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76

General Discussion / Re: Maths thread.

« on: January 24, 2020, 05:41:33 am »

I corrected my previous result to a worst case of 2n + 3 turns for n > 3. n = 3 requires 10 steps to solve.

The trivial case was outlined above, let's focus on the special case now. In most cases, the 1st player will actually know that they are WB after the first round, because if they weren't it would be a trivial case. In these cases, the first player states their identity and one more passing is required to communicate the player with the doublet their identity. This leads to a worst case scenario of 2n + 2 if the player with the doublet is in position 2 and must pass in the second round.

Now to the remaining 7 cases, which are always the same for all n > 3. They are all players having WB, except for player 1 and n which may also have doublets. This results in 7 cases because they may not have the same doublet. In all these 7 cases, the first player must pass in the second round followed by (n - 2) players who all hold WB and using selective passing to communicate the doublets to player 1 and n. Because in the worst case three options are available for player 1, this requires up to 2 players passing. Combined with the passing of the first player in the second round, we get 2n + 3 turns.

77

General Discussion / Re: Maths thread.

« on: January 24, 2020, 04:01:34 am »

Trivial case: There is a least one of each of WW and BB. After the first round we know exactly the hidden cards and are done after the second round.

I'm not sure I understand; that's what the point of the second round is. The players with WW and BB can't see that both WW and BB are on the board, assuming there's only one of each, so the second round has to communicate that to them.

You are right, I forgot about one more special case. If there is exactly one of WW and BB and one of them occupies the last spot, then the simple solution will not work. If there is at least one player left in round 1 with WB, it works like this immediately after both the WW and the BB player have passed, it becomes common knowledge among all WB that the hidden cards are WB, so they can deduce their own cards. Hence, if the WW and BB player see any WB player not passing before the end of the first round the hidden cards are WB.

I'll check how this additional instance modifies the special case treatment.

78

General Discussion / Re: Maths thread.

« on: January 23, 2020, 10:43:54 am »

I think you can do even better. Splitting it in two cases

Trivial case: There is a least one of each of WW and BB. After the first round we know exactly the hidden cards and are done after the second round.

Special case: There is either exactly one player with WW or BB or all players have WB. Naturally the corresponding hidden cards are BB, WW, and WB, respectively. After the first round, these 3 cases are not distinguishable by the player who has the special configuration (or by any player in the case of all players WB). However, after one more action is taken, the three configurations separate and everybody knows their cards. Hence the worst case scenario is 2n + 1.

79

Non-Mafia Game Threads / Re: Decrypto

« on: January 22, 2020, 10:53:49 am »

faust's guess and your interception are correct

Summary

team Watno + scolapasta
1 Interception tokens
1 Miscommunication tokens
Round 1 Fall - Line - Jam (code: 3-4-1, guess: 3-4-1, interception: N/A)
Round 2 Prize - Ocean - Fire (code: 4-3-1, guess: 4-3-1, interception: 2-3-4)
Round 3 Smithy - Blood - Rock (code: 4-2-3, guess: 1-2-3, interception: 2-3-4)
Round 4 SCALE - MIRROR - CHILD (code: 3-2-4, guess: 3-2-4, interception: 3-1-2)
Round 5 Kill - Small - Climb (code: 1-2-3, guess: 1-2-3, interception: 1-2-3)
Round 6 DaVinci - Vision - Financial (code: ?, guess: ?, interception: 1-2-3)

