Life and Luck Puzzle

February 2, 2022

Guess the Card Puzzle: Life and Luck

Solve the Life and Luck Puzzle.
Two friends A and B are caught by gangsters and are made to play a game involving cards. The rule of the game is that both A and B will pick a card each and hold up such that A cannot see the card he chose and similarly B cannot see the card he chose. But of them are able to see the card the other chose. The objective is to correctly guess which card they have picked. If they can guess correctly, the gangsters will let them go. Whoever guesses wrong will die.

Considering the above situation, who has a greater chance of surviving between the two?

Solution

Among the two whoever guesses second has a higher chance of survival, if they follow the given strategy.

Now we are assuming that A and B, somehow were able to discuss and come up with a plan of survival.

Let us assume that A will go first at guessing and B will go second. Now in a deck there are 52 cards, and A has picked one while B has picked the other. A can see the card B has picked so he knows his card is not the same one.

Therefore other than B’s card there are 51 different cards, among which one A has picked. Therefore A’s probability of guessing correctly is 1/51.

Now onto B. A can see B’s card but obviously cannot call out that card to B. Instead what A can do is that in his guess A calls out the preceding card to B’s card. For example, B has picked 9 of spades, A calls out 8 of spades. Or if B has picked king of hearts then A will call out Ace of hearts.

Therefore using this strategy, B can survive and A has a probability of 1/51 chances of guessing correctly.

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