相关论文: Computational bounds for the 2048 game

We theoretically analyze the popular mobile app game `2048' for the first time in $n$-dimensional space. We show that one can reach the maximum value $2^{n_1n_2+1}$ and $2^{\left({\prod_{i=1}^{d} n_i}\right)+1}$ for the two dimensional…

The game of 2048 is a highly addictive game. It is easy to learn the game, but hard to master as the created game revealed that only about 1% games out of hundreds million ever played have been won. In this paper, we would like to explore…

2048 is a single-player stochastic puzzle game. This intriguing and addictive game has been popular worldwide and has attracted researchers to develop game-playing programs. Due to its simplicity and complexity, 2048 has become an…

2048 is a stochastic single-player game involving 16 cells on a 4 by 4 grid, where a player chooses a direction among up, down, left, and right to obtain a score by merging two tiles with the same number located in neighboring cells along…

We analyze the computational complexity of the popular computer games Threes!, 1024!, 2048 and many of their variants. For most known versions expanded to an m x n board, we show that it is NP-hard to decide whether a given starting…

The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by…

The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot succeed with probability greater than 1-ln2 \approx 0.31, no matter how many players are…

A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…

Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…

An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number…

We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an…

We prove an explicit upper bound on the amount of entanglement required by any strategy in a two-player cooperative game with classical questions and quantum answers. Specifically, we show that every strategy for a game with n-bit questions…

The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…

A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it…

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…

We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide…

In a recent work on quantum state preparation, S{\o}rensen and colleagues explore the possibility of using video games to help design quantum control protocols. The authors present a game called "Quantum Moves" in which gamers have to move…

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…

We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…