Research in the original Master of Orion Game
In the original Master of Orion, each technology has a cost C. After you spend a certain amount of money on research (usually less than C), you will have a 1% chance per turn of discovering the technology. If you spend more money, then the probability of discovery increases. Some technologies give you an immediate boost in income—for example, improved eco restoration and reduce industrial waste 80%. If you only have a 1% chance per turn of discovering these technologies, it would seem to be a good idea to spend a little more on research to improve the probability of discovery thereby decreasing the average time to discovery. The optimal probability of discovery can be deduced from the cost of increasing the probability of discovery and the amount of income the new discovery will produce. Suppose that it costs C/100 dollars to increase your discovery probability by 1%. Further suppose that upon discovery, your income will increase by i doll...