![]() Many algorithms rely on a huge pre-generated database and are effectively nothing more.Īs a simple example of a strong solution, the game of tic-tac-toe is easily solvable as a draw for both players with perfect play (a result manually determinable). However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate a move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time. Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree. ![]() However, these proofs are not as helpful in understanding deeper reasons why some games are solvable as a draw, and other, seemingly very similar games are solvable as a win. The resulting proof gives an optimal strategy for every possible position on the board. īy contrast, "strong" proofs often proceed by brute force-using a computer to exhaustively search a game tree to figure out what would happen if perfect play were realized. "Ultra-weak" proofs require a scholar to reason about the abstract properties of the game, and show how these properties lead to certain outcomes if perfect play is realized. Strong solution Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or both sides.ĭespite their name, many game theorists believe that "ultra-weak" proofs are the deepest, most interesting and valuable. Weak solution Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play. Solving such a game may use combinatorial game theory and/or computer assistance.Ī two-player game can be solved on several levels: Ultra-weak solution Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance It's not something you should necessarily do every game, but exchanging is often the difficult decision that needs to be made.Game whose outcome can be correctly predictedĪ solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. If you exchange your tiles and score zero points on one turn, but then score 25 points on the next turn with your replacement tiles, you're in better shape than having scored 10 points and 10 points. They don't just consider how many points they can score on this turn, but how each move they make will affect their ability to score on future turns. Scrabble players are always thinking ahead. You could play IF or FOE or OAF for minimal points - or you could exchange all seven of your letters and get a fresh start next turn. Imagine you're holding the letters AEFIIOO. One scenario where you'd be wise to exchange is a situation every Scrabble player has faced: a rack full of vowels. But expert players know that in many situations, exchanging is the right thing to do. Scrabble players are allowed to use their turn to exchange some (or all) of their tiles for new ones.Įxchanging is a strategy many casual players are afraid to try because it doesn't score any points. Ridding yourself of the Q reopens the door to high-scoring moves in the future. When you find yourself with the Q, in many cases it's best to cut your losses and play one of those words, even if it scores poorly. The easiest to remember are QI (the vital life force in traditional Chinese culture) and QAT (a shrub that is cultivated for use as a drug). In reality, there is a small handful of words that contain a Q with no U, many of which are loanwords from other languages. They also might assume that a Q needs to be paired with a U, although that isn't the case. First, because the Q is worth a game-high 10 points, they might assume that it will guarantee them a high-scoring play sometime down the road. There are a couple reasons why players do this. That's why one of the biggest mistakes inexperienced players make is holding on to the Q for more than one turn. The Q is the most dreaded tile in Scrabble - it appears in relatively few words, usually needs to be paired with a U to be effective, and it drastically reduces your odds of making a high-scoring play. Account icon An icon in the shape of a person's head and shoulders.
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