I am not a student, just trying to work this out for myself.
Given a a standard deck of 52 cards (clubs, diamonds, hearts, spades, 13 of each suite, no joker).
I split the deck in three stacks
Stack A: 10 cards
Stack B: 37 cards
Stack C: 5 cards
I know all the content of stack C.
With this information I can fairly easily calculate the for each of the cards in stack C the probability of B containing a higher card of the same suite.
The solution for this I based on the question I asked here http://www.freemathhelp.com/forum/threads/85251-Combinations-of-card-hands?highlight=euchre.
Now the problem I have is that when I add the following information
I know that at least 3 of the cards in A isn't a spade (meaning the other 7 can be).
This changes the probability calculation quite a bit, but I am not really sure how to approach that.
I can handle it for the case where its at least 3 of the cards in B that isn't a spade. But when its on A I am stuck at the moment.
A real world use case of this could be a card game AI to to evaluate the chance of the opponent having a better card than the ones that it has (rating each card in turn).
So basically the AI know that there is A cards left in the deck , the opponents has a total of B cards and it has C cards on hand.
Given a a standard deck of 52 cards (clubs, diamonds, hearts, spades, 13 of each suite, no joker).
I split the deck in three stacks
Stack A: 10 cards
Stack B: 37 cards
Stack C: 5 cards
I know all the content of stack C.
With this information I can fairly easily calculate the for each of the cards in stack C the probability of B containing a higher card of the same suite.
The solution for this I based on the question I asked here http://www.freemathhelp.com/forum/threads/85251-Combinations-of-card-hands?highlight=euchre.
Now the problem I have is that when I add the following information
I know that at least 3 of the cards in A isn't a spade (meaning the other 7 can be).
This changes the probability calculation quite a bit, but I am not really sure how to approach that.
I can handle it for the case where its at least 3 of the cards in B that isn't a spade. But when its on A I am stuck at the moment.
A real world use case of this could be a card game AI to to evaluate the chance of the opponent having a better card than the ones that it has (rating each card in turn).
So basically the AI know that there is A cards left in the deck , the opponents has a total of B cards and it has C cards on hand.