What can I use in place of Fudge Dice? [closed]

If someone doesn’t have any fudge dice, what are the best methods to replace them and why?

Term: Fudge Dice are six sided dice with two sides labeled with a +, two sides with a -, and two sides that are blank. They are usually rolled in groups of four, and the + and – sides are added together to get a number between -4 and +4, with positive usually being better.

Asymptotic of divide-and-conquer type recurrence with non-constant weight repartition between subproblems and lower order fudge terms

While trying to analyse the runtime of an algorithm, I arrive to a recurrence of the following type :

$ $ \begin{cases} T(n) = \Theta(1), & \text{for small enough $ n$ ;}\ T(n) \leq T(a_n n + h(n)) + T((1-a_n)n+h(n)) + f(n), & \text{for larger $ n$ .} \end{cases}$ $ Where:

  • $ a_n$ is unknown and can depend on $ n$ but is bounded by two constants $ 0<c_1\leq a_n \leq c_2 < 1$ .
  • $ h(n)$ is some “fudge term” which is negligeable compared to $ n$ (say $ O(n^\epsilon)$ for $ 0\leq \epsilon < 1$ ).

If $ a_n$ was a constant, then I could use the Akra-Bazzi method to get a result. On the other hand, if the fudge term didn’t exist, then some type of recursion-tree analysis would be straight-forward.

To make things a bit more concrete, here is the recurrence I want to get the asymptotic growth of:

$ $ \begin{cases} T(n) = 1, & \text{for n = 1;}\ T(n) \leq T(a_n n + \sqrt n) + T((1-a_n)n+\sqrt n) + n, & \text{for $ n \geq 2$ } \end{cases}$ $ Where $ \frac{1}{4} \leq a_n \leq \frac{3}{4}$ for all $ n\geq 1$ .

I tried various guesses on upper bounds or transformations. Everything tells me this should work out to $ O(n\log(n))$ and I can argue informaly that it does (although I might be wrong). But I can only prove $ O(n^{1+\epsilon})$ (for any $ \epsilon>0$ ), and this feels like something that some generalization of the Master theorem à la Akra-Bazzi should be able to take care of.

Any suggestions on how to tackle this type of recurrence?

Is DM allowed to fudge dice in Adventurer League play?

You’re Empowered. Make decisions about how the group interacts with the adventure; adjusting or improvising is encouraged, so long as you maintain the adventure’s spirit. This doesn’t allow you to implement house rules or change those of the D&D Adventurers League, however; they should be consistent in this regard. AL DMG, pg. 5

Does this mean the DM may fudge a success/fail ability check/attack roll/saving throw?

Usually I’d say yes, but then if a PC is failing his death saves three times, and the DM say that he counts that as save/neutral, I feel a little bit uncomfortable.

How do I model a fudge roll with rerolls in Anydice?

I need a little help with a probability calculation in anydice. We are making a fudge based game using 4 fudge dice, so basically a d3 system: -1,0,1

We are allowing your attribute or stats in the game go to go from -3 to 4 and high stats allows you to reroll a dice.

So basically on any fudge roll a character can reroll a number of dice up to his stat maximum. If he has a negative stat he has to take away dice from the initial roll.

I figured out how to determine the probabilities of rolling with 4 dice and lower representing a negative stat:

output 4d{-1,0,1}  

What I need help with is determining the probability of rerolling a dice when a character has a positive stat.

An example of what I am talking about: My fighter has a 1 strength and I roll my 4 fudge dice I get 3 blanks and 1 – on the dice. I decide to reroll the 1 – to try and get a better result on the second roll.

A formula I tried in any dice to represent the example above is 4d{-1,0,1}-1

The problem with this forumla is it only works if the second reroll is better their is a possibility the second reroll will be the same so it does not quite work.

Does anyone have some insight on a way I can make a proper formula in anydice to represent a reroll of 4 fate dice with the possibility of 1-4 dice being rerolled and the possibility that the second reroll has only a 66% chance of being better than the first reroll.

I am making assumptions that a player will only reroll dice if they have a negative appear on the fudge dice.

When should I fudge dice rolls?

