There are two ways that spells are rolled for in D&amp;D 5e, depending on the spell: attack rolls rolled by the players and saving throws rolled by the DM.  But as far as I can see, saving throws could be made as attack rolls instead. I know D&amp;D 4e did it this way, with players making attacks against AC/Fortitude/Reflex/Will Defenses instead of the DM making Fort/Ref/Will saving throws and players making attack rolls against AC.  I don't really see why the designers of D&amp;D 5e would choose to have two different ways to roll something that, as far as I can tell, could be simplified into one mechanic (and ), so I wondered if I'm missing something important that distinguishes the two methods.  I guess it boils down to: Is there any difference in probabilities or practical concerns between one or the other method, or are they interchangeable?  This is related to  and  This question is focused on if there is any practical difference, regardless of why they actually made that design decision.
In , they give rules so that players can make all the rolls, rather than the DM sometimes rolling for enemies. In one section, there are specifically , which the players roll against, rather than the DM. However, after doing some math, I think they've made a mistake. They say that you convert a Saving Throw into a Saving Throw Check by adding 11 to the defender's saving throw modifiers, and using that as the DC for the check.  The player then rolls against this DC, adding their spellcasing ability modifier and proficiency bonus.  However, according to the following math, this conversion does not produce the same results. In this math, I compare the chances of a player succeeding on a saving throw check, using the rules in the UA article, and of a monster failing its saving throw using the standard PHB rules. If the math is correct, both of these results should have the same chance. These are the formulas I used.  Chance to succeed Saving Throw Check = (20 - DC + 1 + proficiency + casting mod) / 20 Chance to FAIL a Saving Throw = (DC - 1 - save proficiency - save mod) / 20  Assuming a proficiency bonus of +2, +0 for all ability mods, and no save proficiency:  Monster's Saving throw Check DC = 11 + save mod = 11 Chance to succeed a saving throw check DC11: (20 - 11 + 1 + proficiency + casting mod) / 20 = 12/20 = 60% Player's Saving throw DC = 8 + proficiency + spellcasting ability mod = 10 Chance for monster to fail saving throw DC10: (10 - 1 - save proficiency - save mod) / 20 = 9/20 = 45%  If this were a valid conversion, both formulas would result in the same chance of success for the player, and failure for the monster respectively, however, they are off by 15%. This suggests that the unearthed Arcana's rules are not a valid conversion. Are the Unearthed Arcana rules wrong, or is my math wrong?
Update iOS 5.1.1 on iPad 1 to at least iOS 6 Do DOM tree elements with ids become global variables? PHP "header (location)" inside IFRAME, to load in _top location? Strange black shading. Cannot fully light mesh. (Cycles) Continuous function whose right hand derivative equals 0 is constant? locale not found/setting locale failed - what should I do? I've installed Debian 7 i386 on my VPS (OpenVZ). Everything works fine, except locales - any attempt to install anything shows:  [...] perl: warning: Setting locale failed. perl: warning: Please check that your locale settings:     LANGUAGE = (unset),     LC_ALL = (unset),     LANG = "pl_PL.UTF-8"     are supported and installed on your system. perl: warning: Falling back to the standard locale ("C"). locale: Cannot set LC_CTYPE to default locale: No such file or directory locale: Cannot set LC_MESSAGES to default locale: No such file or directory locale: Cannot set LC_ALL to default locale: No such file or directory [...]   What I've tried:   Generating locales myself - update-locale LC_ALL="pl_PL.UTF-8" - shows:  apt-get install --reinstall locales  The same with dpkg-reconfigure locales + setting pl_PL.UTF-8, pl_PL.ISO-8859-2 or even en_US:  export LC_ALL=pl_PL.UTF-8 (even on root):  -bash: warning: setlocale: LC_ALL: cannot change locale (pl_PL.UTF-8)    Here is what shows locale:  root:~# locale locale: Cannot set LC_CTYPE to default locale: No such file or directory locale: Cannot set LC_MESSAGES to default locale: No such file or directory locale: Cannot set LC_ALL to default locale: No such file or directory LANG=pl_PL.UTF-8 LANGUAGE= LC_CTYPE="pl_PL.UTF-8" LC_NUMERIC="pl_PL.UTF-8" LC_TIME="pl_PL.UTF-8" LC_COLLATE="pl_PL.UTF-8" LC_MONETARY="pl_PL.UTF-8" LC_MESSAGES="pl_PL.UTF-8" LC_PAPER="pl_PL.UTF-8" LC_NAME="pl_PL.UTF-8" LC_ADDRESS="pl_PL.UTF-8" LC_TELEPHONE="pl_PL.UTF-8" LC_MEASUREMENT="pl_PL.UTF-8" LC_IDENTIFICATION="pl_PL.UTF-8" LC_ALL=   Nothing interesting found in /var/log. Even changing repo to official + purge and manual installation locales doesn't solve my problem, which manifests itself on each fresh installation of Debian 7. Windows 10 lets you 'schedule' a reboot for later. I want to disable it.  