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Posted: Thu Mar 19, 2020 6:56 am
by Username17
Roog wrote:Why not set the standard DC based on the median (or whatever cdf percentage works) instead of the average?
That makes the shape of the tail independent of the standard success chance, and allows the game effect of the distribution's tail shape to be considered separately.
The mean value is generally also the most common value. So while the Median won't be the same as the Mean when the TN isn't exactly 4+, it will usually round to the same number. Consider the 3 die dicepool at TN 5+:
- There are twenty-seven possible results as it's essentially three 3-sided dice.
- The values are read in-game as: 0 (eight), 1 (twelve), 2 (six), 3 (one)
- The Median value is the fourteenth number, which is 1, same as the Mean.
So you have an 8/27 chance of rolling below Mean
and Median and a 7/27 chance of rolling above.
-Username17
Posted: Thu Mar 19, 2020 10:28 am
by Roog
Ok, that is true.
Any binomial distribution will have the mean, median, and mode(s) that are very close (all must lie within a one unit interval).
Interestingly this exposes an oddity.
Take n as the number of dice and p as the chance of success on each dice.
Then mean = np, and median = round(np)
This means that the chances or rolling below the mean depend on how close np is to an integer.
With success on 5+:
11 dice has mean 7.1/3, median 7, and 28.8% chance to roll lower than median and 52.7% chance to roll below the mean.
12 dice has mean 8, median 8, and 36.8% chance to roll lower than mean and median.
13 dice has mean 8.2/3, median 9, and 44.8% chance to roll lower than mean and median.
Posted: Thu Mar 19, 2020 7:04 pm
by Orion
With a target number of 4+ or 5+, each die you roll is an opportunity to be surprised in a good way. Something positive might happen that you weren't expecting. With a target number of 3+, each individual die can only generate a negative surprise. You expect each individual die to be a hit, so you roll your dice and count up to see how many times your dice betrayed you. Whichever outcomes is more rare becomes more salient and that becomes the number people will remember. If the target number if 3+, then people won't talk about rolling 5 hits on 8 dice, they'll talk about rolling 3 fails on 8 dice. If you're going that route, you might as well admit that the dice are not on the player's side. Give each character a static skill value. When they attempt a task, tell them to roll a pile of difficulty dice to find out how much they subtract from it.
Posted: Fri Mar 20, 2020 10:44 am
by OgreBattle
That's a neat consideration
Having two sets of rolls to resolve something is another way to reduce total amount of dice needed. Or opposed rolls.
FrankTrollman, if you made WarpCult today would you go with 3/4+ pools, would you still have "1's are botches"?
"FrankTrollman 2008" wrote:When you perform an action, you roll a pile of d6s called a dicepool. Dice which come up as a 5 or 6 are hits. Those that show a number 1 are botches. A task will normally require a number of hits to succeed equal to the Difficulty Threshold, and throughout the game this will often just be abbreviated as “Threshold.” Any hits gained in addition to the difficulty threshold are Net Hits. If you get 4 or more net hits, you get a Critical Success. This basic terminology will be most familiar to those who have played Shadowrun, but it is really not much different from the Storytelling System (save that it uses d6s rather than d10s, and critical success is measured by how much you exceed the threshold rather than by getting an arbitrary number of hits and exceeding the threshold). Tasks also have an Error Threshold. If the total number of dice that come up as anything that isn't a botch match the Error Threshold, nothing happens. If they fall short of that, an error occurs whether the task succeeded or not.
http://www.tgdmb.com/viewtopic.php?p=72842
Posted: Fri Mar 20, 2020 4:33 pm
by Username17
erik wrote:The notion being that you can trade in dice so 4 dice can automatically succeed at DC needing 2 hits. 6 dice automatically can succeed at DC needing 3 hits.
that sounds kind of terrible. At TN 4+, you get 4+ hits on 6 dice just 34.4% of the time - about one in three. If you can 'take ten' on a 3 hit task, then you go from a 100% chance of task success to about a two thirds chance of failure with the very first difficulty step. That's extremely intense.
-Username17
Posted: Fri Mar 20, 2020 6:00 pm
by erik
FrankTrollman wrote:erik wrote:The notion being that you can trade in dice so 4 dice can automatically succeed at DC needing 2 hits. 6 dice automatically can succeed at DC needing 3 hits.
that sounds kind of terrible. At TN 4+, you get 4+ hits on 6 dice just 34.4% of the time - about one in three. If you can 'take ten' on a 3 hit task, then you go from a 100% chance of task success to about a two thirds chance of failure with the very first difficulty step. That's extremely intense.
-Username17
What if I had a bonus die in non-combat situations? So it would still be 33% when you go from the most difficult sure thing to do something hard with explosions around you, but if you’re just making a very difficult skill roll in a leisurely setting then you will succeed about half the time. Still too steep? DC 4 is supposed to be pretty hard and 5 is supposed to be extremely hard. They’re the rolls where just being skilled alone isn’t enough. Need equipment or something to push you over the top.
Posted: Fri Mar 20, 2020 6:27 pm
by Omegonthesane
After Sundown and Warp Cult have rules for "buying hits" at 4 dice to 1 hit to represent "taking 10". This is in a context where that's a below average rate of expected hits.
Since you've changed what target number you would use in a hypothetical new system, has your position on being able to buy hits at any rate changed, or is it still basically OK so long as you aren't going from "100% chance to take 10" to a large failure chance in a single step.
Posted: Fri Mar 20, 2020 10:29 pm
by Username17
Small dicepools are pretty low variance. The difference in chance of success between one difficulty and the next is big. If you seriously expect people to be rolling 4 die pools at TN 4+, just keep in mind that adding or subtracting one from the difficulty changes your absolute chance of success by twenty five percent, and changing the difficulty again pushes you off the RNG entirely. That's just necessarily how things work if your RNG is really really small. A four die pool literally only has 5 results on the whole RNG, and that's not very much.
-Username17