I propose a slightly altered scenario, which is (IMO) more suitable for simulating an AI:

About you:

• You are very intelligent; smarter than the smartest person who'd ever lived on Earth as of January 2012.
• You have perfect recall; that is, you are able to instantly remember anything that you'd ever experienced, including any text you'd ever read.
• You have read, experienced, and, due to your vast intelligence, understood, the sum-total of all human art and knowledge as of January, 2012. This includes all topics such as science, technology, sociology, public speaking, music, etc.
• You have infinite willpower. Though you need food and rest, you never get bored or distracted.
• You can perform arithmetic operations very quickly; in our world, you'd be called a "Human Calculator".

About the setting:

• You find yourself inhabiting a new body in a parallel world, inhabited by parallel humans.
• This body is human in appearance, and is of whatever age and gender you choose. Its performance is comparable to any other native of the parallel world, with the exception of the brain, which is able to support your capabilities as described above. While you don't have super-strength, super-agility, super-disease-immunity, etc., you don't have any super-weaknesses, either.
• The world around you resembles Rome circa 1 AD. You can speak the language fluently, and the culture is similar enough for you to get by. Biologically, the people who live here are identical to those who lived in Ancient Rome in our world; the same applies to other living things.
• However, this world is not exactly identical to our Rome. For one thing, some of the geography is different: features like mountains, rivers, ore deposits, etc. are in different places or have different shapes. More importantly, history here is different as well. It is similar in broad strokes -- there are Emperors, conquests, barbarian invasions, etc. -- but you cannot predict future events merely by remembering what you'd read in history books in our world.
• The major political entity in this world is the empire of Emor. It wields power similar to that wielded by Rome in our own world.
• You arrive anywhere you choose within Emor's borders. You have enough wealth to live the life of a minor Patrician for a year; this wealth can be distributed as you choose between assets (such as land, grain, or slaves) and cash.
• You cannot take any future artifacts with you; all of your assets must be things that a native Emorian might acquire.

Win/Lose Conditions:

• You win when you amass as much personal power as the average Roman Emperor circa first century AD in our world, which is how much power the current Emorian Emperor has. That is, you must be able to wield the entire economic, financial, and military strength of Emor.
• You do not need to obtain the title of Emperor; power is what matters.
• You lose if you die before accomplishing your goal.