Don’t doubt it, do the math (and http://www.wolframalpha.com/ helps a LOT with this. Provide any formula for probability of guessing “Nth wakeup” such that it sums to 1 (or less) from 1 to infinity. Calculate the sum from 1 to infinity of the product of this and the 0.5^n chance that you’re currently on the Nth wakeup.
You will never find one that sums to better than 0.5.
Your weirdness using X and Y is not helping—any algorithm you can state eventually comes out to “some probability for each N of guessing N”. And when you view it that way, you’ll see that the sum has to be less than 50%.
Don’t doubt it, do the math (and http://www.wolframalpha.com/ helps a LOT with this. Provide any formula for probability of guessing “Nth wakeup” such that it sums to 1 (or less) from 1 to infinity. Calculate the sum from 1 to infinity of the product of this and the 0.5^n chance that you’re currently on the Nth wakeup.
You will never find one that sums to better than 0.5.
Your weirdness using X and Y is not helping—any algorithm you can state eventually comes out to “some probability for each N of guessing N”. And when you view it that way, you’ll see that the sum has to be less than 50%.