I designed simple AI for 3x3 Tic Tac Toe game. However I didn't want to do neither complete search, nor MinMax. Instead i thought of a heuristic that would evaluate values for all of 9 fields, and then AI would choose the field with highest value. The problem is, I have absolutely no idea how to determine, whether it is a perfect (unbeatable) algorithm.  And here are the details: Every Field has several WinPaths on the grid. Middle one has 4 (horizontal, vertical and two diagonals), corners have 3 each (horizontal, diagonal and one vertical), sides have only 2 each (horizontal and vertical). Value of each Field equals sum of its WinPaths values. And WinPath value depends on its contents:   Empty: [ | | ] - 1 point One symbol: [X| | ] - 10 points // can be any symbol in any place Two different symbols: [X|O| ] - 0 points // they can be arranged in any possible way Two identical opponents symbols: [X|X| ] - 100 points // arranged in any of three ways Two identical "my" symbols: [O|O| ] - 1000 points // arranged in any of three ways   This way for example beginning situation has values as below:   3 | 2 | 3  ---+---+---  2 | 4 | 2  ---+---+---  3 | 2 | 3    However a later one can be like this (X is moving now):   X | 10| O ---+---+---  O | O |110 ---+---+---  X | 20| 20   So is there any reliable way to find out whether is this a perfect algorithm, or does it have any disadvantages?  PS. I was trying (from the perspective of player) to create a fork situation so I could beat this AI, but I have failed.
In a tic-tac-toe implementation I guess that the challenging part is to determine the best move to be played by the machine.  What are the algorithms that can pursued? I'm looking into implementations from simple to complex. How would I go about tackling this part of the problem?
What is the maximum number of downvotes a question can have I was just wondering what the maximum number of down votes a question can have before it is removed from StackOverflow. What is dconf, what is its function, and how do I use it? Mark Shuttleworth  about the decision to include the Qt libraries in the 11.10 release, with a  Jono Bacon. Mark states that the biggest challenge to integrating apps written in Qt into the larger Ubuntu system is Qt's current non-compatibility with dconf.  What is dconf, and what is the role it plays in Ubuntu? We know that if you (using Polyjuice), take the form of someone who had been injured, you assume that injured form (e.g. Barty/Moody). If you are injured, presumably you would be uninjured while under Polyjuice. My question is, is this in real-time? That is, if you take a Polyjuice, and while you're still under its effects, the person being transformed into gets injured (or even dies), will that injury be transferred onto you? And conversely, if you get injured while in someone else's body, will that transfer over to your real body after the Polyjuice wears off, will it disappear, or will it go to the person you turned into? what is the area of the region [ (x,y):0<x , y<1 , 3/4<x+y<3/2 ]? How to prove that Fibonacci number is integer? "This site is all about getting answers. It's not a discussion forum. There's no chit-chat." Propagate all arguments in a bash shell script Installing AMD & Intel dual graphics Ant-Man, shrinking, and weight Can the rogue repeatedly hide in combat to sneak attack the same enemy? One of my players is a rogue and has been, on his turn, using Cunning Action to hide as a bonus action and immediately afterwards attacking. I have been ruling that this does work to grant him advantage as an unseen attacker as I believe that is the RAW, but it seems a little strange. Is he really, in the span of 6 seconds, ducking behind a corner and popping back out and this completely disorientates his target? I guess I just wanted to make sure I was ruling correctly. Should I put myself last? "me and my friends" vs. "my friends and me" or "my friends and I" How to type \sim above another symbol x? I want to put a "~" above x, just like \hat x but replacing \hat with \sim.   How to do that? How to find Oracle's installed version and release from a program? Why does Ubuntu 14.04 LTS use a non-LTS kernel version? Software for Calendar Designing Which is the best software of making a calendar. Coreldraw or Illustrator? What is the standard size of calendar? And is there any inbuilt format or template fro making calendar in both Corel or Illustrator? Also, even though Photoshop is a rasterised software but still wanted to ask can it be designed in Photoshop also? Who can use magic scrolls? I'm confused about who can use scrolls in 5e. In the DMG, p139 under Magic Item Categories: Scrolls, it states that:     Any creature that can understand a written language can read the   arcane script on a scroll and attempt to activate it.   