  We study the equilibrium distribution of relative strategy scores of agents
in the asymmetric phase ($\alpha\equiv P/N\gtrsim 1$) of the basic Minority
Game using sign-payoff, with $N$ agents holding two strategies over $P$
histories. We formulate a statistical model that makes use of the gauge freedom
with respect to the ordering of an agent's strategies to quantify the
correlation between the attendance and the distribution of strategies. The
relative score $x\in\mathbb{Z}$ of the two strategies of an agent is described
in terms of a one dimensional random walk with asymmetric jump probabilities,
leading either to a static and asymmetric exponential distribution centered at
$x=0$ for fickle agents or to diffusion with a positive or negative drift for
frozen agents. In terms of scaled coordinates $x/\sqrt{N}$ and $t/N$ the
distributions are uniquely given by $\alpha$ and in quantitative agreement with
direct simulations of the game. As the model avoids the reformulation in terms
of a constrained minimization problem it can be used for arbitrary payoff
functions with little calculational effort and provides a transparent and
simple formulation of the dynamics of the basic Minority Game in the asymmetric
phase.
