function [ WinProb ] = CardAnalyze( Hand, Table, nPlayers, nIter )
%% Licence Information
%
% Author : Oliver Rice
% Employer : University College London
% Title : PhD Candidate Financial Computing
% Date : May 5, 2012
% Licence : Free for academic use only
%% Instructions/Explanation/Example
%
% This function estimates the probability of each player winning
% a Round of Texas Holdem
% Hand = Matrix of Known Cards (KnownPlayers X 2)
% Table = An Array of Cards Presently on the Table
% nPlayers = Total Number of Players Sitting at the Table
% nIter = Number of Monte Carlo Iters to Estimate Probabilities
% Each Card is designated by the whole number (e.g. 5.2 = 5)
% The suit of each card is represented by the decimal (e.g. 8.1 = .1)
% When size(Hand,2)==nPlayers the function assumes perfect information
% meaning true probabilities are estimated
%
% To estimate the probability of an individual winning under normal
% circumstances, 'Hand' is a 2 x 1 matrix of the individual's cards
%
% To estimate probability of an individual winning when nCollude players
% are colluding, 'Hand' is a 2 x nCollude matrix of the colluder's cards
%
% Example Inputs
% Hand = [2.3, 14.3, 11.4, 9.3; 11.1, 10.1, 13.1, 10.2];
% Table = [9.1, 6.3, 5.2];
% nPlayers = 6;
% nIter = 8000;
%
% Yields P(Win) for each player when 3 players' cards are known
% (i.e. colluding) against an additional 3 unknown players with 3 cards on
% the table.
%%--------------PRE-PROCESSING-------------------------------------------
%% Calculate Which Cards Have Not Been Used
% Create a Deck of Cards
% Whole number = Card Number
% Decimal = Card Suit
Cards = 2:.1:15;
Cards(mod(Cards,1)>.41 | mod(Cards,1)<.09)=[];
% Find Used Cards
UsedCards = horzcat(reshape(Hand,1,size(Hand,1)*size(Hand,2)), Table);
% Calculate Remaining Cards by Removing Used Cards from Full Deck
Remaining = Cards;
Remaining(ismember(Remaining,UsedCards))=[];
clear UsedCards Cards
%% Generate Samples from Remaining Cards to Estimate Probabilities
%Create Function to Randomly Sample from Remaining Cards
% Randomly Select Pocket Cards For Unknown Players & Table Cards for All
PermutRemain = zeros(nIter,(5)+2*(nPlayers-size(Hand,2)));
parfor i = 1:nIter
PermutRemain(i,:) = randsample(Remaining,(5)+2*(nPlayers-size(Hand,2)));
end
clear SampleRandomly Remaining
%% Generate Cards Available to Known Players for Each Iteration
% Pre-allocate size for efficiency
PlayerHands = zeros(nPlayers,nIter,7);
for i = 1:size(Hand,2)
PlayerHands(i,1:nIter,1:2)=repmat(transpose(Hand(:,i)),nIter,1);
PlayerHands(i,1:nIter,3:7)=reshape(PermutRemain(:,end-4:end),...
1,nIter,5);
if ~isempty(Table)
PlayerHands(i,1:nIter,3:3+length(Table)-1)=...
repmat(Table,nIter,1);
end
end
%% Generate Cards Available to Unknown Players for Each Iteration
% Pre-allocate size for efficiency
UnknownPlayerHands = zeros(nPlayers-size(Hand,2),nIter,7);
if size(Hand,2)<nPlayers
for i = 1:nPlayers-size(Hand,2)
UnknownPlayerHands(i,1:nIter,1:2) = ...
reshape(PermutRemain(:,i*2-1:i*2),1,nIter,2);
UnknownPlayerHands(i,1:nIter,3:7) = ...
reshape(PermutRemain(:,end-4:end),1,nIter,5);
if ~isempty(Table)
UnknownPlayerHands(i,1:nIter,3:3+length(Table)-1)=...
repmat(Table,nIter,1);
end
end
end
%% Concatenate Known and Unknown Player's Cards to Single Matrix
PlayerHands(size(Hand,2)+1:nPlayers,:,:)=...
