Related papers: Finding Blackjack's Optimal Strategy in Real-time …
This study presents a rigorous mathematical approach to the optimization of round and betting policies in Blackjack, using Markov Decision Processes (MDP) and Expected Utility Theory. The analysis considers a direct confrontation between a…
Computer calculations for most exact expected values in blackjack have been available since the 1960's, but exact results for pair splitting and resplitting have previously been too computer intensive. This paper describes a new algorithm…
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…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
Blackjack or "21" is a popular card-based game of chance and skill. The objective of the game is to win by obtaining a hand total higher than the dealer's without exceeding 21. The ideal blackjack strategy will maximize financial return in…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
Composition theory can be used to analyze and enumerate the number of ways a dealer in Blackjack can reach any given point total. The rules of Blackjack provide several restrictions on the number of compositions of a given number. While…
Quantum computers that process information by harnessing the remarkable power of quantum mechanics are increasingly being put to practical use. In the future, their impact will be felt in numerous fields, including in online casino games.…
We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed…
Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…
The subject of this paper is a variation of a blackjack game, mainly popular in some parts of Europe where it is known as einz (in German slang: one). We describe the rules of this game, indicate its main characteristics, give some…
In this paper, we calculate a basic strategy for several variations of a simplified version of Blackjack. In short, for these variants the player has only the two options of hit or stand, and they may only make either decision once. Other…
We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, we focus on Kelly optimization as a metric, optimizing the…
We introduce a variant of the classic poker game blackjack -- the continuous blackjack. We study the Nash Equilibrium as well as the case where players deviate from it. We then pivot to the study of a large class of adaptive strategies and…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a…
Consider a game consisting of independent turns with even money payoffs in which the player wins with a fixed probability $p \geq 1/3$ and loses with probability $1 - p$. The Labouchere system is a betting strategy which entails keeping a…
There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
For a balanced cardcounting system we study the random variable of the true count after a number of cards are removed from the remaining deck and we prove a close formula for its standard deviation. As expected, the formula shows that the…