Clue for 1 Jam, Fire, Kill
Clue for 2 Blood, MIRROR, Small
Clue for 3 Fall, Ocean, Rock, SCALE, Climb
Clue for 4 Line, Prize, Smithy, CHILD

team faust + ghost
1 Interception tokens
1 Miscommunication tokens
Round 1 Grow - India - Thumb (code: 4-2-1, guess: 4-2-1, interception: N/A)
Round 2 Oranges - Blueberries - Cucumbers (code: 2-1-4, guess: 2-3-1, interception: 4-3-1)
Round 3 Tank - Explode - Gas (code: 2-3-4, guess: 2-3-4, interception: 1-4-3)
Round 4 America - Hunt - Court (code: 3-2-1, guess: 3-2-1, interception: 1-3-4)
Round 5 Paris - Game - Pattern (code: 4-1-2, guess: 4-1-2, interception: 1-2-3)
Round 6 Building - Monarch - Water (code: 4-1-3, guess: 4-1-3, interception: 4-1-3)
Clue for 1 Thumb, Blueberries, Court, Game, Monarch
Clue for 2 India, Oranges, Tank, Hunt, Pattern
Clue for 3 Explode, America, Water
Clue for 4 Grow, Cucumbers, Gas, Paris, Building

80

Non-Mafia Game Threads / Re: Decrypto

« on: January 20, 2020, 07:32:27 am »

My clue for round 6:

Building - Monarch - Water

81

Non-Mafia Game Threads / Re: Decrypto

« on: January 20, 2020, 03:03:38 am »

I let faust check this, otherwise it is game over anyway.

Summary

team Watno + scolapasta
0 Interception tokens
1 Miscommunication tokens
Round 1 Fall - Line - Jam (code: 3-4-1, guess: 3-4-1, interception: N/A)
Round 2 Prize - Ocean - Fire (code: 4-3-1, guess: 4-3-1, interception: 2-3-4)
Round 3 Smithy - Blood - Rock (code: 4-2-3, guess: 1-2-3, interception: 2-3-4)
Round 4 SCALE - MIRROR - CHILD (code: 3-2-4, guess: 3-2-4, interception: 3-1-2)
Round 4 Kill - Small - Climb (code: 1-2-3, guess: 1-2-3, interception: 1-2-3)
Clue for 1 Jam, Fire, Kill
Clue for 2 Blood, MIRROR, Small
Clue for 3 Fall, Ocean, Rock, SCALE, Climb
Clue for 4 Line, Prize, Smithy, CHILD

team faust + ghost
1 Interception tokens
1 Miscommunication tokens
Round 1 Grow - India - Thumb (code: 4-2-1, guess: 4-2-1, interception: N/A)
Round 2 Oranges - Blueberries - Cucumbers (code: 2-1-4, guess: 2-3-1, interception: 4-3-1)
Round 3 Tank - Explode - Gas (code: 2-3-4, guess: 2-3-4, interception: 1-4-3)
Round 4 America - Hunt - Court (code: 3-2-1, guess: 3-2-1, interception: 1-3-4)
Round 5 Paris - Game - Pattern (code: 4-1-2, guess: 4-1-2, interception: 1-2-3)
Clue for 1 Thumb, Blueberries, Court, Game
Clue for 2 India, Oranges, Tank, Hunt, Pattern
Clue for 3 Explode, America
Clue for 4 Grow, Cucumbers, Gas, Paris

82

Non-Mafia Game Threads / Re: Decrypto

« on: January 19, 2020, 12:56:48 pm »

I saw neither Watno's clue nor Faust 's comment

83

Non-Mafia Game Threads / Re: Decrypto

« on: January 18, 2020, 04:53:17 pm »

faust guessed correctly 3-2-1

Summary

team Watno + scolapasta
0 Interception tokens
1 Miscommunication tokens
Round 1 Fall - Line - Jam (code: 3-4-1, guess: 3-4-1, interception: N/A)
Round 2 Prize - Ocean - Fire (code: 4-3-1, guess: 4-3-1, interception: 2-3-4)
Round 3 Smithy - Blood - Rock (code: 4-2-3, guess: 1-2-3, interception: 2-3-4)
Round 4 SCALE - MIRROR - CHILD (code: 3-2-4, guess: 3-2-4, interception: 3-1-2)
Clue for 1 Jam, Fire
Clue for 2 Blood, MIRROR
Clue for 3 Fall, Ocean, Rock, SCALE
Clue for 4 Line, Prize, Smithy, CHILD

