7.7 Deck of Pokers

[Shantanu Kumar]

A deck of pokers. Three choices: A: 26 black, 26 Red; B: 13 black, 13 Red; C: random 26 card from the deck. Take the first two cards, if same color, the win $1, otherwise lose $1. Which deck is best for you if you are playing? Why? How to do simulations? How to draw the random pile of 26 cards?


I did solve the problem but its hard to compare all those probability numbers without doing all the calculations.
Anyone knows how to compare the three probabilities with minimal calculations?

 

[Math Andrew]

Without any calculation I would say that the answer is C since there is an higher probability that it will be unbalanced, i.e. you will a have greater probability to take two cards of the same colour. This is just my intuition.

 

[ferdowsi]

B is the best at 13/25. If you're drawing 2 random from a random sample w/o replacement, then you are just taking 2 random from the whole population, so A and C are the same at 26/51.

 

[Shantanu Kumar]

B is the best at 13/25. If you're drawing 2 random from a random sample w/o replacement, then you are just taking 2 random from the whole population, so A and C are the same at 26/51.

Shouldn't those numbers be for B: 12/25 and A & C: 25/51. Am I missing something?

 

[Math Andrew]

Yes I got those two numbers too

 

[mark_yao]

Choose A, you win with 26/52* 25/51, Choose B, you win with 13/26*12/25. 26/52 = 25/52 = 1/2, but 25/51 > 12/25. So, A will give you a better winning odds. C is equivalent to A, you can argue this by Total Probability Theorem.