Binomial distribution to design the crafting in the social game

Earlier this week I was involved as consultant into analysis/design task of the crafting feature of social game. The player is doing some actions, actually clicks. The result of such action would be a random set of special items, or maybe just one item, or even nothing. Later player can combine several items to create (craft) some special unique item. Each simple item i has its own probability pi to appear after single click. There is also the approximate number of actions it needs to click for getting all simple items of the combination with some acceptable probability (let’s say 0.5). The goal is to gues the number of instances of each simple item. All simple items appear independently. So, we can use binomial distribution to choose some suitable values.

Combination of items i1,i2,…,in should be collected in N clicks with probability 0.5.

So,

CkN * pk * (1-p)(N-k) >= 0.5

for every item in combination, where p is the probability of simple item and k is the number of appropriate simple item instances in the whole combination.

Excel spreadsheets tool has implementation of formula above as standard BINOMDIST() function already. So, it’s easy to do such calculations for game designers.

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