Four of a kind
With four decks of cards, what is the minimum number of cards that you must draw to get four of a kind?
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25 Jan 2010 5:10PM
Sorry people, I should have gone to bed instead of posting. The question should have been:
With four decks of cards, what is the minimum number of cards you must draw to be assured of getting four of the same value, ignoring the suite?
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25 Jan 2010 5:10PM
Sorry people, I should have gone to bed instead of posting. The question should have been:
With four decks of cards, what is the minimum number of cards you must draw to be assured of getting four of the same value, ignoring the suite?
Labels: logic
posted by Chris at
7:53 PM
23 Comments:
Is it 45 draws?
4
Interesting ... so the question becomes are we looking for the minimum number of draws to have a chance of getting 4 of a kind ... or are we looking for the minimum number of draws to be assured of getting 4 of a kind.
So if we are looking for the minimum number of draws to have a chance of getting 4 of a kind, then Anonymous has a correct, clever answer.
yeah Zaux...just wanted to make myself seem smart by pointing out that the minimum number of draws to be ASSURED of 4 of a kind would be the same if you had 1 deck of cards,4 decks,or 1728.
an clever answer ... I like it ... I took the other approach and got all lost ... heh heh.
In poker, 4 of a kind means 4 of the same rank (e.g. all the nines) plus one other.
But this depends on how you interpret the question: is it the minimum number you must draw to HAVE A CHANCE of getting 4 of a kind, or is it the minimum number you must draw TO BE CERTAIN of getting 4 of a kind?
On the first interpretation the answer is 5. On the second interpretation, the answer is one more than the number you get after drawing three of each rank. Then, as Knightmare has said, it doesn't matter how many decks you have. It is 39 plus 1 = 40.
Take your pick of these two answers based on these two interpretations: 5 or 40.
Ina pack of cards to draw 4 of a kind:-
Worst case scenario draw three of each card 3 x 13 = 39, the 40th card will give you 4 of a kind
Best case scenario = first 4 cards.
4 it is then.
Is the Joker(s) still in the pack? Then the answer will be.... 4.
What about asking the question...
What is the probability of the first four cards drawn from a shuffled deck of 52 cards being four of a kind? The probability if it were 2 shuffled decks, 3 decks, 4 and so on?
theres this word MINIMUM that was stated in the problem.. so to get a four of a kind, it should be 4.. or in the pokers case, its 5.. its only the minimum that is being asked, assured or by chance, it would still be 4, 5 for poker..
its 24 draws. four different cards can be chosen in4*3*2*1 times
SORRY PEEPS. I've amemded the problem.
changing my earlier post of 45 to 40 ... I agree with Wiz
The answer to the amended problem is 157
The answer is still 39+1 = 40
As long as there are no Jokers! The number of decks is irrelevant, as there are only 13 different card faces regardless of the suit.
Welcome to my comedy of errors.
40 is the correct answer to the problem that I finally posted.
The number of decks is irrelevant as Knightmare first pointed out.
Thanks Wiz, I didn't know that poker stuff.
1st place Wiz, 2nd Karl (just by post date).
Now I'd better go and hang my head in shame for goofing up such a short question.
From one mis-worder to another ... no hanging is necessary... heh heh
Hi Zaux. You've now had a(nother) demo of why I can forgive other peeps messed up posts so easily. ;)
Chris ... as accurate and thorough as you normally are, you have nothing for which to apologize. The question was always one of my concerns ... "is the statement worded correctly?".
As Anon pointed out (4.51 am above) it is the word MINIMUM that is causing the problem.
The question is how many draws . . . to be ASSURED . . . So what is being asked is the ACTUAL number - minimum or maximum doesn't come into it.
By the way, it would be convenient if the software behind this blog could be made to generate a serial number for each post, rather than have to refer to a particular one by date and time.
Hi Wiz. In the final form of the question, the word "minimum" is important, otherwise any number greater than 39 would be OK.
You're right, Chris - point conceded.
Phew! I'm relieved that you agree. I don't trust my brain at the moment.
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