This is just a theoretical problem that I found in the wild and want to know your solution.
A stack of plates is made between you a cousin and a few others.
Every (4 to 7) many random hours the plate on the top of the stack is given a slice of pie yet at this point you can instantly replace the pie with a new empty plate the goal of the exercise is having your plate on top the longest to get the most pie.
Cousin 1: Watches when you have placed your plate on top of the pile and then after a random interval of time about long enough to avoid being called out for being unfair lets say 45min-1h places his plate on top of yours.
Cousin 2: Watches when Cousin 1s plate is on top of his and then waits the same interval to avoid being unfair.
The goal of the problem is to get more pie the most pie. And the only way that I see it as possible is to cheat more then your cousins.
IF you put down a plate then wait the minimum random interval after cousin 2 has placed his plate then you are likely only getting an equal share of time and probability of getting pie.
Cheating method: You do the same thing as both cousins but you time the the average time between cousins 1 and 2 placing their plates. Using this average of time you take half the time and the same standard deviation. I then post after cousin 2 in this time period which gives me an equal amount of pie as cousin 1 but more then cousin 2.
Is there any way to get more pie then both cousins?