My Mechanic ; Need some input

[thadrine]

Here is the basis: (based heavily off of Houses of the Blooded)

You have a simple set list of skills, about 6 of them. They are ranked from 2-5 at character creation, and each rank is a d6 that you can roll to beat a target number. Target numbers will fluctuate between 5-15, you choose how many dice you wish to roll, and how many you wish to set aside. The number of dice that you set aside are additional successes on your roll.

The Target Number is determined by the rank of your descriptor. You can have a descriptor of "Fire Magic" at rank 4, or "Sniper Rifle" at rank 3. This is added to the base of five, plus other miscellaneas modifiers, such as cover or concealment.

[Guy Srinivasan]

I'm not sure I understand it. The TN goes up by 4 if you have Fire Magic at 4, and you want to roll high enough to hit the TN? Seems backwards, I must be missing something.

[Vulpinoid]

This makes sense to me...

Is this the right interpretation of your rules?

Let's say you're using "fire magic 4" against a difficulty of 5. This gives you 4 six-sided dice to play with.

Because your fire magic skills is 4, the target number automatically increases to 9 (this offsets the bonus gained by having multiple dice because each die would roll a minimum score of 1).

You now have to decide how may dice to roll for the action (adding together the face values of the dice used).

Rolling 1 die would be stupid, because you'd never reach that target number of 9.

Rolling 2 dice would give you a range of results from 2-12. Anything resulting in a 9 or higher would be a success, and since you held back 2 of the dice, you'd get two extra degrees of success from these (but only if successful).

Rolling 3 dice would give you a range of 3-18, and a better than average chance of rolling a 9 or higher. Since you held back a single die, you'd get one extra degree of success (if you were successful on the roll).

Rolling 4 dice would give you a range of 4-24, with a very good chance of succeeding. But you wouldn't get any extra degrees of success, because all of your dice were used in the roll.

The same task being attempted by a character with "fire magic 2" against a difficulty of 5. This gives you 2 six-sided dice to play with.

Because the fire magic skills is 2, the target number automatically increases to 7.

Decide how may dice to roll for the action (adding together the face values of the dice used).

Rolling 1 die would be still be stupid, because you'd never reach that target number of 7.

Rolling 2 dice would give you a range of results from 2-12. Anything resulting in a 7 or higher would be a success, better than average, but since you've used up all of your dice to achieve the target number you'd only ever get one degree of success.

If this is the right interpretation, I like it.

It allows some good strategic thought.

I like the idea that no task is automatic, but the system allows difficulties that inexperienced characters simply can't achieve...that says something about the setting.

Some other factors I'd consider...

Should a roll of "natural 6" on one of the dice add an additional degree of success?

Conversely, should a roll of "natural 1" have remove additional degrees of success?

Should target number be modified by the rank of the opponent's descriptor in opposed tests?

How do multiple characters work together to achieve tasks? 

Just some ideas...

V

[Guy Srinivasan]

Oh, I see... so it's like the dice roll 0-5 vs TN 5. Only removing one of those dice for a success only has opportunity cost of EV 2.5 pips rather than 3.5 for the full die. I wonder if it would be better to phrase as "TN 5, plus/minus modifiers like cover, advantage, etc. You may choose any number of your dice to not roll. For each you choose to leave out, increase the TN by 1 and increase your successes by 1 if you succeed. 6s count as 0!"

I don't know which is more natural, but as a data point, the first one did confuse me...

Also, if 6s don't count, it's a bit easier to add and has exactly the same probability distribution. But it does mean players will be sad about rolling 6s while happy about rolling high, which is unfortunate. Although if you have 6s do something wacky...?

[chronoplasm]

Does each individual die have to beat the target number, or is it the sum of all dice that has to beat the target number?

[Wordman]

I also like this system, though I would refrain from doing the "six gives a success and 1 takes one away" thing, as this a) makes the math hard to analyze, b) makes figuring out a result slower, c) makes rolling more an exercise in luck than strategy and c) runs counter to incentive in the basic system. What I mean by the last bit is that the mechanic as written has a very clear "succeed with as few dice as you think you can get away with" structure, giving incentive to roll fewer dice for the extra successes. If you only added the "six gives an extra success", this acts counter to that, giving incentive to roll more dice. Likewise, if you added only the "ones take success away", I'm not sure what kind of incentive this gives, since rolling a one is likely to mean you fail the roll anyway, so holding back dice wouldn't help anyway, but adding them would just give more likelihood of ones. Adding both of these rules at once would muddy these waters even further.

Also, I think your description of the mechanic would be helped by using the "difficulty" terminology that Vulpinoid used. That is, define "difficulty" as a specific game term meaning "five plus modifiers for cover, advantage, etc." and define "target number" as "difficulty plus rank". And definitely explain why rank is added, as Vulpinoid did.

