Statistic Question: Longest Possible Game?

By Nameless1, in Arkham Horror Second Edition

Veet said:

Avi_dreader said:

Ah, but that's assuming that after a certain number of coin flips the order of the universe does not shatter and all laws of physics become undone. I mean, really, have we ever tested what the results of even 100 billion consecutive coin flips to heads would be? I think not. We simply presume that it would be the same as a lesser quantity, lacking evidence to the contrary. But I say that 100 billion consecutive coin flips will bring upon us all unspeakable doom. Unspeakable DOOOOOOOOM!

I have a friend who likes to write computer programs to test this.

I'm uncertain what you are saying. You mean the computer programs that proved that this is true? Or are you suggesting (the audacity!) that a 100 billion e-flips prove that this is false?! Everyone knows that e-flips aren't real flips! How can e-flips cause the implosion of the universe?

P.S. Happy Birthday Julia :'D

cim said:

Tibs said:

For the game to be stymied for N rounds will require a P^N probability. But since P is less than one and N is a positive integer, then P^N converges to zero as N goes to infinity.

It's essentially a more convoluted form of the question, "can you flip a coin infinity times and never get tails?" The answer to that is also "no."

That's only true if P is less than one for any N. I think it's possible given sufficient time and initial luck (and certain expansion elements) to set up a situation such that once you've got into that situation, P is exactly 1: there are no non-deterministic ways of ending the game which cannot deterministically be countered by other effects or prevented from triggering. "

Ignoring the PNs. It looks like Cim has discovered infinite Arkham.

Avi_dreader said:

Ignoring the PNs. It looks like Cim has discovered infinite Arkham.

Maybe THAT'S where Millmaster went.

I'm assuming P will always be less than one. There are a few deterministic effects, but not enough of them.

Remember the old puzzle, "how many locations can be closed at once"? This is a new puzzle. What situation can both stymie the game and eliminate probability from breaking the loop? I'm holding out for "none."

Avi_dreader said:

P.S. Happy Birthday Julia :'D

Thank you, darling :-)

Tibs said:

I'm assuming P will always be less than one. There are a few deterministic effects, but not enough of them.

Remember the old puzzle, "how many locations can be closed at once"? This is a new puzzle. What situation can both stymie the game and eliminate probability from breaking the loop? I'm holding out for "none."

I think my proposal covers that. Let's assume that the players want an infinite game (or at least one in which they cannot be forced to end it by any set of circumstances before they want to, though they may be required to take deterministic actions against it ending), and are willing to use any combination of expansions necessary to achieve this. The state at the start of the infinite loop must be achievable from a normal start, with non-zero probability (though it doesn't have to be high probability).

Setup: Exclude the Black Goat expansion (corruption pile empty can't be held off for ever) and include the rest - though not any heralds (they have useful items or locations)

Step 1: Use the various known methods to keep the terror level and doom track under control during the set up phase. There are plenty of ways to cancel terror increases (since they can't be reversed), and the Thomas Olney encounter in Kingsport can take off an unlimited number of doom tokens at no risk. This makes it unlikely but still possible that the terror level can be maintained at zero and the doom track maintained at a level well below awakening for a long finite length of time. By infinity, it will break, of course, but it can be maintained for an arbitrary long finite time with sufficient luck and skill.

Step 2: Use the Inner Sanctum encounter from Dunwich Horror to return named Mythos Cards to the box. (The worst that can go wrong with this step is various unpleasant things happening personally to investigators, and terror level rises which need to be controlled with Charlie Kane, Director's Diary, Ashcan Pete, and a big pile of money)

Use this encounter repeatedly - over several hundred turns - to return every single mythos card except "Intermission" and "Happy Days Are Here Again" to the box.

Happy Days then becomes the environment, which means that Intermission does absolutely nothing. No movement patterns for Kingsport, no bounces off seals for Innsmouth, no gates opening, no terror level rise.

At this point, nothing is happening in the Mythos phase. Close all open gates, making sure - by spending trophies - not to hit the "win by gate closing" condition in the process.

Step 3: Use the deputy salary, alchemical process, Jenny's trust fund, and other things to get unlimited money and buy every item. This means that when an item is used, it can immediately be re-bought.

Infinity is now ready to start.

No more gates will open except by encounters. If one does, the monster that appears will never move, so there are several ways to get rid of it reliably without a fight (Silver Key + Time Bomb, for instance). The doom token can be removed safely in Kingsport, the gate can be closed by De Vermis without having to get near it, and the Other World encounters aren't going to awaken any ancient ones permanently. The unlucky investigator can be retrieved by casting Plumb the Void with Ancient Language, or just get back later via LiTaS.

Provided that the number of people adventuring in gate opening places is limited (drawing eight separate "a gate and a monster" encounters in the same turn will mess things up, but you can control how many people go adventuring in unstable locations), and the proper safety precautions are taken I don't believe anything can go wrong so severely that it can't be deterministically reversed at this point. Terror level increases are the only irrevocable ones and the environment blocks that - I don't believe there's any encounter that forces the current environment to be discarded, but if both the Director's Diaries are held, one intermission can be blocked anyway until it returns.

You might get into a situation where you had to stop exploring all locations, and get out into the streets and particular control locations (Thomas Olney, shops, etc.) while you calmed things down again, but I don't think that would ever fail.

Black Goat breaks it, because eventually adventuring at cult locations will get someone a corruption, and since they're never recycled the deck will run out and awaken the ancient one. You'd need to avoid those locations entirely if Black Goat was in. But again, you could avoid those locations deterministically even then.

Well Cim, it seems you found the crack into Infinite Horror, but you clearly have not explored it properly. To insure that infinity lasts for infinity, a standard turn will go like this:

Investigator moves to the street. Investigator ends turn in street. Next turn. Repeat ad infinitum.

Very nice. You didn't take all that long to figure that out either.

Thanks for the responses guys!