Starting with the code in ThreeOfaKind.m create a new mfile named Flush_LastName

Question

Starting with the code in ThreeOfaKind.m create a new mfile named Flush_LastName.m that computes the probability of a flush.

A flush is 5 cards of the same suit. Compute the analytic probability. Look up the probability on Wikipedia. Compare the three values.

% ThreeOfaKind.m
% Generate a random shuffle
% deal 5 cards
% check to see if there 3 of a kind but no full house

clc, clear, close all, close all hidden
Len=1000; %1e6; % 00; %000; %0000; %000; % do this many hands
Den=(1:13)'; % card denomination A 2 3 ... K
Sut=ones(13,1); % suit 1 2 3 4 for diamond heart club spade
Dek0=[Den Sut*1 % Make a deck of cards 52x2. Col 1 is den, col 2 is suit
Den Sut*2
Den Sut*3
Den Sut*4];
Dek1=Dek0(:,1)*10+ Dek0(:,2); % make up a new column DD.S Denomination.Suit
Dek=[rand(52,1) Dek1 Dek0]; % add a column of random numbers
%% do a large number of hands and determine if the hand is 3 of a kind
TreKnd=0; % initialize three of a kind counter
h=waitbar(0, 'Look for three of a kind'); % start a waitbar
for i=1:Len % for each hand   
%% shuffle the cards
kDekRnd=[rand(52,1) Dek1 Dek0]; % Fresh Deck columns are [rand nns nn s]
kDek=sortrows(kDekRnd,1); % Shuffle the cards
kHnd=kDek(1:5,:); % draw a hand
%% calculate the number of cards for each denomination
kDen=kHnd(:,3); % extact the denomiantion
nDen=zeros(13,1); % zero out the denomiantion counter
for iDen=1:13; % for each denominaton
fDen=kDen==iDen; % generate a flag if this denomination is in the hand
nDen(iDen)=sum(fDen); % calculate the number of times this denomination is in the hand
end
%% decide if this is three of a kind
nDenSrt=sortrows(nDen, -1); % sort the denomination count from highest to lowest
if nDenSrt(1)==3 && nDenSrt(2)==1 % for three of a kind the sorted denomation must be 3 1 1 0 0 0 0 0 0
TreKnd=TreKnd+1; % increment 3 of a kind counter
fprintf('%2d %1d ', kHnd(:,3:4)'); fprintf(' '); % print the hand (debug)
waitbar(i/Len); % start a waitbar % update waitbar inside of if to save time
end
end
close(h);
%%
NumPrbTreKnd=TreKnd/Len; %
AnaPrbTreknd=52/52* 3/51* 2/50* 48/49* 44/48 * factorial(5)/factorial(3)/factorial(2); %(52*51*50*49*48)*5*4/2; % 0.021128451380552
WikPrbTreknd=54912/2598960; % 0.021128451380552 from http://en.wikipedia.org/wiki/Poker_probability
fprintf('Num Prb: %10.8f, True Prb: %10.8f ', NumPrbTreKnd, AnaPrbTreknd);
tmp=0;

Explanation / Answer

function fid = fopen0(varargin) %FOPEN0 Wrapper for fopen that throws an error if the file could not be % opened. % % FID = FOPEN0(VARARGIN) is a wrapper for fopen that throws an error if % the file could not be opened. % $Author: rcotton $ $Date: 2010/04/12 10:36:31 $ $Revision: 1.2 $ % Copyright: Health and Safety Laboratory 2010 fid = fopen(varargin{:}); if fid == -1 error('fopen0:CouldNotOpenFile', 'Could not open file'); end end

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