You are sat down at a terminal that prints out a "1" or a "0" at regular intervals and told that if you can correctly predict what will be printed next you will get a dollar, but if you predict incorrectly you will lose a dollar.
What strategy do you employ to maximize your monetary reward?
Wait until I get 1 correct answer then stop.
Sounds like a boring job with little possibility to actually earn money.
You're leaving a potentially infinite amount of money on the table so F-
>prints out a "1" or a "0"
At random?
Do the "1"s and "0"s appear at random? Or, at least, with no obvious pattern.
Are there equal numbers of "1"s and "0"s?
It both answers are "yes", there is no winning strategy.
This sounds like a re-tread of a recent post on Veeky Forums which claimed a method of making money by opting to bet (or not bet) based on an expectation of "runs".
IT DOESN'T WORK!
Stop bothering us.
Or go to Vegas and come back with a fortune so you can laugh at us doubting brainlets.
>"I predict a 1 or a 0 will be printed"
Assuming that you have infinite time/can witness an infinte amount of intervals, I'd just use the theories behind random walks, realise that it's a 1-dimensional process and that the diffusion happens rather fast; just set a cut-off whereever you like, it will (with a chance of kind-of 1) land on that spot some time.
You are not told. All you can assume is that it is independent of your guessing so that you know it's not just going to output the opposite of whatever you say.
you're playing a fair zero sum game against an opponent with infinite money
if you go up at any point it's just random luck and you're almost surely going to go bankrupt anyways