Chance based denial game ("easy" mode)

[herpderp42]

Hi everybody.
I have had recently an idea for a denial game based on chance.
The whole point about using a chance based system to earn release is obviously to add some additional excitement. You don´t know how long you will be denied.
However, it is important to think about the system to understand how long exactly the denial might end up being (some systems can (as most people will know) theoretically deny you forever ).

So this system is quite easy to understand and has a maximal amount of days. It is very flexible to adjust to each person´s experience level regarding denial.
Plus it involves a second person and thus you can make it more interactive if you both wish to but I will come to this after presenting the game:

Everybody who wants to join does so by saying how long he wishes or rather expects to be denied. We will call this number n. For simplicity I will always give an example afterwards in brackets (those ones -> []) where n has the value 50.

His partner will roll one number between 1 and 2*n on random.org [between 1 and 100 in the example] and make a screenshot including the timestamp.
Save this number. It will stay the same.
After each succesful day of denial the denied person will guess a number inbetween 1 and 2*n and state this number to his partner, who checks if it is the correct one. If it is: Great, the denial ends immediately. If not: Try again tomorrow with a different number but keep track of the ones you have already guessed.

The nice thing is that the probability to be denied at most j days is always j/(2*n) [for example n=50 and j=10: 10/100=1/10 which is 10%].
This means that you are with a probabily of 50% at most as long denied as you wished for and with an equally high probabily longer but as long as you don´t guess the same number twice the maximal amount of denial is twice your starting value n.

Spoiler:

I called this "easy" mode since the probabilities should behave really "tame" in the sense above. A 'problem' is that the denial is as equally likely to be shorter or longer than wished for.
If this is a problem for you there is an easy fix: multiply with 3 instead of 2 and the maximum amount of days will be 3*n and the expected time of denial 1.5*n, so you will most likely be denied for longer than you wished for.

If you want to try feel free to post here. I am willing to be the partner for a few people but not for too many of course.

If you are interested about the interactive variant: The partner does know the number and maybe the denied person can please him by doing dares or similar to earn tips or extra guesses. It is basically up to you how far you want to go.

If people are interested I thought about a snakes & ladders denial game aswell (just roll a few times each day, not that complex), but the probabilities are way more wild and can mean way longer denial times.

Soooo, if you want to join or would be willing to be somebody´s partner or just want to add something (maybe I had messed up something even if I don´t think so ) just command.

Edit: One thing to think about: The higher your starting value n, the smoother this whole thing would work of course even if the principle works with low numbers aswell. A very short denied time just gets more likely.

[Ilovechoco]

I'd like to join with the number of days set to 30 please

[pepem6066]

Id like to join with a n value of 14 days