UnknownPlayerHands(:,:,:);
clear UnknownPlayerHands PermutRemain
%----------END-PRE-PROCESSING-------------------------------------------
%----------HAND-EVALUATION-LOGIC----------------------------------------
% Used Later to Calcualte Straights
Straight = horzcat(11:14, 2:14);
for i = 1:size(PlayerHands,1)
% Create Matrix to Hold Best Possible Hand
BestHand = zeros(nIter, 6);
% Reduce Dimension of Player Hands for Ease of Use
CurrentPlayerHand=reshape(PlayerHands(i,:,:),nIter,7);
% Find Any Multiples of A Card Number
FreqMatrix = histc(CurrentPlayerHand,.5:1:15,2);
% Logical Matrix for Each Frequency
oKind4 = FreqMatrix==4;
oKind3 = FreqMatrix==3;
oKind2 = FreqMatrix==2;
oKind1 = FreqMatrix==1;
% Since the Max Function Returns the First Value of a Given Max Freq
% The FreqMatrix is flipped left to right to make sure the highest
% Card value for the given max frequency is returned
% Calculate High Card
Index = sum(oKind1>0,2)==7;
if sum(Index)>=1
[~,Loc]=max(fliplr(FreqMatrix(Index,:)==1),[],2); % Find 2ofK
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,1)=1; % High Card Index
BestHand(Index,2)=Loc; % Card Number
FreqMatrixW=FreqMatrix(Index,:); % Working Copy
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)=Loc; % Card Num of 2nd Highest Remaining Card
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,4)=Loc; % Card Num of 2nd Highest Remaining Card
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,5)=Loc; % Card Num of 2nd Highest Remaining Card
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,6)=Loc; % Card Num of 2nd Highest Remaining Card
clear Loc FreqMatrixW
end
clear Index
% Calculate Pair
Index = sum(oKind2>0,2)==1 & sum(oKind3>0,2)==0 & sum(oKind4>0,2)==0;
if sum(Index)>=1
[~,Loc]=max(fliplr(FreqMatrix(Index,:)==2),[],2); % Find 2ofK
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,1)=2; % Pair Index
BestHand(Index,2)=Loc; % Card Number
clear Loc
FreqMatrixW=FreqMatrix(Index,:); % Working Copy
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)=Loc; % Card Num of Highest Remaining Card
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,4)=Loc; % Card Num of 2nd Highest Remaining Card
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,4)=Loc; % Card Num of Last Remaining Card
BestHand(Index,5:6)=0;
clear Loc FreqMatrixW
end
clear Index
% Calculate 2 Pair
Index = sum(oKind2>0,2)>=2 & sum(oKind3>0,2)==0 & sum(oKind4>0,2)==0;
if sum(Index)>=1
[~,Loc]=max(fliplr(FreqMatrix(Index,:)==2),[],2); % Find Best 2ofK
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,1)=3; % 2 Pair Index
BestHand(Index,2)=Loc; % Card Number
FreqMatrixW=FreqMatrix(Index,:); % Working Copy
FreqMatrixW(FreqMatrixW==3)=0; % Ensure Max Card Isn't 2oK Card
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==2),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)=Loc; % Card Num 2nd Highest Pair
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW==1),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,4)=Loc; % Card Num of Remaining Card
BestHand(Index,5:6)=0;
clear Loc FreqMatrixW
end
clear Index
% Calculate Straights
for j = 1:13
Index = sum(FreqMatrix(:,Straight(j:j+4))>0,2)==5;
if sum(Index)>=1
BestHand(Index,1)= 5; % Straight Index
BestHand(Index,2)= Straight(j+4); % Highest Card In Straight
BestHand(Index,3:6)=0;
end
clear Index
end
clear j
% Calculate Flush
SuitFreq = histc(mod(CurrentPlayerHand,1),...
.05:.1:.45,2); % Find Frequencies of Each Suit
for j = 1:4
Index = sum(SuitFreq(:,j),2)>=5;
if sum(Index)>=1
CPH = CurrentPlayerHand; % Working Copy
CPH(round(mod(CPH,1)*10)~=j)=0; % Ignore Other Suits
FreqMatrixBySuit = histc(CPH,.5:1:15,2); % New FreqMat by Suit
BestHand(Index,1)= 6; % Flush Index
[~,Loc]=max(fliplr(FreqMatrixBySuit(Index,:)>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,2)=Loc; % Card Num Highest
for k = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixBySuit(k,Loc(k))=0;
end
clear Loc
[~,Loc]=max(fliplr(FreqMatrixBySuit(Index,:)>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)=Loc; % Card Num Highest
for k = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixBySuit(k,Loc(k))=0;
