  We study a very small three player poker game (one-third street Kuhn poker),
and a simplified version of the game that is interesting because it has three
distinct equilibrium solutions. For one-third street Kuhn poker, we are able to
find all of the equilibrium solutions analytically. For large enough pot size,
$P$, there is a degree of freedom in the solution that allows one player to
transfer profit between the other two players without changing their own
profit. This has potentially interesting consequences in repeated play of the
game. We also show that in a simplified version of the game with $P>5$, there
is one equilibrium solution if $5 < P < P^* \equiv (5+\sqrt{73})/2$, and three
distinct equilibrium solutions if $P > P^*$. This may be the simplest
non-trivial multiplayer poker game with more than one distinct equilibrium
solution and provides us with a test case for theories of dynamic strategy
adjustment over multiple realisations of the game.
  We then study a third order system of ordinary differential equations that
models the dynamics of three players who try to maximise their expectation by
continuously varying their betting frequencies. We find that the dynamics of
this system are oscillatory, with two distinct types of solution. We then study
a difference equation model, based on repeated play of the game, in which each
player continually updates their estimates of the other players' betting
frequencies. We find that the dynamics are noisy, but basically oscillatory for
short enough estimation periods and slow enough frequency adjustments, but that
the dynamics can be very different for other parameter values.