[Wordman]

My previous post left me sufficiently curious to write some quick code (might want to set verbose to True at the top to see what the code is really doing) that exhaustively runs all possible rolls and compares the average number of successes generated under each of the four rules variations (basic, using 1's to subtract only, using 6's to add only, and using both 1's to subtract and 6's to add). Assuming my code is right (probably a bad assumption), you get this:

Code Select Expand


Average successes for rank 2

Rules: basic
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.58 0.42 0.28 0.17 0.08 0.03 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes and 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.86 0.69 0.50 0.33 0.19 0.08 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.53 0.42 0.28 0.17 0.08 0.03 0.00 0.00 0.00 0.00 0.00

Rules: 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.92 0.69 0.50 0.33 0.19 0.08 0.00 0.00 0.00 0.00 0.00


Average successes for rank 3

Rules: basic
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.84 0.74 0.62 0.50 0.38 0.26 0.16 0.09 0.05 0.02 0.00
1 0.83 0.56 0.33 0.17 0.06 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes and 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 1.05 1.02 0.94 0.83 0.69 0.54 0.37 0.23 0.13 0.06 0.02
1 1.11 0.78 0.50 0.28 0.11 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.56 0.53 0.49 0.42 0.33 0.25 0.16 0.09 0.05 0.02 0.00
1 0.83 0.56 0.33 0.17 0.06 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 1.34 1.23 1.08 0.92 0.74 0.55 0.37 0.23 0.13 0.06 0.02
1 1.11 0.78 0.50 0.28 0.11 0.00 0.00 0.00 0.00 0.00 0.00


Average successes for rank 4

Rules: basic
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.95 0.90 0.84 0.76 0.66 0.56 0.44 0.34 0.24 0.16 0.10
1 1.48 1.25 1.00 0.75 0.52 0.32 0.19 0.09 0.04 0.01 0.00
2 0.83 0.50 0.25 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes and 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 1.10 1.10 1.09 1.07 1.02 0.94 0.83 0.69 0.54 0.40 0.27
1 1.76 1.57 1.33 1.07 0.80 0.53 0.32 0.18 0.08 0.02 0.00
2 1.06 0.67 0.36 0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.48 0.48 0.47 0.46 0.43 0.39 0.34 0.27 0.21 0.15 0.09
1 1.27 1.11 0.92 0.71 0.50 0.32 0.19 0.09 0.04 0.01 0.00
2 0.83 0.50 0.25 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 1.61 1.57 1.50 1.40 1.27 1.11 0.94 0.75 0.57 0.41 0.27
1 1.97 1.71 1.42 1.11 0.81 0.53 0.32 0.18 0.08 0.02 0.00
2 1.06 0.67 0.36 0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00


Average successes for rank 5

Rules: basic
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.98 0.97 0.94 0.90 0.85 0.78 0.69 0.60 0.50 0.40 0.31
1 1.81 1.68 1.52 1.33 1.11 0.89 0.67 0.48 0.32 0.19 0.11
2 1.88 1.50 1.12 0.78 0.49 0.28 0.14 0.06 0.01 0.00 0.00
3 0.67 0.33 0.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes and 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 1.14 1.14 1.14 1.14 1.13 1.12 1.08 1.02 0.93 0.82 0.69
1 1.98 1.92 1.82 1.68 1.50 1.27 1.03 0.78 0.56 0.36 0.22
2 2.19 1.83 1.44 1.06 0.69 0.42 0.22 0.10 0.03 0.00 0.00
3 0.83 0.44 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 1's subtract successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 0.40 0.40 0.40 0.40 0.39 0.39 0.37 0.35 0.31 0.27 0.23
1 1.31 1.27 1.19 1.08 0.94 0.78 0.61 0.45 0.31 0.19 0.11
2 1.74 1.42 1.08 0.76 0.49 0.28 0.14 0.06 0.01 0.00 0.00
3 0.67 0.33 0.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Rules: 6's add successes
                           vs. Difficulty
Hold 5 6 7 8 9 10 11 12 13 14 15
0 1.82 1.80 1.77 1.73 1.66 1.57 1.45 1.30 1.13 0.95 0.77
1 2.47 2.34 2.16 1.93 1.67 1.38 1.09 0.81 0.57 0.37 0.22
2 2.33 1.92 1.49 1.07 0.69 0.42 0.22 0.10 0.03 0.00 0.00
3 0.83 0.44 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


Some things I notice:

• With x dice, you can never succeed if you hold x-1 of them.
• The net result of using both the 1 and 6 rules is that you get more successful on average.
• The amount of additional success provided by using both 1 and 6 rules (vs. the basic system) generally increases as your pool size gets larger, though this is not universally true.
• There is a "correct" number of dice to withhold (that is, on average, withholding that number will gain more successes) based on the size of the pool and the difficulty.
• For any given pool size, the optimal number of die to withhold decreases as difficulty increases (not surprisingly).
• The optimal number of die to withhold is almost identical for both the basic and "1 and 6" systems.