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Topic: Alpha-beta pruning

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Alpha-beta pruning - Wikipedia, the free encyclopedia Alpha-beta pruning is a technique to reduce the number of nodes evaluated in the search tree by the minimax algorithm. The algorithm maintains two values, alpha and beta, which represent the minimum score that the maximizing player is assured of and the maximum score that the minimizing player is assured of respectively. Initially alpha is negative infinity and beta is positive infinity. en.wikipedia.org /wiki/Alpha-beta_pruning   (688 words)

Talk:Alpha-beta pruning - Wikipedia, the free encyclopedia Alpha-beta pruning reduces the number of searches required under the minimax algorithm by the square-root of what the total number would otherwise be. The pseudocode is correct, regardless of whether alpha or beta is returned at the cut-offs. Assuming I had time to search 4 plys deep previous to pruning, I would have had time for 6^1+6^2+6^3+6^4=1554 nodes. en.wikipedia.org /wiki/Talk:Alpha-beta_pruning   (539 words)

Alpha-Beta Search If a move results in a score that is greater than alpha, but less than beta, this is the move that the side to move is going to plan to play, unless something changes later on. The same thing is done with this alpha-beta function. Beta is the worst-case scenario for the opponent. www.seanet.com /~brucemo/topics/alphabeta.htm   (1809 words)

CS 161 Recitation Notes - Minimax with Alpha Beta Pruning Alpha-beta pruning gets its name from two bounds that are passed along during the calculation, which restrict the set of possible solutions based on the portion of the search tree that has already been seen. If we had pruned when alpha and beta were tied at this node, then we would have had two nodes at the top level that were both 3, so we would assume them to be a tie. Likewise the final value of alpha in a max node is passed on to possibly change the beta value of its parent. www.cs.ucla.edu /~rosen/161/notes/alphabeta.html   (2452 words)

Alpha Beta Pruning We will go through a simple example that will illustrate how alpha-beta pruning works. To begin, we initialize alpha with a value of - infinity and beta with a value of + inifity (refer back to the definitions of alpha and beta if you're wondering why we are doing this). Due to the nature of alpha and beta, there are instances in a search tree where we can ignore, or "prune" a tree. pages.cpsc.ucalgary.ca /~sueng/533/AlphaBetaPruning.html   (2072 words)

Alpha-Beta Pruning In fact, pruning happens exactly when alpha becomes greater than or equal to beta -- that is, when the alpha and beta lines hit each other in the node value diagram above. As we discussed earlier, this is a point where alpha-beta pruning kicks in: we know the minimizer would never let the game reach this node, so we don't have to look at its remaining children. At each node, the alpha and beta values may be updated as we iterate over the node's children. www.cs.berkeley.edu /~milch/cs188/alpha-beta.html   (760 words)

alpha-beta pruning Frank's Home Page Each node gets the alpha and beta value from its parent and then adjusts these according to the results from the children (and obviusly passes these values on to the remaining children). So in the algorithm, for each node you have an alpha and a beta value. The alpha value is the best max value known so far along the path to the current node. www.langbein.org /node/94   (373 words)

MiniMax Alpha-beta pruning is a technique that reduces the amount of work your software has to do to implement the minimax strategy. Often this will be combined with Alpha-Beta pruning but more of that later. Beta pruning is a bit more complex to follow and needs a larger diagram to explain it clearly. www.adit.co.uk /html/minimax.html   (1359 words)

clarification-hw4.txt On the other hand, running Alpha-Beta pruning on the same input sets the variable *Counter* to 6. If no pruning is possible (or if the pruning mechanism is disabled) during the search, then after the search is performed, the variable *Counter* should be equal to the number of leaves in the tree. Thus, after running a search algorithm which does not do any pruning, the value of counter should be 8. www.cs.ucla.edu /classes/spring02/cs161/l1/clarification-hw4.txt   (274 words)

Computer Science Game Trees The same pruning condition applies if you are the min player, except instead of finding the move that yields alpha, you would find the move that yields beta. To guarantee that this algorithm returns a move, we can start alpha with -infinity (the best you can do is lose) and beta with infinity (the worst your opponent can do is to let you win), and update these values as we examine more nodes. If at any time, alpha >= beta, then your opponent's best move can force a worse position than your best move so far, and so there is no need to further evaluate this move. www.ocf.berkeley.edu /~yosenl/extras/alphabeta/alphabeta.html   (1087 words)

