Thought Experiment Part 1

You awaken in the middle of the night to a neon blue beam of light shining down from the dark cloudy sky above. Down floats a solid metal cube with a piece of paper taped to the top.

You look at the paper — it outlines some rules:

1. Every day, once a day at the same time, a number will pop out of the box
2. You have 3 options when the number pops out:

• Bet an increase the next day
• Bet a decrease the next day
• Bet nothing

Assume that this metal cube will work perfectly everyday, it will make no noise or internal indications on what is going on inside to generate these numbers. The bet you place is independent of the next days number i.e. the cube won’t decrease just because you picked increase.

What strategy could you use here to win the most bets in 100 days?