Saturday 24 January 2015

A trip to South Island, New Zealand (3): Mt. Cook

Mount Cook is the highest mountain in New Zealand and remains to be one of the most amazing scene there. You can simple leave everything behind and spend a few days here to enjoy the grand nature.

Taking around 4 hours of bus trip from Christchurch we planned to stay here for another two days. We walked along various tracks which sum up to 16km and every centimetre is well-deserved to have a go.

Wednesday 7 January 2015

On card drawing problem

Faithful greetings here and wish everyone to do well in 2015. Before I continue to write about my journey, let's consider a game-related modelling problem here.

Recently there are a series of electronic games mainly on mobile platforms that collects various cards for the game system. There can be a lot of variation on the game like tower defence, card battling, action shooting etc. but these aren't really important. They can all characterized to be a card collection game (CCG).

What elements must a card collection game contain? A free way to obtain cards through events, and a paying way to obtain cards, that we call it an invocation. A basic model would contain a card pool where every time a card is chosen, at a certain probability and given to the player.

In order to attract the players to spend further, we can usually find some alternate option to invoke cards that apparently a better option. A typical way is to guarantee a rarer card when the invocation is done in a larger batch. Without a further assumption in the rate of appearance for the rare cards we ought to see which option is better.

In this entry we will simply our model to two types of cards: common and rare cards. A binary model would allow binomial distribution and make everything easier.

Since the number of cards is finite, and of course countable, the following calculations will be done with respect to discrete distributions.