When I started my first D&D campaign as a DM, I accidentally rolled and confirmed a crit on a PC from a goblin. It was an instant kill as our campaign had no cleric. That time I decided to fudge the dice. Now, there’s a similar problem, but this time the PCs are at 3rd level and they are dealing with a very important NPC. If they fail this one diplomacy check, the entire game world will fall apart, as the king would then send his entire army against the PC’s homeland and will destroy it, plunging my entire game world into chaos, at which time drow that I wanted to save for a later adventure will have to come out, which will instigate a wizard’s guild to release their secret ultra-deadly virus, and everything in my game world, including the PCs, will die. So should I fudge the dice roll? When is it good to fudge it?

NTP Stratum Won’t “Fudge”

I have two servers, blue and green. I want blue to pull time from green but it won’t because the stratum on green is too high. Green has a regular internet connection. Blue does not. In googling the topic, I should be able to “fudge” the stratum value, but it doesn’t seem to take.

At the bottom of the code, the client affirms that the stratum is too high.

Recommendations to force the ntp server to lie?

Ubuntu 18.04.2

root@ntpserver:/home/green# ntpq -pn      remote           refid      st t when poll reach   delay   offset  jitter ==============================================================================     .INIT.          16 u    -   64    0    0.000    0.000   0.000 +2610:20:6f97:97 .NIST.           1 u   14   64   17  102.882  -34.929  35.299 +2001:67c:1560:8    2 u   16   64   17  161.268  -13.182  12.489 root@ntpserver:/home/green# cat /etc/ntp.conf # /etc/ntp.conf, configuration for ntpd; see ntp.conf(5) for help  driftfile /var/lib/ntp/ntp.drift leapfile /usr/share/zoneinfo/leap-seconds.list logfile /var/log/ntp.log   # You must create /var/log/ntpstats (owned by ntp:ntp) to enable logging. statsdir /var/log/ntpstats/ statistics loopstats peerstats clockstats filegen loopstats file loopstats type day enable filegen peerstats file peerstats type day enable filegen clockstats file clockstats type day enable  # Comment this out if you have a refclock and want it to be able to discipline # the clock by itself (e.g. if the system is not connected to the network). tos minclock 4 minsane 3  # Specify one or more NTP servers.  # Use servers from the NTP Pool Project. Approved by Ubuntu Technical Board # on 2011-02-08 (LP: #104525). See http://www.pool.ntp.org/join.html for # more information. server time.nist.gov  server fudge stratum 8  # Use Ubuntu's ntp server as a fallback. server ntp.ubuntu.com preempt  # Access control configuration; see /usr/share/doc/ntpsec-doc/html/accopt.html # for details. # # Note that "restrict" applies to both servers and clients, so a configuration # that might be intended to block requests from certain clients could also end # up blocking replies from your own upstream servers.  # By default, exchange time with everybody, but don't allow configuration. restrict default kod nomodify nopeer noquery limited  # Local users may interrogate the ntp server more closely. restrict restrict ::1 root@ntpserver:/home/green#    root@blue:/etc# ntpdate -dv  1 Mar 18:13:34 ntpdate[122014]: ntpdate 4.2.6p5@1.2349-o Fri Jul 22 17:30:52 UTC 2016 (1) transmit( receive( transmit( receive( transmit( receive( transmit( receive( Server dropped: strata too high server, port 123 stratum 16, precision -23, leap 11, trust 000 refid [], delay 0.02589, dispersion 0.00005 transmitted 4, in filter 4 reference time:    00000000.00000000  Mon, Jan  1 1900  0:00:00.000 originate timestamp: e023f4ea.f1a932d2  Fri, Mar  1 2019 18:14:02.943 transmit timestamp:  e023f4d4.5f61696f  Fri, Mar  1 2019 18:13:40.372 filter delay:  0.02594  0.02596  0.02611  0.02589          0.00000  0.00000  0.00000  0.00000 filter offset: 22.57128 22.57129 22.57125 22.57120          0.000000 0.000000 0.000000 0.000000 delay 0.02589, dispersion 0.00005 offset 22.571203   1 Mar 18:13:40 ntpdate[122014]: no server suitable for synchronization found root@blue:/etc#