% 1-card poker: each player draws a card from 1 to ncards without
% replacement.  Player 1 bets 0 or 1.  Player 2 bets 0 or 1 (meaning
% call/raise or fold/call depending on P1's bet).  On 0 followed by
% raise, player 1 may fold or call (betting 0 or 1).

% How many cards in the deck?
ncards = 13;

% Constraints on sequences.  A's states are [A-K] and [A-K]01 (latter
% is any hand after check&raise). A's actions are [A-K][0-1] (sorted
% with least-significant character on left) followed by [A-K]01[0-1]
% (LSC on left).  B's states are [A-K][0-1] (LSC on left) and actions
% are [A-K][0-1][0-1] (LSC on left).
A = [ eye(ncards) eye(ncards) zeros(ncards, 2*ncards); -eye(ncards) zeros(ncards) eye(ncards) eye(ncards)];
a = [ ones(ncards,1); zeros(ncards,1) ];
B = [ eye(2*ncards) eye(2*ncards) ] ;
b = ones(2*ncards,1);

% Construct reward matrix, with one element for each pair of an A
% sequence and a B sequence.  Most sequence pairs are inconsistent
% with each other and so get zero reward; there are 5 nonzero blocks
% corresponding to a showdown with a pot of 2, A folding, B folding,
% and 2 ways of getting to a showdown with a pot of 4 depending on
% whether A bet or passed in the first round.
zz = zeros(ncards);
fold = ones(ncards) - eye(ncards);
card = ones(ncards,1) * (1:ncards);
showdown = (card > card') - (card' > card);
RA = [showdown zz zz zz; zz fold zz zz; zz zz -fold 2*showdown; zz 2*showdown zz zz];

% effect of chance: there are n * (n-1) deals, each with equal
% probability.
RA = RA / ((ncards-1) * ncards);

% B's payoff is negative of A's
RB = -RA';