This implies that anyone can try to cast a spell using a scroll. However, on p.200 in the Spell Scroll entry it states that:     If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible.   Then there is the bit about a DC 10 + scroll spell level ability check if the spell is higher than a spell slot that you can cast.     If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + spell's level. On a failed check, the spell disappears from the scroll with no other effect.    So, which is it? Can anyone who can read a language use a scroll (like a fighter) if they make an arcana check, or just a PC with that specific spell in their spell list (only spell casters)? Almost universal class I so stuck with a problem of set theory. But first a recursive definition:   Define $R_0=\emptyset$ If $R_\alpha$ is defined, then $R_{\alpha+1}=\mathcal{P}(R_\alpha)$ (the power set). For a limit ordinal $\gamma$, if $R_\alpha$ is defined for all $\alpha&lt;\gamma$, then define $R_\gamma=\displaystyle\bigcup_{\alpha&lt;\gamma} R_\alpha$   We define $\text{BF}=\displaystyle\bigcup_{\alpha\in\text{OR}} R_\alpha$ (the class of well founded sets).  Next, my problem     Take $A\subseteq \text{BF}$ a proper transitive class such that $(A,\in)\models\text{ZF}$. Prove that $A$ is almost universal.    I think that the exercise is false because if it was true, then we could conclude that the strongly inaccessible cardinals doesn't exists. This because if $\kappa$ is strongly inaccessible then $R_\kappa$ satisfies the hypothesis but $R_\kappa$ isn't almost universal. I really appreciate any hint or/and suggestion.   Edit: my counterexample is wrong. But, then, how can I solve the exercise? Defining the Product of Ideals Where does the &quot;naive definition&quot; of the product of two ideals $I$ and $J$, $IJ = \{ ij \mid i \in I, j \in J \}$ fall apart? (The product of two ideals $I$ and $J$ is defined to be $IJ := \sum_i a_ib_i$, where each $a_i$ is in $I$ and each $b_i$ is in $J$.)  Note: This is a question from a problem set I'm working on. I am not expecting a full solution for the answers, but I'd like some help knowing where to look. It seems to work fine in $\mathbb{Z}$ and $\mathbb{C}[x]$. I am asking this question because I've always had the impression that manuscripts submitted to a journal in my field (theoretical linguistics) take an insanely long time to get published, and sometimes I get the impression that this is because, most of the time, nobody other than the author cares about getting things done within a reasonable amount of time. Some examples from personal experience follow.   For the last paper I submitted before getting my PhD, I had to wait nine months from the submission date to get reviews back from the referees. Last week I got a review request from a journal I had never reviewed for previously. The review deadline is March 15 (almost four months). In early October, I submitted a manuscript to a journal that I know asks reviewers to return reviews within 6 weeks. I checked the status of the manuscript online and it still says "with editor". Earlier this year, I was about to start writing a review when my wife went into labor. By the time we came back from the hospital, I had forgotten about the review, so I missed the deadline. The editor didn't contact me to ask about the review until two months after the deadline. Late in 2013, I was asked to write a survey chapter for a handbook. The expected publication date of the handbook is summer 2016.   All of this is not me being unlucky with editors and referees. In private conversations through the years, many colleagues have confirmed that it is virtually unheard of to get reviews back within 3 months of submission; 5 or 6 months seems to be a good average, but in some cases it can take longer (see my first point above). In general, everybody seems to have accepted that the submission-to-printed-journal process is going to take a bare minimum of one year, and that's assuming that the manuscript is accepted without revisions. If revisions are required, two years is not out of the question. Also, it's not like our papers are ridiculously long. I've reviewed about 100 papers so far, and the longest one was about 50 single-space pages; 30-35 single-spaced pages is closer to average.  I remember that, when I was a postdoc, my astrophysics housemate mentioned that in his field the entire submission-to-printed-journal process took only three or four months. I really can't see a good reason why theoretical linguistics shouldn't operate on similar timeframes, other than the fact that everybody seems to have grown used to things taking way longer than they really need to. What are the wait times in other fields? How do you manage to get things done quickly? Prepend phone numbers with a calling card dial in number