Im away for the weekend. Thanks for reserving a seat.

If we're not doing this real time, whats the difference between that and a forum game?

I would prefer a speed play at some previously agreed upon time slot, where everyone takes two hours to play live. Otherwise we don't need a chat channel.

Noprobs

The difference is the chat format allows for faster paced games since you just type in a message and send it. You don't have to write a whole forum post about it. Add to that that since Discord is present (nearly) everywhere, and it's easy to open it up and get straight to some server, I can see a game finishing in a couple days tops, instead of two months long.

I was going to try a swing at coding something for a bot so that said bot can act as the host instead of a human, but I found out there's more work to be done - mainly that the bot framework would be updated, which means I have to do some changes to the "cogs" (collections of commands) which I need to study.

I'm thinking of finding a co-host to help me handle things while I am asleep (My times are more suited for Europeans than Americans), but given I had a hard time finding players to begin with, that may be a stretch.

Either way, I am cool with what you guys think. I just believe a text-chat based game would be a spectacle to watch like this one was (except I get to sit up in the clouds and watch my game unfold like if I was God).

Oh, right! Thanks for reminding me, I meant to post that afterwards.

The deck, after the game was done, consisted of F, then L, then L, then the rest were all F cards.

...


Ouch

So the only way the Liberals would have won was through electing one of the unknown Liberals (rtcvb or flub, heck even Joe) as Chancellor in the nearest government. Damn, we sure had the liberals in our palms very thoroughly.
Oh, ZFR, just letting you know that the game will launch as soon as you join the Discord server. We have all ten seats taken!

I've also generated the secret roles you guys will have. Needless to say, it'll be a fun spectacle that I'll god o- I mean watch over.

Ariund 10 hrs from now. On my way home then need sleep.

regarding your puzzle - does beatrice have to give me a 1 with a chance > 33% that make an attempt, or do I have to get to a position where Beatrice will give me a 1 with a chance > 33% within 4 attempts?

Does that make sense?

I'm assuming it's the first one, because that's much more complicated and it's already hurting my brain.

Yup, I just read it back.


Are you asking what's the highest number I can choose which guarantees I get to 2 (chance greater than 33% of getting a 1) in 4 moves or less?

And no, probably what you're asking me is,

actually - just considering this one, the only possible answer is two, because if you start with three you can't guarantee that she won't give you 3, 3, 3, 3. That's a nice thought.

Anyway, to what I think you're answering. I'll begin with a little brute force ('brute' is perhaps misleading...)

Say we start with 8 with a 12.5% chance of getting 1. There's 8 outcomes - 8 (12.5%), 7, (uhhhh... 14.3ish% ), 6 (16.5%), 5 (20%), 4 (25%), 3 (33%), 2 (50%) and 1.

So to work out what your SECOND roll's chance of giving you a 1 is, you take the average of the 8 possible outcomes? And the third's is.... the same as the second? Do we need to eliminate stuff from the subsequent rolls to take into account that we won't make the roll if we get a 1? Probably not....

And then we take the average of... something... in order to establish...

halp!

Because the higher numbers are removed, there's a 1/8 chance of having an 8 on the second roll, a 2/8 chance of having a 7, 3/8 of having a six etc. I need to take this into account somehow!!

OK, for anyone else reading this, let me repost the puzzle here, so you know what I'm talking about. This is the puzzle I shared on discord channel.

Beatrice is a bot. If I ask her "roll n" she gives me a random number between 1 and n. n is a natural number greater than 1.

I play a game with Beatrice where I start with "roll n" and then do a roll to whatever result she gives me and so on until I end up with 1.

What's the maximum n I can start with that ensures I end up with 1 in four tries or less more than 33% of the time.

This does not halp me at all! I already knew all this

OK. Let me explain what I mean further.

An alternative way of asking for the same thing would be: What's the maximum number of n I can select to ensure that there is a 33% chance or less that the game will last 4 rounds or less.
(or to put it yet another way, the game lasts 5 rounds or more at least 66% of the time).


For example, let's say n is equal to 2.

In this case, the only way the game will last 5 rounds or more is if roll n returns 2,2,2,2. This means 1 in 16 times, or 6.25% of the time. This is much smaller than 33%.

Now let's say n is equal to 3.
In this case, the game will still last 4 rounds or less quite often. I mean there is a 33% chance of it ending on round 1 if you get 1. If not, you may get 2 which will increase its chances of ending quicker. Or you may get 3 which will give you three more tries.
Regardless the chance is greater than 6.25% from n=2, but smaller than 33%

Now let's say n is equal to 1000000
You can see that the game will very often last more than 4 rounds. Definitely more than 33% of the time.

So what's the maximum value n can take for the chance to be 33% or less?

Is that clearer now?
Sorry, was typing. Just wanted to post the problem first.

Does the above make it clearer of what the problem is?

Also, just wanted to note that I do not have an answer. Just some observations on how to approach and a quick and dirty way of getting an approximation. But I'm happy to share any insights. And if I find some spare time, I might give it a proper try too.