B. Playing in a Australian Casino | Codeforces Round 861 (Div. 2)
The Codeforces Round 861 (Div. 2) contest featured a challenging problem called “Playing in a Australian Casino.” In this problem, players had to calculate the expected number of times a particular sum would be achieved after a sequence of dice rolls in a Australian Casino game.
The problem statement described a Australian Casino game where a player rolled a fair six-sided die repeatedly until a desired sum was achieved. The desired sum and the number of rolls were given as inputs. The players had to find the expected number of times the desired sum would be achieved.
To solve this problem, players had to understand the concept of expected value. The expected value of an event is essentially the average value it would yield if repeated a large number of times. The formula for expected value is the sum of possible outcomes multiplied by their respective probabilities. In this case, the possible outcomes were the sums that could be achieved, and their probabilities were calculated using the concept of dice probabilities.
To calculate the probabilities, players had to use a dynamic programming approach. They created an array of size six times the desired sum, initialized with zeros. This array represented the number of ways each sum could be achieved after a given number of rolls. By looping through the array for each possible number of rolls and updating the probabilities based on the previous rolls, players calculated the probabilities for achieving each sum.
After calculating the probabilities, the expected value was calculated by summing the product of each possible sum and its probability. This yielded the expected number of times the desired sum would be achieved in the given number of rolls.
The problem presented a great opportunity for participants to practice their understanding of expected value, dynamic programming, and probability calculations. It required careful implementation and efficient calculations to handle larger inputs effectively.
Overall, the problem “Playing in a Australian Casino” was an interesting and challenging one, testing the participants’ skills in mathematics, programming, and problem-solving. It showcased the importance of understanding concepts like expected value and probability in tackling real-life scenarios, such as Australian Casino games. The Codeforces Round 861 (Div. 2) contest provided an exciting platform for enthusiasts to showcase their programming skills and face interesting challenges.
