Cards Simulation

samplesize = 10000;
confidence = 0.95;

decksize = 34;
nbplayers = 11;
drawsize = 5;

groupmatches = zeros(samplesize,1);
individualmatches = zeros(samplesize,nbplayers);
deck = (1:decksize)';


for m = 1:samplesize
hands = zeros(drawsize,nbplayers);
for n = 1:nbplayers
    hands(:,n) = datasample(deck,5,'Replace',false);
end
cardsdrawn = unique(hands);
percardcount = histcounts(reshape(hands,nbplayers*drawsize,1),[cardsdrawn; (decksize+1)]);
groupmatches(m) = sum(percardcount-1);

for n = 1:nbplayers
    index = true(1,nbplayers);
    index(n) = false;
    individualmatches(m,n) = nnz(ismember(hands(:,n),hands(:,index)));
end


end

individualmatches = reshape(individualmatches,nbplayers*samplesize,1);

groupmatches_estimator = mean(groupmatches);
groupmatches_error = std(groupmatches)/sqrt(length(groupmatches));
individualmatches_estimator = mean(individualmatches);
individualmatches_error = std(individualmatches)/sqrt(length(individualmatches));

Z = norminv(1 - 0.5*(1-confidence),0,1);
groupmatches_interval = groupmatches_estimator + (Z*groupmatches_error).*[-1 1];
individualmatches_interval = individualmatches_estimator + (Z*individualmatches_error).*[-1 1];

clearvars n index margin m cardsdrawn percardcount hands;