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Forum Games / Re: Drunk Mafia VI: Phoenix
« on: March 02, 2019, 07:28:40 pm »Vobes are the same as votes to mehmmm? seems like we lost
#imprecise
Congrats Umbrage and liopoil!! first win of the night.
Vobes are the same as votes to mehmmm? seems like we lost
#imprecise
Congrats Umbrage and liopoil!! first win of the night.
NO NUMBER CLAIMINGI already claimed #5 though
That's one of the very few rules of Drunk Mafia
Well, I have a 1/3 chance of hitting scum. So, vote: Umbragehmm, I have a 2/3 chance
Also discord sucks.I just went and turned off PPE-warnings in my settings
Also also my greatest joy in life is ignoring PPEs over and over
I have better f(n)= 2^2^2^(O(n) times) kingdom kc, workshop, city quarter, training, tfair, bridge, gardens. Deck contains starting cards one gardens, rest are action. Training on workshop
Turn starts by drawing deck with log(d) cq where d is deck size, play kc-bridge. Then you start multiplying workshops/kc. Assume that deck has k kc and k workshops. play k/2 kc on k/2 workshops to gain 3/4k workshops and 3/4k kc then play cq to draw these and repeat by number of cq in deck. If you start with 3 kc and 3 workshops and l cq you will end with 2^l workshops. Coins from training allow you to buy 2^l/10 cq which shows that f(n+1)>=2^f(n) and bound follows.
I think what luser originally wrote works but tim's suggestion is more clear and is technically better (improves the base of the exponent, pretty much). A more explicit (but still not totally optimized) description of luser's solution with additions (it took me a bit of work to decipher exactly what was happening):
Kingdom: KC, stonemason, city quarter, fortress, gardens, training, travelling fair, inheritance (3 events, oh well). Training on stonemason, inheritance on KC (okay add a cost-reducer to the kingdom). When our deck has size d: Deck has 1 gardens, 1 fortress, ~7d/22 estates, ~14d/22 Stonemasons, ~d/22 City Quarters where x = o(d).
Turn:
Play ~log2(d) City Quarters to draw the deck
Play the estates as d/4 KC on d/2 stonemasons for 3d gains, make them d estates and 2d stonemasons.
We have d/4 cards left in hand, so play 4 city quarters to draw everything again.
Play 3d/4 estates on 3d/2 stonemasons for 9d gains, which are 3d estates and 6d stonemasons...
Repeat like before until we run out of city quarters. We now have over d' = 3d/88d cards in our deck, and the number of stonemason plays a bit over half of that. From training we could buy d'/20 city quarters, but just buy d'/22 instead (using travelling fair for buys).
Each turn d' = (31/88)d, so we end up with around 31/88 ↑↑ n points.
I wouldn't be surprised at all if three arrows is possible though... I'll think about it...
I've been asking (Math and CS) friends this question for a while now. In particular some variant of question 2.I've also talked about this question with some friends before; in fact, I suspect that we have some mutual friends. The simplest way of stating my question is: Is the decision problem "is there a way to get at least n points this turn?" decidable for any game state? I do not know the answer for finite piles OR infinite piles. In the case of infinite piles, game states must still have a finite description. My suspicion is that the answers are yes and no, respectively, but it's possible that new card could make the finite piles case undecidable as well. It's also possible that the infinite case is decidable; I do not have a proof
Being able to embed a turing machine (which is not a totally well defined notion) doesn't seem to (necessarily) have any implication for the undecidability for the game.
Dominion with finite piles is really complicated (i.e. question 2 and variants i.e. winning in 1, getting from 1 state to another presumably these are all the same computability strength). . It seems that the win in turn one question is likely decidable (though proving this seems ferociously hard). But I have no idea about infinite pile dominion.
Sorry for the necro.Oh, yes, you are right. Wow, it's been a while.
Note that if we're already willing to subtract a constant number of turns from n (e.g. to set up the deck), it doesn't really matter what number you have as the base of the tetration. Here's a proof that 2 ↑↑ (n+2) >= 4 ↑↑ n.
Lemma 1: If x >= 4y and y >= 1, then 2^x >= 4*4^y.
Proof: x => 4y implies 2^x >= 2^(4y) = 4^(2y) = (4^y)*(4^y) >= 4*(4^y).
Now we can show that 2 ↑↑ (n+2) >= 4 * (4 ↑↑ n) for all n with induction. For n=1, both sides equal 16. If 2 ↑↑ (k+2) >= 4 * (4 ↑↑ k), then by Lemma 1, 2^(2 ↑↑ (k+2)) >= 4 * 4 ^ (4 ↑↑ k), or 2 ↑↑ (k+3) >= 4 * (4 ↑↑ (k+1)).
The same idea can be extended to show that for any A,B, there's a constant c such that A ↑↑ (n+c) >= B ↑↑ n for all n.
In summary, all of the c ↑↑ n solutions are about as good as each other for this question.
Sometimes I feel like I'm the only one playingIs this post the current longest necro?
It's okay, the necro game thread prompted me several times back in the day...I would have taken it tonight too :/ I blame the necro game thread for prompting you
That is what did it!