Minimax search and alpha-beta pruning When the optimal child is selected at every opportunity, alpha-beta pruning causes all the rest of the children to be pruned away at every other level of the tree; only that one child is explored. This is pseudo-code for minimax search with alpha-beta pruning, or simply alpha-beta search. If children of a node are visited in the worst possible order, it may be that no pruning occurs. www.cs.cornell.edu /courses/cs312/2002sp/lectures/rec21.htm   (1634 words)

Algorithms Alpha-beta pruning can be applied to trees of any depth and it often allows to prune away entire subtrees rather than just leaves. 1, Alpha-Beta search updates the values of a and ß as it goes along and prunes the remaining branches at a node as soon as the value of the current node is known to be worse than the current values of a and ß. Borrowing the idea of pruning, or eliminating possibilities from consideration without having to examine them, the algorthm allows us to discard large parts of the tree from consideration. www.stanford.edu /~msirota/soco/alphabeta.html   (364 words)

G13GAM -- Game Theory -- alpha-beta pruning So the alpha level, the `floor', will become the beta level, the ceiling, for the subsidiary analysis; the higher we can make the floor, the lower will be the resulting ceiling, and so the more efficient will be that analysis. The [potentially huge] savings made by pruning the moves in the blue box are [slightly] offset by the loss of information and the return of a lower bound rather than a true value. Note that the advantage is maximised by having the beta level as low as possible, and by having `good enough' moves as early in the list of moves as possible. www.maths.nott.ac.uk /personal/anw/G13GAM/alphabet.html   (1648 words)

Minimax and Alpha-Beta Pruning By contrast, alpha beta pruning only visits a node and its descendants if there is a possibility that the maximin or minimax values will be changed. Stated in words, the essence of alpha-beta pruning is that maximizing nodes return just as soon as they learn that they will not affect the decision of its minimizing parent by continuing further search. The method of alpha beta pruning is a more efficient depth-first search-based method for finding the maximin solution via an exhaustive search. students.cs.byu.edu /~cs670ta/Lectures/Minimax.html   (1818 words)

Alpha-beta pruning Beta cutoff: Given a Max node n, cutoff the search below n (i.e., don't generate or examine any more of n's children) if alpha(n) >= beta(i) for some MIN node ancestor i of n. Note: The alpha values start at -infinity and only increase, while beta values start at +infinity and only decrease. Alpha cutoff.: stop searching below MIN node n if beta(n) <= alpha(i) for some MAX node ancestor i of n. www.cs.umbc.edu /471/notes/games/sld015.htm   (97 words)

ICS 180, April 22, 1997 At depth D-2, however, nobody can prune, because all the children returned values greater than or equal to the values of beta they were passed, which at depth D-2 are negated and become less than or equal to alpha. Alpha and beta define an interval of the real number line (alpha,beta) of the evaluations we consider interesting. If a value is greater than beta we prune and immediately return, because we know it's not part of the principal variation; we don't really care about the exact value, only that it's greater than beta. www.ics.uci.edu /~eppstein/180a/970422.html   (1369 words)

CSC-105 2000S : The algorithms Dewdney describes assume that both players make the ``best'' possible move. How would the min-max and alpha-beta pruning algorithms change if one player selected a move randomly? What this means is that in the case of a randomly choosen move, the computer would have to eliminate all pruning strategies, min-max or alpha-beta, and evaluate all possible moves equally without regard to player strategy, which is unlikely to be effective, since the player is using 'only random moves' as their strategy. The alpha-beta pruning algorithm might change in response to random moves by a player by pruning fewer or no branches and leaving all legal moves as possiblities rather than only the "correct" legal moves; that would allow the game tree machine to respond faster, however, would use more space. The alpha-beta algorithm, on the other hand, where pruning is involved, seems like it would be affected much more by random moves, given that branches are cut off upon the assumption that red is making the best possible move. www.math.grin.edu /~rebelsky/CS105/Questions/question.34.html   (1191 words)

Alpha-beta Pruning Beta: upper bound on the value that a minimizing node may be assigned Alpha: lower bound on the value that a maximizing node may be assigned Search at a minimizing level can be cut off when a value less than alpha is discovered www.cs.cmu.edu /afs/cs.cmu.edu/academic/class/46927-f97/slides/Lec3/sld017.htm   (74 words)

