Abstract Solutions

Australia v/s Bangladesh
Case1: Australia won the match

Case2: Bangladesh won the match

There is more information in the message-Case2 as compared to that of Case1. But, how can we come up with a precise notion for this intuitive argument?

Consider this problem.How can you compare biodiversity at two different parks?
Say park1 has 10deer, 1 lion and 10 monkeys while park2 has 2lion, 4 deer and 6 monkeys.

This question was answered by setting up a game. Suppose Alice and Bob are the players. Alice is at the national park and Bob is at home. Alice and Bob know the frequencies of all the animals. Bob needs to ask a question to which Alice can only reply Yes/No. Now consider the average number of questions to be asked, to find the answer. If the park has 99.9% deer, Bob would ask "is it a deer" and guess it with a probability of 0.999. The average number of questions to be asked is close 1.However, if all the animals have similar frequencies, it takes more questions.

Consider a simpler example. Suppose Sheldon, a sumo and Mr Bean are wrestling. To find the winner's name I would ask "Is it Mr Sumo?" and the next question would be "Is it Sheldon". I would get my answer, within two questions. However, there is a good chance that  we would obtain the answer in just one step. Thus, the average number of questions will close to 1. If all the players are well matches, with one-third chance, a question will suffice and with two-third of a chance two questions will be needed and the average number of questions would be equal to 1.66

Leaving the math and the abstractions aside. The central argument is- Can we define the problems properly and seek sophisticated and robust solutions using the power of abstraction, like how we did, in this example?