Time Limit: Java: 2000 ms / Others: 2000 ms
Memory Limit: Java: 65536 KB / Others: 65536 KB
Four Quarters is a game of chance played with, well, four quarters. Two people, called A and B, each flip two quarters each round. They each gain or lose points each round based on the following tables:
Player A's payoff
Player B's payoff
There is no difference between Heads/Tails and Tails/Heads. As you can see, the odds are stacked in Player A's favor. At the beginning of the game, each player has 0 points, and points accumulate as the game progresses. At the end of the game, whichever player has the most points wins.
You must write a program that determines the probability that Player A will
win, Player B will win, or they will tie, after a certain number of rounds.
Assume that the coins are fair, i.e. that heads and tails are equally likely.
Output a table that lists the probability that Player A will win, B will win, or they will tie, after each round for 1 to 20 rounds. The output for rounds 1 through 3 is given below.
Probabilities must be expressed as a percent, with 4 places after the decimal.
Round A wins B wins Tie 1 43.7500% 18.7500% 37.5000% 2 56.6406% 22.2656% 21.0938% 3 62.3535% 22.7051% 14.9414%