Golden Arm: A Probabilistic Study of Dice Control in Craps

This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting possible dice control, that in which the four faces on a rotating (horizontal) axis are favored. This is the model that we analyze in this paper

A simple evolutionary game with feedback between perception and reality

We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which perception affects reality. By varying the `reality map', which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers, to a purely subjective game in which probabilities equal the amount wagered. The reality map can reflect self-reinforcing strategies or self-defeating strategies. In self-reinforcing games, rational players can achieve increasing returns and manipulate the outcome probabilities to their advantage; consequently, an early lead in the game, whether acquired by chance or by strategy, typically gives a persistent advantage. We investigate the game both in and out of equilibrium and with and without rational players. We introduce a method of measuring the inefficiency of the game and show that in the large time limit the inefficiency decreases slowly in its approach to equilibrium as a power law with an exponent between zero and one, depending on the subjectivity of the game.Comment: 11 pages, 6 figure

Kelly Criterion revisited: optimal bets

Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a explanation of this fact. Kelly's approach allows for an interesting financial interpretation of the Boltzmann/Shannon entropy. A "no-go" hypothesis for big investors is suggested.Comment: APFA5 Conference, Torino, 200

A New Relative Skill Measure for Games with Chance Elements

An interesting aspect of games is the relative extent to which a player can positively influence his results by making appropriate strategic choices. This question is closely related to the issue of how to distinguish between games of skill and games of chance. The distinction between these two types of games is definitely interesting from a juridical point of view. Borm and Van der Genugten (2001) presented a method to measure the skill level of a game. In principle, their measure can serve as a juridical tool for the classification of games with respect to skill. In this paper we present a modification of the measure. The main difference is that this new definition does not automatically classify incomplete information games without chance moves as games of skill. We use a coin game and a simplified version of standard drawpoker as an illustration.games of skill;games of chance