Computing a good strategy in a large extensive form game often demands an extraordinary amount of computer memory, necessitating the use of abstraction to reduce the game size. Typically, strategies from abstract games perform better in the real game as the granularity of abstraction is increased. This paper investigates two techniques for stitching a base strategy in a coarse abstraction of the full game tree, to expert strategies in fine abstractions of smaller subtrees. We provide a general framework for creating static experts, an approach that generalizes some previous strategy stitching efforts. In addition, we show that static experts can create strong agents for both 2-player and 3-player Leduc and Limit Texas Hold'em poker, and that a specific class of static experts can be preferred among a number of alternatives.

Video game virtual characters should interact with the player, each other, and the environment. However, the cost of scripting complex behaviors becomes a bottleneck in content creation. Our goal is to help game designers to more easily populate their open world with background characters that exhibit more believable behaviors. We use a cyclic scheduling model that generates dynamic schedules for the daily lives of virtual characters. The scheduler employs a tiered behavior architecture where behavior components are modular and reusable. This research validates the designer usability of an implementation of this model. We present the results of a user study that evaluates the scheduling system versus manual scripting based on three metrics of behavior creation: behavior completeness, behavior correctness and behavior implementation time. The results indicate that the behavior architecture produces more reliable behaviors and improves designer efficiency which will reduce the cost of generating more believable character behaviors.

As the video game industry grows, both developers and creative authors seek new ways to simplify the process of controlling story content using scripts. This paper describes a story model and its software implementation, ScriptEase II, designed to solve this game design bottleneck. ScriptEase II is the second generation of the ScriptEase system, whose goal was to enable game authors with no programming ability to generate scripting code from high-level game patterns. ScriptEase II differs from the original in two important ways. First, ScriptEase II uses game-dependent translators to generate scripts for any game engine. Second, ScriptEase II uses a drag-and-drop interface that simplifies the story component creation menus that grew cumbersome in the original ScriptEase. The feasibility of code generation has been validated using three different game engines and the advantages of the simple drag-and-drop interface have been validated by a user study.

Counterfactual Regret Minimization (CFR) is a popular, iterative algorithm for computing strategies in extensive-form games. The Monte Carlo CFR (MCCFR) variants reduce the per iteration time cost of CFR by traversing a smaller, sampled portion of the tree. The previous most effective instances of MCCFR can still be very slow in games with many player actions since they sample every action for a given player. In this paper, we present a new MCCFR algorithm, Average Strategy Sampling(AS), that samples a subset of the player's actions according to the player's average strategy. Our new algorithm is inspired by a new, tighter bound on the number of iterations required by CFR to converge to a given solution quality. In addition, we prove a similar, tighter bound for AS and other popular MCCFR variants.

Characters are vital to large video game worlds as they bring a sense of life to the world. However, background characters are known to rarely exhibit any sign of motivated behavior or emotional state. We want to change this by assigning these characters emotions that can be identified through their non-verbal behavior. We feel the addition of emotion will allow players to feel more connected to the game world and make the game world more believable. This paper presents the results of an experiment to test two ways of conveying emotion: 1) through a character's gait and 2) through a character's interactions with the game world. Results from the experiment suggest that a combination of gait and interactions is the most effective method to convey emotion.

In large extensive form games with imperfect information, Counterfactual Regret Minimization (CFR) is a popular, iterative algorithm for computing approximate Nash equilibria. While the base algorithm performs a full tree traversal on each iteration, Monte Carlo CFR (MCCFR) reduces the per iteration time cost by traversing just a sampled portion of the tree. On the other hand, MCCFR's sampled values introduce variance, and the effects of this variance were previously unknown. In this paper, we generalize MCCFR by considering any generic estimator of the sought values. We show that any choice of an estimator can be used to probabilistically minimize regret, provided the estimator is bounded and unbiased. In addition, we relate the variance of the estimator to the convergence rate of an algorithm that calculates regret directly from the estimator. We demonstrate the application of our analysis by defining a new bounded, unbiased estimator with empirically lower variance than MCCFR estimates. Finally, we use this estimator in a new sampling algorithm to compute approximate equilibria in Goofspiel, Bluff, and Texas hold'em poker. Under each of our selected sampling schemes, our new algorithm converges faster than MCCFR.

In extensive-form games with a large number of actions, careful abstraction of the action space is critically important to performance. In this paper we extend previous work on action abstraction using no-limit poker games as our test domains. We show that in such games it is no longer necessary to choose, a priori, one specific range of possible bet sizes. We introduce an algorithm that adjusts the range of bet sizes considered for each bet individually in an iterative fashion. This flexibility results in a substantially improved game value in no-limit Leduc poker. When applied to no-limit Texas Hold'em our algorithm produces an action abstraction that is about one third the size of a state of the art hand-crafted action abstraction, yet has a better overall game value.

Computing a good strategy in a large extensive form game often demands an extraordinary amount of computer memory, necessitating the use of abstraction to reduce the game size. Typically, strategies from abstract games perform better in the real game as the granularity of abstraction is increased. This paper investigates two techniques for stitching a base strategy in a coarse abstraction of the full game tree, to expert strategies in fine abstractions of smaller subtrees. We provide a general framework for creating static experts, an approach that generalizes some previous strategy stitching efforts. In addition, we show that static experts can create strong agents for both 2-player and 3-player Leduc and Limit Texas Hold'em poker, and that a specific class of static experts can be preferred among a number of alternatives. Furthermore, we describe a poker agent that used static experts and won the 3-player events of the 2010 Annual Computer Poker Competition.

Multi-agent decision problems can often be formulated as extensive-form games. We focus on imperfect information extensive-form games in which one or more actions at many decision points have an associated continuous or many-valued parameter. A stock trading agent, in addition to deciding whether to buy or not, must decide how much to buy. In no-limit poker, in addition to selecting a probability for each action, the agent must decide how much to bet for each betting action. Selecting values for these parameters makes these games extremely large. Two-player no-limit Texas Hold'em poker with stacks of 500 big blinds has approximately 10 71 states, which is more than 10 50 times more states than two-player limit Texas Hold'em. The main contribution of this paper is a technique that abstracts a game's action space by selecting one, or a small number, of the many values for each parameter. We show that strategies computed using this new algorithm for no-limit Leduc poker exhibit significant utility gains over epsilon-Nash equilibrium strategies computed with standard, hand-crafted parameter value abstractions.