Evidently Windows scheduled itself for a reboot last night when I wasn't looking and just closed everything I had been working on the night before.  I reboot on the regular; I don't need Windows to do that for me.  Can I disable it completely? I don't mind if it downloads everything, and then says "hey, you should reboot," but it should never reboot itself, ever.  I'm using the "Pro" edition of Windows 10. I've been using gksudo nautilus and sudo nautilus through Alt+F2.   What's the difference? They look very similar! If there are 5 points on the surface of a sphere, then there is a closed half sphere, containing at least 4 of them.  It's in a pigeonhole list of problems. But, I think I have to use rotations in more than 1 dimension.  Regards I unintentionally and stupidly wiped my Clash of Clans game data. I went to Application Manager on my Android and clicked 'Clear data'. (I used this for fixes before and it never started a new game.)   Now, my level 60 or so base has been wiped as if was to start a new game. Have I doomed myself to starting again or is there a way in which I can retrieve my old game save? Maybe by contacting Supercell? I have a snapshot of my base. Flowchart using Tikz I'm trying to create a fine flowchart that is a bit complicated. Therefore I need a block for a predefined process and a connector block as well as a data block. Can someone help me? In comment is what I'd like to see in my code to keep my code nicely arranged. The rest of the code is a simple example for the Tikz site.  \documentclass{article}  \usepackage[latin1]{inputenc} \usepackage{tikz} \usetikzlibrary{shapes,arrows} \begin{document} \pagestyle{empty}   % Define block styles \tikzstyle{decision} = [diamond, draw, fill=blue!20,      text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt] \tikzstyle{block} = [rectangle, draw, fill=blue!20,      text width=5em, text centered, rounded corners, minimum height=4em] \tikzstyle{line} = [draw, -latex'] \tikzstyle{cloud} = [draw, ellipse,fill=red!20, node distance=3cm,     minimum height=2em]  %\tikzstyle{subroutine} = [draw,rectangle split, rectangle split         horizontal,rectangle split parts=3,minimum height=1cm]  %\tikzstyle{connector} = [draw,circle,...] %\tikzstyle{data} = [draw, trapezium, ...]  \begin{tikzpicture}[node distance = 2cm, auto]     % Place nodes     \node [block] (init) {initialize model};     \node [cloud, left of=init] (expert) {expert};     \node [cloud, right of=init] (system) {system};     \node [block, below of=init] (identify) {identify candidate models};     \node [block, below of=identify] (evaluate) {evaluate candidate models};     \node [block, left of=evaluate, node distance=3cm] (update) {update     model};     \node [decision, below of=evaluate] (decide) {is best candidate     better?};     \node [block, below of=decide, node distance=3cm] (stop) {stop};     % Draw edges     \path [line] (init) -- (identify);     \path [line] (identify) -- (evaluate);     \path [line] (evaluate) -- (decide);     \path [line] (decide) -| node [near start] {yes} (update);     \path [line] (update) |- (identify);     \path [line] (decide) -- node {no}(stop);     \path [line,dashed] (expert) -- (init);     \path [line,dashed] (system) -- (init);     \path [line,dashed] (system) |- (evaluate); \end{tikzpicture}   \end{document} Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$. I'm looking for some guidance in solving this. I have read through my text multiple times trying to find something similar to this and I'm coming up with nothing. I'm not really sure where to start on solving this problem.  The question simply states     Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.   I'm very new to binomial coefficients, and extremely lost. I am trying to solve this exercise from Royden's 3rd edition.     The question is as follows: Let $f$ be a real-valued function defined for all real numbers. Show that the set of points at which $f$ is continuous is a $G_{\delta}$.    Let $$A_n = \{y : \text{there is a }~\delta_y \gt 0 : |f(s)-f(t)|\lt 1/n ~ \text{whenever}~ s,t \in (y-\delta, y+\delta)\}\;.$$     Then by the definition of open sets, $A_n$ is open.     To complete the proof, I need help in showing that $f$ is continuous at say $x$ if and only if $x\in \cap A_n$.     If $f$ is continuous at $x$, the there is a $\delta \gt 0$ such that $|f(x) - f(a)| \lt 1/n$ whenever, $x\in (a-\delta, a+\delta)$. so $x \in A_n$ son it must be in $\cap A_n$.  Thanks. As linguistics student, I have to put more than one thing on a character every now and then. For example, I need to type ā̆. I thought I could simply do that by typing \={\u{a}}, but then the macron is placed above an empty space in front of the character.  