Related papers: Card Dealing Math
In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.
In this paper, we study the problem of evaluating the addition of elements to a set. This problem is difficult, because it can, in the general case, not be reduced to unconditional preferences between the choices. Therefore, we model…
The time proximity of high-frequency trades can contain a salient signal. In this paper, we propose a method to classify every trade, based on its proximity with other trades in the market within a short period of time, into five types. By…
We define a natural equivalence relation on collections of cards from the card game SET, and enumerate some of the equivalence classes, vastly generalizing the standard game. On this basis, we describe several alternative games for the SET…
Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…
Skat is a fascinating combinatorial card game, show-casing many of the intrinsic challenges for modern AI systems such as cooperative and adversarial behaviors (among the players), randomness (in the deal), and partial knowledge (due to…
Retrograde analysis is used in game-playing programs to solve states at the end of a game, working backwards toward the start of the game. The algorithm iterates through and computes the perfect-play value for as many states as resources…
This research project investigates the application of several computer vision techniques for playing card detection and recognition in the context of the popular casino game, blackjack. The primary objective is to develop a robust system…
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…
We investigate the $k$-cycle shuffle on repeated cards, namely on a deck consisting of $l$ identical copies of each of $m$ card types, with total size $n=ml$. We establish asymptotic results for the total variation mixing of this shuffle,…
The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the…
The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to different groups. We concentrate on two types of generalization:…
We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of…
This paper studies properties of the back end of a sorting network and illustrates the utility of these in the search for networks of optimal size or depth. All previous works focus on properties of the front end of networks and on how to…
We study games in which every action requires planning and preparation. Moreover, before players act, they can revise their plans based on partially revealing information that they receive on their adversary's preparations. In turn, we…