end
clear Loc
[~,Loc]=max(fliplr(FreqMatrixBySuit(Index,:)>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,4)=Loc; % Card Num Highest
for k = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixBySuit(k,Loc(k))=0;
end
clear Loc
[~,Loc]=max(fliplr(FreqMatrixBySuit(Index,:)>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,5)=Loc; % Card Num Highest
for k = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixBySuit(k,Loc(k))=0;
end
clear Loc
[~,Loc]=max(fliplr(FreqMatrixBySuit(Index,:)>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,6)=Loc; % Card Num Highest
for k = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixBySuit(k,Loc(k))=0;
end
clear Loc FreqMatrixBySuit CPH
end
clear Index
end
% Calculate 3 of a Kind
Index = sum(oKind3>0,2)==1 & sum(oKind2>0,2)==0 & sum(oKind4>0,2)==0;
if sum(Index)>=1
[~,Loc]=max(fliplr(FreqMatrix(Index,:)==3),[],2); % Find Best 3ofK
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,1)=4; % 3 of a Kind Index
BestHand(Index,2)=Loc; % Card Number
clear Loc
FreqMatrixW=FreqMatrix(Index,:); % Working Copy
FreqMatrixW(FreqMatrixW==3)=0; % Ensure Max Card Isn't 3oK Card
[~,Loc] = max(fliplr(FreqMatrixW>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)=Loc; % Card Num Highest Remainder
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc] = max(fliplr(FreqMatrixW>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,4)=Loc; % Card Num 2nd Highest Remainder
BestHand(Index,5:6)=0;
clear Loc Index FreqMatrixW
end
clear Index
% Calculate Full House
Index = sum(oKind3,2)==2 | (sum(oKind3,2)==1 & sum(oKind2,2)>0);
if sum(Index)>=1
BestHand(Index,1)=7; % Full House Index
[~,Loc]=max(fliplr(FreqMatrix(Index,:)==3),[],2); % Find Best 3oK
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,2)= Loc; %Save Card Num
FreqMatrixW = FreqMatrix(Index,:);
for j = 1:length(Loc) % Cant figure out how to get rid of this
FreqMatrixW(j,Loc(j))=0;
end
clear Loc
[~,Loc]=max(fliplr(FreqMatrixW(:,:)>=2),[],2); % Find Best 2oKind
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)= Loc; %Save Card Num
clear Loc
end
clear Index
% Calculate 4 of a Kind
Index = sum(oKind4,2)>0;
if sum(Index)>=1
[~,Loc]=max(fliplr(FreqMatrix(Index,:)==4)...
,[],2); % Find Best 4 of A Kind
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,1)=8; % 4 of a Kind Index
BestHand(Index,2)=Loc; % Card Number
clear Loc
FreqMatrixW=FreqMatrix(Index,:); % Working Copy
FreqMatrixW(FreqMatrixW==4)=0; % Ensure Max Card Isn't 4oK Card
[~,Loc] = max(fliplr(FreqMatrixW>0),[],2);
Loc = size(FreqMatrix,2)-Loc+1; % Get Card Number
BestHand(Index,3)=Loc; % Card Number of Highest Remainder
BestHand(Index,4:6)=0;
clear Loc FreqMatrixW
end
clear Index
% Calculate Straight Flush
for j = 1:13
Index = sum(FreqMatrix(:,Straight(j:j+4))>0,2)==5;
if sum(Index)>=1
for q = 1:4
if sum(round(CurrentPlayerHand(Index,:)*10)/10==...
Straight(j)+q/10)+...
sum(round(CurrentPlayerHand(Index,:)*10)/10==...
Straight(j+1)+q/10)+...
sum(round(CurrentPlayerHand(Index,:)*10)/10==...
Straight(j+2)+q/10)+...
sum(round(CurrentPlayerHand(Index,:)*10)/10==...
Straight(j+3)+q/10)+...
sum(round(CurrentPlayerHand(Index,:)*10)/10==...
Straight(j+4)+q/10)==5
BestHand(Index,1)= 9; % Straight Flush Index
BestHand(Index,2)= Straight(j+4); % Highest Card In Straight
BestHand(Index,3:6)=0;
end
end
end
clear Index
end
clear j
% Score Each Hand as Single Value For Direct Comparison
ScoreHands(i,:) = BestHand(:,1)*10000000000+BestHand(:,2)*...
100000000+BestHand(:,3)*1000000+BestHand(:,4)*10000+...
BestHand(:,5)*100+BestHand(:,6)*1;
clear CurrentPlayerHand FreqMatrix BestHand oKind1 oKind2 oKind3 oKind4
end
%% Compute Winner of Each Iteration
% Create Function Handle to Avoid Loop
RetrieveMax = @(x) max(ScoreHands(:,x));
% Retrieve Best Score Per Hand
[HandMax,~] = RetrieveMax(1:nIter);
% Create nPlayer Rows of Hand Max for Logic Matrix Comparison
HandMax = repmat(HandMax,nPlayers,1);
% Create Logical Index of Winners By Score
WinnerMatrix = HandMax==ScoreHands;
% Calculate the Probability of Each Player Winning Adjusted for Ties
WinProb = WinnerMatrix/sum(WinnerMatrix,1);
end
