Hi,
I have a interesting hypothetical situation and am keen to get some different advice / points of view on what the best strategy is. Here it goes:
You are given $5k daily, the money is put into a account that you can access only once to withdraw. You can view the balance anytime. The maximum amount you can recieve is 100 days payments ($500k). At any point the amount of money in the safe can start to go down at a rate faster than $5k/day. It may drop by 5% per day, 20% per day or go to zero - this is unknown and unpredictable.
When do you take the money, and what factors affect your strategy?

If it goes to 0 one day, is the game over or can we just start over and (hopefully) get $5k the next day and start rebuilding?

Do we have any sense of the chance of having a losing day?

And I presume that the chances of losing different amounts are the same?

If the answer to the first question is yes and second question is no (and yes to the third), I probably go for a few months just to see how things are shaping up, get a sense of how often we have losing days, and then based on that, come up with an exit strategy game plan.

If during those first few months the total amount is $300kish, I probably pull the trigger, although a lot will depend on how often I've had losing days.

Obviously, the higher your total, the lower you EV per day because losing a percentage is a higher amount.

At $300k, the average loss is $150k on a losing day, so the days of winning to losing would have to be 30 to 1 just to be break even EV. Even at $200k the breaking point is 20 to 1. So probably by the time I get to $150-$200k, I'd have to see evidence that losing days are super rare to keep going.

I would try to infer the likely trajectory based on other people who have played, or the circumstances where someone offered me this.

If that doesn't give me anything, I'd assume there's roughly a 1 in (100 - N) chance that any given day will be the day it starts dropping, where N is the number of days I've played already. To be conservative I'll assume that the drop will be 100%.

Using that estimate, at day 50, holding has a $0 EV. I'd probably quit a bit earlier than that, day 40 or so, to maximize EU.

You could make other assumptions -- maybe the chance of dropping is lower, maybe the distribution of drop rates is flat between 0% and 100%. That would lead you to hold on longer.

But most people, I expect, would probably quit after a week or so. A substantial number would quit after the first day.