Workshop

We present a combinatorial ruleset which has a position in each equivalence class of short normal-play games (acyclic games with finite ranks and out-degrees). One could think of this as a CGT analogy of a universal Turing machine: one ruleset encodes it all.

The boiling point of a class of games $S$ is the supremum of all temperatures in $S$. We show that the boiling point can be bound by the maximum length of the confusion intervals of games in $S$. Further, we give a technique of how to bound, in turn, the length of the confusion interval. As an application example, we show that the boiling point of certain Domineering snakes is at most 3.

This is joint work with Richard Nowakowski and Carlos Santos.

In this talk we will discuss restricted and unrestricted Yellow-Brown Hackenbush, introduced by Berlekamp in Games of No Chance 3. In particular we will consider the appearance of the values of these games as incentives of all-small games.

Pic Arete is Strings-and-Coins (Dots-and-Boxes) without the extra move. In the partizan version, games are assigned to the edges and an edge is finally deleted when the assigned game reaches { | }. I’ll present some general reductions, some canonical values, and consider paths where the assigned games are 1 and -1.

A Beatty sequence is a sequence of integers formed by taking the floor of the positive integral multiples of a positive irrational number $\alpha$.  The complementary sequence is formed in a similar manner using $\beta$, where $\beta$ satisfies the equation $\frac{1}{\alpha} + \frac{1}{\beta}  = 1$.  For a given $\alpha$, we investigate the partizan subtraction game with left and right subtraction sets given by $(1, \alpha)$ and $(1, \beta)$, respectively.  We analyze this family of games using the Atomic Weight Calculus.

We will also report results for the non-atomic version, where the left and right subtraction sets are given by $(\alpha)$ and $(\beta)$, respectively.

Octal games are impartial games that involve removing tokens from heaps of tokens.  These types of games are interesting in that they can be described using an octal code.  Historically, research efforts have focused almost exclusively on octal games with finite codes.  We consider octal games based on infinite octal codes where the heap sizes corresponding to elements of a Beatty $\alpha$ sequence are played according to some fixed removal rule and the heap sizes corresponding to elements of a Beatty $\beta$ sequence are played according to some other fixed removal rule.  Interesting periodicity seems to occur in most cases.

A skillful blackjack player, one who counts cards, maintains some information about the distribution of cards remaining in the deck at all times.  The player adjusts both betting style and play based on this "count" information.  Depending on the rules used by a particular casino, the skillful player may have a slight edge over the casino. Without knowing exactly what the player is counting, we would like to write a program which is able to assess the player's playing skill.

There are two potential benefits from this research.  First and foremost, this is related to the much harder problem of assessing the quality of decisions people make under uncertainty.  For example, a pension fund manager tries to distinguish a good portfolio manager from a lucky one.  Second, there are many gamblers who deceive themselves into thinking they are able to play blackjack well enough to beat the casino.  In fact, casino blackjack revenues skyrocketed after Thorpe published his landmark book, Beat the Dealer, which explained how to effectively count cards.  Players who discover their true skill (usually very poor) will hopefully be deterred from gambling.  (As an aside, I suspect this sort of research is conducted by casinos who, due to their financial interests, are disinclined to
publish results in the area.)