what is the probability of going to war with six decks of cards?

Answer 1

This is the probability that two cards match each other in rank without regard to suit. For six decks of cards there are

6*52 = 312 cards

Each rank has 4*6 = 24 cards

P(2 cards match rank) = 1*(24 - 1)/(312 - 1) = 23/311

Answer 2

This is a tricky question to answer, since the answer depends on what cards have been played before. To go to war, you and your opponent must show the same rank card. If this was the first play, you have 312 cards of which you have half and so does your opponent. The expectation is that you will have half of each rank and so will your opponent, or 12 apiece. So if you show a card of a specific rank, the probability that he will match it is 1 in 13.

This is similar to the reason why Las Vegas went to multiple decks to fustrate people who were counting past-dealt cards in Blackjack. As a certain card (say an Ace) is exposed, the probability that there is an ace in the remaining cards decreases. By keeping count, an astute player could enter a game knowing that certain cards were more likely to occur and play accordingly. This was enough to tip the balance of probability to the player rather than to the dealer, and people made a good bit of money at the Blackjack tables.

Answer 3

Depends, does one deck have nuclear weapons while the other decks have oil?

Answer 4

It would depend upon the size of Army issue pockets.