If they should cut, nobody knows....or do we?
Two people are playing a card game with 18 Black cards, and 3 red cards. The red cards are randomly mixed into the black cards as a group ( the red cards are all together somewhere in the deck at the start of the game example of possible configuration: BBBBBRRRBBBBBBBBBB )
The game is played by drawing cards ( without replacement) from the top of the deck one by one until a red card is drawn. The person that draws red loses. Before any players turn they can choose to draw from the deck as is, or cut the deck. A cut consists of removing anywhere between 1 and number of remaining cards minus 1 cards from the top of the deck and placing them underneath the remaining deck.
The first person goes and draws a black without cutting. What are the probabilities the next person loses if they decide to cut (or not cut ) the deck before their draw?
@joe-shmo
After player 1 draws a black card, there are 20 cards left in the deck.
There are 18 ways to mix in the red cards. If player 2 does not cut, the odds of pulling a red card are 1 in 18. (The case with 3 red at the top.)
1/18 = 0.0555...
There are 19 ways to cut the deck. In the case of 3 reds on top, cutting results in a 2/19 chance of drawing a red. For the other 17 cases, there is a 3/19 chance of drawing a red.
Total all this up, and there are 3*17+2 = 53 ways to draw a red, after cutting, and 18*19 = 342 possible outcomes of cutting.
53/342 ~= 0.155
Player 2 should NOT cut the cards.
@joe-shmo saidSteady on Joe,one at a time mate.(I believe the correct expression is lol-(I don't use these things or the silly faces)
If they should cut, nobody knows....or do we?
Two people are playing a card game with 18 Black cards, and 3 red cards. The red cards are randomly mixed into the black cards as a group ( the red cards are all together somewhere in the deck at the start of the game example of possible configuration: BBBBBRRRBBBBBBBBBB )
The game is played by drawing card ...[text shortened]... probabilities the next person loses if they decide to cut (or not cut ) the deck before their draw?
So to begin, including a question at the end.
Let's call the red cards r1 r2 and r3 and 14 black cards after one has been drawn
The probability of a red card being the top card is 1:15 =.066.(It can only be r1)
With a cut it becomes a lot more complicated:-
Question After the cut can the red cards be split or do they still have to be in the order r1 r2 r3 with no black cards in between?
@bigdoggproblem saidSpot on BigDoggProblem!
@joe-shmo
After player 1 draws a black card, there are 20 cards left in the deck.
There are 18 ways to mix in the red cards. If player 2 does not cut, the odds of pulling a red card are 1 in 18. (The case with 3 red at the top.)
1/18 = 0.0555...
There are 19 ways to cut the deck. In the case of 3 reds on top, cutting results in a 2/19 chance of drawing a re ...[text shortened]... d 18*19 = 342 possible outcomes of cutting.
53/342 ~= 0.155
Player 2 should NOT cut the cards.
Well Done!
@venda said"Steady on Joe,one at a time mate."
Steady on Joe,one at a time mate.(I believe the correct expression is lol-(I don't use these things or the silly faces)
So to begin, including a question at the end.
Let's call the red cards r1 r2 and r3 and 14 black cards after one has been drawn
The probability of a red card being the top card is 1:15 =.066.(It can only be r1)
With a cut it becomes a lot more complicated:-
In my defense I did post this yesterday!
"Let's call the red cards r1 r2 and r3 and 14 black cards after one has been drawn
The probability of a red card being the top card is 1:15 =.066.(It can only be r1)
With a cut it becomes a lot more complicated:-"
Correction, they start with 3 red 18 Black. After the first person goes there are 17 Black, 3 red
for a chance of losing without cutting of 1/18.
Question After the cut can the red cards be split or do they still have to be in the order r1 r2 r3 with no black cards in between?
Yes, its a random cut. After the cut is complete there may be black cards in between red cards.
@joe-shmo saidAs they teach you at school,READ THE QUESTION!!
"Steady on Joe,one at a time mate."
In my defense I did post this yesterday!
"Let's call the red cards r1 r2 and r3 and 14 black cards after one has been drawn
The probability of a red card being the top card is 1:15 =.066.(It can only be r1)
With a cut it becomes a lot more complicated:-"
Correction, they start with 3 red 18 Black. After the firs ...[text shortened]... s, its a random cut. After the cut is complete there may be black cards in between red cards.
At least I had a go.
I'll look at the code thing later without looking at Bigdoggs answer.