Hi there. I really hope I'm posting the right place and right way since this is my first time here, please excuse me if this has been done wrong and tell me how to fix, but moving on.
I'm a student who while playing a card game with 3 friends got curious about how the math with probability works in this particular game. In the game each player has 13 cards and one has to choose an ace, the player with the chosen ace in hand will end up playing with the one choosing for the rest of the game. In the game you make a stack of 3 cards which the player choosing the ace can exchange for their own. If the player choosing the ace chooses an ace which lies in the stack of cards they exchange with, they will end up playing the game alone against 3 instead, however, this is incredibly rare, I just want to find out how rare.
I started by trying to find the following:
The possibility of one of the four aces from the deck of the 55 cards (it has 3 jokers) ending up in the stack of the three randomly chosen cards, and after that I wanted to find out what the chances were of the player choosing exactly that ace after it had ended up there. To do the first part I thought I could do the following:
3/55*4/55, because there are 3 cards in the stack and 4 aces in the 55 cards, but I was then told that it seems unlikely that this is the answer since that after you draw the first card there are only 54 remaining and so on. Because of that I thought I could it like this: (1/(4*55)*(1/(4*54)*(1/(4*53) but that doesen't really seem to make sense after thinking about it, and looking at the result. And so after browsing various math sites I figured I would try asking on a forum instead.
So, in conclusion, I want to find out the possibility of one of the 4 aces ending up in the stack of 3 randomly chosen cards, and that ace then being chosen by the player who's choosing one of the 4. Thanks in advance.
I'm a student who while playing a card game with 3 friends got curious about how the math with probability works in this particular game. In the game each player has 13 cards and one has to choose an ace, the player with the chosen ace in hand will end up playing with the one choosing for the rest of the game. In the game you make a stack of 3 cards which the player choosing the ace can exchange for their own. If the player choosing the ace chooses an ace which lies in the stack of cards they exchange with, they will end up playing the game alone against 3 instead, however, this is incredibly rare, I just want to find out how rare.
I started by trying to find the following:
The possibility of one of the four aces from the deck of the 55 cards (it has 3 jokers) ending up in the stack of the three randomly chosen cards, and after that I wanted to find out what the chances were of the player choosing exactly that ace after it had ended up there. To do the first part I thought I could do the following:
3/55*4/55, because there are 3 cards in the stack and 4 aces in the 55 cards, but I was then told that it seems unlikely that this is the answer since that after you draw the first card there are only 54 remaining and so on. Because of that I thought I could it like this: (1/(4*55)*(1/(4*54)*(1/(4*53) but that doesen't really seem to make sense after thinking about it, and looking at the result. And so after browsing various math sites I figured I would try asking on a forum instead.
So, in conclusion, I want to find out the possibility of one of the 4 aces ending up in the stack of 3 randomly chosen cards, and that ace then being chosen by the player who's choosing one of the 4. Thanks in advance.