We consider zero-sum game which is usually called poker. Each of
two players ( I and II ) independently draws a number ($x$ and
$y$, respectively) according to uniform distribution in $[0,1]$.
Also they jointly draw a number $z$ according to the
distribution with cdf $F(z), 0(<) \ y$,
getting reward $z\ (-z)$. If both players choose $R$, then the
numbers are rejected and the game proceeds to the next round
with the newly drawn numbers $x',y'$, and $z'$. If players
choose different choices, then arbitration comes in, and forces
to take the same choices as I's ( II's ) with probability $p\ (\bar
{p})$. Arbitration is fair (unfair) if $p=(\neq)\ \frac{1}{2}$.
The game is played in $n$ rounds . Player I (II) aims to
maximize (minimize) the expected reward to I. Explicit solution
is derived to this sequential game, and examples are shown for
the cases where $z$ obeys discrete and continuous uniform
distributions.