after the first contributes less and less you could consider each step contributes a further D6 with a 1 still being the success (the number of 1's being irrelevant). you then get each step increasing by 13.9%, 11.57%, 9.64%, 8.04%. It might suit your rules and is certainly easier to remember where steps =number of D6.

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