Body: <p>I need help with a probability problem in the card game of Cambio. In this game, two players are dealt four cards each from a deck of 52 cards . At the start of the game, the bottom cards of each player are observed and there are four hidden top cards (two in each player's hand). I am using minimax for my AI where a shallow copy of the game object is generated. Then possible moves are calculated based on the dealt card from the top of the deck. If 7,8 was at the top of the deck, our AI is able to peek a card in its hand(enemy’s hand if the card is 9 or 10). The problem is we are not allowed to reveal the card. Ai has to guess the probabilities of every card type that could be the card we want to reveal.  For example, here:
  <a href="https://i.sstatic.net/dMGe0.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dMGe0.jpg" alt="enter image description here" /></a>
  Heart 7, spades 8, spades, diamond 7. And x's are hidden.
  How would one guess the card above Heart 7? We would have to assume that either all the hidden cards are of type 7, none of the cards are or some of the cards are of type 7.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-09-11T11:34:13.033Z
Comments.Text: I'm not sure I understand the game rules from your description. I expect the question summary is fine if someone already knows the rules, but if you could link something more complete, like a Wikipedia article then it may help.
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-09-11T11:36:23.160Z
Comments.Text: Also you are asking about guessing a hidden card. The answer is likely to be a probability distribution - it may help to understand why you want this guess data - e.g. are you writing a bot that can play the game?
Comments.UserDisplayName: Neil Slater
Tags: <minimax><probability><probability-theory><expectiminimax>
Title: How to guess a card in the game of Cambio with limited information?
UserDisplayName: Ali Qaqan
ThreadText: # How to guess a card in the game of Cambio with limited information?
  
  (Asked by: username_0 on 2023-09-07)
  
  I need help with a probability problem in the card game of Cambio. In this game, two players are dealt four cards each from a deck of 52 cards . At the start of the game, the bottom cards of each player are observed and there are four hidden top cards (two in each player's hand). I am using minimax for my AI where a shallow copy of the game object is generated. Then possible moves are calculated based on the dealt card from the top of the deck. If 7,8 was at the top of the deck, our AI is able to peek a card in its hand(enemy’s hand if the card is 9 or 10). The problem is we are not allowed to reveal the card. Ai has to guess the probabilities of every card type that could be the card we want to reveal. For example, here:
  [![enter image description here](https://i.sstatic.net/dMGe0.jpg)](https://i.sstatic.net/dMGe0.jpg)
  Heart 7, spades 8, spades, diamond 7. And x's are hidden.
  How would one guess the card above Heart 7? We would have to assume that either all the hidden cards are of type 7, none of the cards are or some of the cards are of type 7.
  
  **Tags:** minimax, probability, probability-theory, expectiminimax
  > **Comments:**
  > **username_1**: I'm not sure I understand the game rules from your description. I expect the question summary is fine if someone already knows the rules, but if you could link something more complete, like a Wikipedia article then it may help.  
  > **username_1**: Also you are asking about guessing a hidden card. The answer is likely to be a probability distribution - it may help to understand why you want this guess data - e.g. are you writing a bot that can play the game?  
  
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  ## 0 answers
  
  