How can I solve this? Thanks  P.S. I'm using MiKTeX 2.9, running on Windows 8; in case it might be of use. Why an abstract class implementing an interface can miss the declaration/implementation of one of the interface's methods? How do I choose a macro lens for a Canon APS-C camera? How to convince longtable to do a page break earlier using the longtable package to typeset page spanning tables, I run into a nasty behaviour: only a dummy table head and the caption are put on the following page. The contents of the table is extracted from program sources. I don't have much influence here.  \documentclass[a4paper,twoside,DIV10,BCOR1.5cm]{scrbook} \usepackage{longtable} \newlength{\tablcol} \setlength{\tablcol}{4.7cm} \newlength{\tabrcol} \setlength{\tabrcol}{8.1cm} \itemsep0ex plus0.2ex % \begin{document} \begin{longtable}{p{\tablcol}p{\tabrcol}}% % \hline \multicolumn{1}{l}{{\bfseries Feld}} &amp; \multicolumn{1}{l}{{\bfseries Beschreibung}}\\ \hline \endfirsthead % \hline \multicolumn{2}{l}% {{\small\slshape Fortsetzung der vorherigen Seite}}\\ \hline \multicolumn{1}{l}{{\bfseries Feld}} &amp; \multicolumn{1}{l}{{\bfseries Beschreibung}}\\ \hline \endhead % \hline \multicolumn{2}{l}% {{\small\slshape Fortsetzung auf der n\"achsten Seite}}\\ \hline \endfoot % \hline \caption[show user output]{Beschreibung der Output-Struktur des show user Statements} \endlastfoot % \label{tucshowxuser}% {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ {\scshape changer} &amp; Name des Benutzers der dieses Objekt zuletzt ge\"andert hat \\ {\scshape change\_time} &amp; Datum und Uhrzeit der letzten \"Anderung \\ {\scshape privs} &amp; Zeichenkette die K\"urzel f\"ur die Benutzerrechte auf dieses Objekt enth\"alt \\ {\scshape commenttype} &amp; Typ des Kommentars \\ {\scshape comment} &amp; Kommentar zum Objekt, wenn vorhanden \\ {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ {\scshape changer} &amp; Name des Benutzers der dieses Objekt zuletzt ge\"andert hat \\ {\scshape change\_time} &amp; Datum und Uhrzeit der letzten \"Anderung \\ {\scshape privs} &amp; Zeichenkette die K\"urzel f\"ur die Benutzerrechte auf dieses Objekt enth\"alt \\ {\scshape commenttype} &amp; Typ des Kommentars \\ {\scshape comment} &amp; Kommentar zum Objekt, wenn vorhanden \\ {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ {\scshape changer} &amp; Name des Benutzers der dieses Objekt zuletzt ge\"andert hat \\ {\scshape change\_time} &amp; Datum und Uhrzeit der letzten \"Anderung \\ {\scshape privs} &amp; Zeichenkette die K\"urzel f\"ur die Benutzerrechte auf dieses Objekt enth\"alt \\ {\scshape commenttype} &amp; Typ des Kommentars \\ {\scshape comment} &amp; Kommentar zum Objekt, wenn vorhanden \\ {\scshape id} &amp; Die Nummer des Repository Objektes \\ {\scshape name} &amp; Der Name des Objektes \\ {\scshape creator} &amp; Name des Benutzers der dieses Objekt angelegt hat \\ {\scshape create\_time} &amp; Datum und Uhrzeit der Erstellung \\ \end{longtable}  \end{document}   The problem is that I don't find a method to force a page break earlier. A page that isn't filled entirely, followed by a page with the last part of a table is better than this.  I tried to add "\needspace{someLength}" at the beginning or end of the rows, but that doesn't work either. It simply makes the rows someLength high instead of forcing a page break if there's no more than someLength room left on the page.  I'd be more than grateful for some solution or even a good hint.  TIA Radical change of favourite tags doesn't reflect in questions list Reading file contents on the client-side in javascript in various browsers unable to reset root password of mysql I need to reset the root password of my local mysql installation but it woudln't let me. I've tried this:  $ sudo /etc/init.d/mysql stop  * Stopping MySQL database server mysqld                                                                                                              [ OK ]  [1]-  Exit 1                  sudo /usr/sbin/mysqld --skip-grant-tables --skip-networking [2]+  Exit 1                  sudo /usr/sbin/mysqld --skip-grant-tables --skip-networking reg@regDesktopHome:~$ sudo mysqld --skip-grant-tables &amp; [1] 13651 reg@regDesktopHome:~$ 140627 19:02:02 [Warning] Using unique option prefix key_buffer instead of key_buffer_size is deprecated and will be removed in a future release. Please use the full name instead.  reg@regDesktopHome:~$ mysql -u root mysql ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO) reg@regDesktopHome:~$ sudo mysql -u root mysql ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO) [1]+  Exit 1                  sudo mysqld --skip-grant-tables   How can I get the password reset? edit 1 I got this:  $ ps ax| grep mysql 16515 ?        Ssl    0:00 /usr/sbin/mysqld 16551 pts/23   S+     0:00 grep --color=auto mysql reg@regDesktopHome:~/semios/v3upgrade$ sudo kill -9 16515 reg@regDesktopHome:~/semios/v3upgrade$ ps ax| grep mysql 16678 ?        Ssl    0:00 /usr/sbin/mysqld 16715 pts/23   S+     0:00 grep --color=auto mysql reg@regDesktopHome:~/semios/v3upgrade$ mysql -u root ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)   looks like a process is automatically restarting mysql as soon as I kill it...