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    <p>Here's a vectorized version, where 1M hands can be calculated in about a minute. I got about 28:1 with it, so there might still be something a little off with finding 'all different' sets. My guess is that this is what your solution has trouble with, as well.</p> <pre><code>%# initialization K = 12; %# cards to draw NF = 4; %# number of features (this is hard-coded to 4) nIter = 100000; %# number of iterations %# each card has four features. This means that a card can be represented %# by a coordinate in 4D space. A set is a full row, column, etc in 4D %# space. We can even parallelize the iterations, at least as long as we %# have RAM (each hand costs 81 bytes) %# make card space - one dimension per feature, plus one for the iterations cardSpace = false(3,3,3,3,nIter); %# To draw cards, we put K trues into each cardSpace. I can't think of a %# good, fast way to draw exactly K cards that doesn't involve calling %# unique for i=1:nIter shuffle = randperm(81) + (i-1) * 81; cardSpace(shuffle(1:K)) = true; end %# to test, all we have to do is check whether there is any row, column, %# with all 1's isEqual = squeeze(any(any(any(all(cardSpace,1),2),3),4) | ... any(any(any(all(cardSpace,2),1),3),4) | ... any(any(any(all(cardSpace,3),2),1),4) | ... any(any(any(all(cardSpace,4),2),3),1)); %# to get a set of 3 cards where all symbols are different, we require that %# no 'sub-volume' is completely empty - there may be something wrong with this %# but since my test looked ok, I'm not going to investigate on Friday night isDifferent = squeeze(~any(all(all(all(~cardSpace,1),2),3),4) &amp; ... ~any(all(all(all(~cardSpace,1),2),4),3) &amp; ... ~any(all(all(all(~cardSpace,1),3),4),2) &amp; ... ~any(all(all(all(~cardSpace,4),2),3),1)); isSet = isEqual | isDifferent; %# find the odds fprintf('odds are %5.2f:1\n',sum(isSet)/(nIter-sum(isSet))) </code></pre>
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    1. COthanks. Although the result looks better and the speed is amazing, I think there is something wrong with the test for set. So hard to think in 4D space. isEqual looks ok, and it probably means that 3 card exist with all but one features the same. isDifferent I still didn't get. I understand about subvolume, but how it relates to a set rules? If you think it's all right, would you explain it please?
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    2. CO@yuk: I should just have done it in 3D - but hey, it was Friday after a few beers. Anyway, I don't think the tests are correct - I have misinterpreted the rules. I'm testing for either one feature equal or all features different, not "for each dimension, are the features either all the same or all different". I have not yet come up with a logic for that (though I admit I haven't tried very hard).
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    3. COThanks, Jonas. No problem.
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