Counting Cards
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Slick Willie is trying his hand at blackjack on a two deck table in Las Vegas. The dealer rolls through 3 hands in which Willie counts 17 face cards and 29 non face cards. On the fourth hand he sees 4 face cards and 9 nonface cards, of which he has a SEVEN and a FIVE and the dealer has an ACE showing. What are the odds that Willie will bust if he takes one card?
Answer
There are 32 cards that can make him bust. (Don't forget the nonface TENS) 21 face cards have already been seen. And of the 37 non face cards played anywhere between 0 and 8 could have been TENS. So of the possible bust cards, between 21 and 29 have been played. This leaves between 3 and 11 bust cards still in the deck of 44 remaining cards. (Remember: The dealer has one card down but we know it is not a face card or a 10 because the dealer would have already shown a blackjack). So his odds of drawing a bust card are between 3/44 and 11/44 or 6.8% and 25%. He has to take a hit.
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Comments
rayneeday
Mar 08, 2002
 Come on, tell me what you think. I am of the opinion that the Comment box is way under used. If you like it great, If you hate it, tell me. So I can fix the problem in future puzzles. Personally I think more feedback both good and bad can only help the website produce more fun for all. Even a little trash talkin' can be fun.

captbob61
Mar 26, 2002
 That's a really tricky one. I tried to do it in my head, but got caught up in the fractions. I know it's a good math/probability riddle when I have to bust out the pencil! 
rohddawg
Mar 27, 2002
 good puzzle.. i used to be good at counting cards.. but ya.... all i know is with my luck i'd easily bust 
kristofer
Mar 28, 2002
 If slick was slick he would count 10 cards as face cards! 
starlust
Jun 05, 2002
 too bad I don't understand blackjack this sounds inteeesting. 
kool_lil_girl
Jul 03, 2002
 i like it
it was hard but i couldnt get it
but nm
i like your teasers 
dewtell
Aug 21, 2002
 If you assume that "face cards" includes tens,
you not only have a more sensible way to count the
cards, but you also get a unique answer of 11/44, or 1/4th.
Having a unique answer makes a better teaser, and having
that answer be 1/4th is aesthetically pleasing.
No real counter would count tens any differently from jacks,
queens, or kings, since they all function identically
in Blackjack (they all count as 10).

electronjohn
Nov 15, 2002
 I agree 100% with dewtell because he is right. 
Quax
Jun 21, 2006
 Adding "Don't forget the 10s" in a Hint may be helpful here. 
bbbz
Aug 14, 2008
 In the context of a blackjack game, if someone uses the terms "face card", "face", "ten" or even "big" or "big card", all these words are understood to mean the same thing to everyone at the table: any card with a value of ten. Namely a TEN, JACK, QUEEN, or KING.
Card counting is based around the idea that when the remainder of the deck or shoe is rich in "tens" and aces, this swings the advantage towards the player and one should then increase the bet. This knowlegde can then also be used to alter basic strategy(hit, stand, dbl down, etc.) to increase your success.
No card counting system worth using would distinguish a TEN from a JACK, QUEEN or KING and it certainly would not count ACES as part of a group of non face cards. Really the most common systems group 2 thru 6 together; the four "tens" and ace together as another group and then 7 thru 9 are neutral. 
Aaronnp
Jul 18, 2010
 i got 1/14 because i forgot about the 10s 
sillybrain
Nov 29, 2016
 how do we get 37 nonface cards, i thought there was 29 nf on the first three hands and 9 nf on the fourth hand so a total of 38 non face cards yes? Or is it that we play on the fourth hand and hence can see one of the nonface cards? I just don't understand this explanation at all ... y are we separating the 10's from the j, q, k? as far as value they're the same and all can lead to 'bust'! ". So of the possible bust cards, between 21 and 29 have been played. This leaves between 3 and 11 bust cards still in the deck of 44 remaining cards.' I don't understand this line of reasoning. Finally how do we conclude there are 44 cards remaining in deck when in fact according to this problem we have dealt 59 cars already? Shouldn't there be 45 cards left in deck not 44?!! Really confused w/ this problem please help! 
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