Two-player card game, combined probability

In summary, the conversation discusses a card game where players are dealt three cards and must discard one without showing it to their opponent. The total number of deals can be calculated using the combination formula, but if one player knows their discarded card, it may affect the distribution. If the discarded card is not chosen at random, it should be accounted for in the formula.
  • #1
Lenus
20
1
There is a card game where one player gets three cards and only uses two (the third one is discarded without showing to an opponenet), and the second player gets also three cards and uses only two, discarding the third card in the similar way - without showing.

I am trying to enumerate all possible deals, but stuck with the logic. Do I account for the mucked (the third cards) or not?

If I have a 52-card standard deck, the first players hands number would be C(52,3) and the second players number of hands would be C(49,3)? Thus the total number of the deals would be C(52,3)xC(49,3).

What if I am one of the players and know the third discarded card of mine, but don't know the discarded card of my opponent, will it affect the above-mentioned formula?
 
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  • #2
If the disposed card is not chosen at random, then you should account for it - it will influence the distributions.
Lenus said:
Thus the total number of the deals would be C(52,3)xC(49,3).
Yes, if the two players are different.
Lenus said:
What if I am one of the players and know the third discarded card of mine, but don't know the discarded card of my opponent, will it affect the above-mentioned formula?
The formula is true independent of your knowledge. If you know some cards and some not, you can calculate how many different options are left - then your cards (including the disposed one - the opponent cannot have it) are relevant of course.
 
  • #3
mfb

If the disposed card is not chosen at random, then you should account for it - it will influence the distributions.

The term "not chosen at random" was the key, thanks a lot!
 
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1. What is a two-player card game?

A two-player card game is a game where two players compete against each other using a deck of cards. The objective of the game can vary, but it typically involves players using their cards to win points, achieve a specific goal, or defeat their opponent.

2. What is combined probability in a two-player card game?

Combined probability in a two-player card game refers to the likelihood of certain events occurring when both players' actions are taken into account. This can include the probability of drawing a specific card, winning a specific hand, or achieving a certain outcome in the game.

3. How is combined probability calculated in a two-player card game?

Combined probability is calculated by multiplying the individual probabilities of the events in question. For example, if the probability of Player A drawing a specific card is 1/52 and the probability of Player B drawing that same card is 1/51, the combined probability of both players drawing that card is (1/52) * (1/51) = 1/2652.

4. How does combined probability affect strategy in a two-player card game?

Combined probability can affect strategy in a two-player card game by informing players of the likelihood of certain events happening. Players can use this information to make more calculated decisions and adjust their strategy accordingly. For example, if a certain play has a high combined probability of success, a player may choose to make that move over another with a lower combined probability.

5. Can combined probability be used to predict the outcome of a two-player card game?

Combined probability can give an indication of the likelihood of certain outcomes in a two-player card game, but it cannot predict the exact outcome. There are many variables and factors that can influence the game, such as player skill and luck, that cannot be accounted for in a simple probability calculation.

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