MidtermReview.ppt Alpha and beta are bounds for the minimax values. Beta: at a MIN node, the smallest minimax value so far, amongst the daughters. Alpha: at a MAX node, the largest minimax value so far, amongst the daughters. www2.hawaii.edu /~binsted/ics461/MidtermReview.ppt   (136 words)

delucm.scm ; ; The underlying search algorithm is Minimax with improved alpha-beta pruning. cur_val (delucm-minimax cursucc (+ depth 1) delucm-opponent alpha beta)) (if (> cur_val alpha) (begin ; record this state if it could be the move ; we need to make (if (= depth 0) (set! b or all successor states have been examined ((or (>= i n) (> alpha beta)) (if (= player delucm-me) alpha beta)) ; examine current successor (else (set! www.cs.rpi.edu /~hollingd/ai/tournament/player-code/delucm.scm   (382 words)

Trees and Adversarial Search Remark: The “final” back-up value in  α-β pruning is not the same as the backed-up value in MINIMAX search, but using the “final” value gives the same results in selecting the best move as a full MINIMAX. The beta value is a upper bound on the minimizing level. The alpha value is a lower bound on the maximizing level. users.adelphia.net /~agwunn/lectureNotes/409LectureNotes/AdversarialSearch.html   (408 words)

MiniMax with Alpha-Beta Cutoff As the algorithm evolves, the alpha and beta values of a node may change, but the alpha value will never decrease, and the beta value will never increase. When a node is visited last, its score is set to the alpha value of that node, if it is a MAX node, otherwise it is set to the beta value. The score of a node will always be no less than the alpha value and no greater than the beta value of that node. www.cs.unca.edu /~bruce/Spring98/csci373/ch5/game-lecture.html   (1366 words)

Alpha-Beta Pruning for Minimax Most algorithmic descriptions of this process say to pass back the beta score for a min node and the alpha score for a max node, rather than the minimum or maximum of the children. alpha = the best score the search has found so far for Max (initialized to the lowest possible score) beta = the best score the search has found so far for Min (initialized to the highest possible score) While this may be appropriate if all you want is to rate the root node of a given tree, students have run into problems if they don't pass back the actual min or max of the children's scores. www.macalester.edu /~fox/cs65/alphabeta.html   (368 words)

Computer Chess Programming Theory Alpha-beta pruning is just a complicated-sounding name for "Don't check moves which cannot possibly have an effect on the outcome of your search." The theory is essentially simple, but takes a bit of thought before you get used to it. If the score is between alpha and beta then it will reduce the score of the opponent's previous move, but not enough to make the same previous move bad. If a move scores less than alpha then we're not interested in it because it's not good enough to worsen the score of the move to which it is a reply. www.frayn.net /beowulf/theory.html   (8273 words)

Min-Max Principle and Alpha-Beta Pruning Alpha-beta pruning can be expressed in terms of the min-max algorithm using a special kind of accumulator. In computing the min/max value of a game tree node, we can skip ("prune") the evaluation of some of the children nodes using what is known as alpha-beta pruning. If the value v of a child of C is greater or equal to beta, then we can use v as a value for C and skip the rest of the children of C. This is called "beta pruning". www.owlnet.rice.edu /~comp212/02-fall/lectures/38   (1176 words)

as2.doc Algorithms 2.1 Without Alpha-Beta pruning While (there are some leaves have not evaluate){ Copy global board array to local board array. Sushil Louis Assignment #2 Game: Connect N Note: Without Alpha-Beta pruning, the program is working very well. 2.1 With Alpha-Beta pruning After studying from the book, I come up with two rules: 1. www.scs.unr.edu /~sbuntha/class/fall2004/as2.doc   (855 words)

Alpha - Beta Pruning Notes If the score at the parent is greater than Alpha, set the Alpha value of the parent to this score and proceed with the next child, sending Alpha and Beta down. If the score at the parent is less than Beta, set the Beta value of the parent to this score and proceed with the next child, sending Alpha and Beta down. If the score at the parent is now less than Alpha stored at that parent, ignore any further children of this parent and backtrack the parent's value of Alpha and Beta up the tree. sern.ucalgary.ca /courses/CPSC/533/W99/presentations/L2_5B_Lima_Neitz/search.html   (1720 words)

Game Theory It should be noted however that all assumptions made concerning the optimality of alpha beta pruning assume an optimized tree model. This is what alpha beta pruning attempts to accomplish in game trees. This is alpha beta pruning and it can be quite effective. sern.ucalgary.ca /Courses/CPSC/533/W99/presentations/L1_5B_McCullough_Melnyk   (4130 words)

2620 Webtext: Alpha-Beta Pruning a complete description of game trees, minimax search, and alpha-beta pruning, try this example which discusses the game of Nim. the best case of alpha-beta pruning for an imaginary game. If you would like to see just how alpha-beta pruning works, try these animated examples to see www.atkinson.yorku.ca /~sychen/ITEC2620/webtext/alphaBeta.html   (183 words)

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