team faust + ghost
0 Interception tokens
1 Miscommunication tokens
Round 1 Grow - India - Thumb (code: 4-2-1, guess: 4-2-1, interception: N/A)
Round 2 Oranges - Blueberries - Cucumbers (code: 2-1-4, guess: 2-3-1, interception: 4-3-1)
Round 3 Tank - Explode - Gas (code: 2-3-4, guess: 2-3-4, interception: 1-4-3)
Round 4 America - Hunt - Court (code: 3-2-1, guess: 3-2-1, interception: 1-3-4)
Clue for 1 Thumb, Blueberries, Court
Clue for 2 India, Oranges, Tank, Hunt
Clue for 3 Explode, America
Clue for 4 Grow, Cucumbers, Gas

back to Watno and faust

84

Non-Mafia Game Threads / Re: Decrypto

« on: January 17, 2020, 02:03:10 pm »

Out of curiosity, where is everyone located (at least time zone wise). I'm in USA, East coast.
(though next week I'm traveling for work in Norway.

Austria

85

Non-Mafia Game Threads / Re: Decrypto

« on: January 17, 2020, 11:01:35 am »

Our guess for your clue is 3-1-2

86

Non-Mafia Game Threads / Re: Decrypto

« on: January 15, 2020, 12:58:39 pm »

Next clue
America - Hunt - Court

87

Non-Mafia Game Threads / Re: Decrypto

« on: January 13, 2020, 03:13:12 am »

I tried to be too clever for my own good  . Sorry, faust.

Summary

team Watno + scolapasta
0 Interception tokens
0 Miscommunication tokens
Round 1 Fall - Line - Jam (code: 3-4-1, guess: 3-4-1, interception: N/A)
Round 2 Prize - Ocean - Fire (code 4-3-1, guess: 4-3-1, interception: 2-3-4)
Clue for 1 Jam, Fire
Clue for 3 Fall, Ocean
Clue for 4 Line, Prize

team faust + ghost
0 Interception tokens
1 Miscommunication tokens
Round 1 Grow - India - Thumb (code: 4-2-1, guess: 4-2-1, interception: N/A)
Round 2 Oranges - Blueberries - Cucumbers (code 2-1-4, guess 2-3-1, interception: 4-3-1)
Clue for 1 Thumb, Blueberries
Clue for 2 India, Oranges
Clue for 4 Grow, Cucumbers

faust and Watno, your turn to give clues again

88

Non-Mafia Game Threads / Re: Decrypto

« on: January 10, 2020, 02:32:11 pm »

Actually, one more question about what I do.

I'll go to that decrypto site, ignore the words (since we already have ours), and just click generate new code. Then using that code, I'll come up with a clue (x-y-z) and post that here.

Correct?

Correct. Just keep in mind that you cannot get 3-4-1 (in this order) again, so if that happens just generate another code.

Also, I think it is my turn, too, so I have a code for faust.

Oranges - Blueberries - Cucumbers

89

Non-Mafia Game Threads / Re: Decrypto

« on: January 10, 2020, 08:01:16 am »

According to the rules all clues must be based on public information, so I agree that one should only use the QT to discuss the other team's clues and to submit the guess. There are just 24 different codes, so even very little extra information can make it easy to beat the system.

Summary

team Watno + scolapasta
0 Interception tokens
0 Miscommunication tokens
Round 1 Fall - Line - Jam (code: 3-4-1, guess: 3-4-1, interception: N/A)
Clue for 1 Jam
Clue for 3 Fall
Clue for 4 Line

team faust + ghost
0 Interception tokens
0 Miscommunication tokens
Round 1 Grow - India - Thumb (code: 4-2-1, guess: 4-2-1, interception: N/A)
Clue for 1 Thumb
Clue for 2 India
Clue for 4 Grow

90

Non-Mafia Game Threads / Re: Decrypto

« on: January 09, 2020, 04:26:37 pm »

Watno gives a second set of clues. You (and your team) guess X-Y-Z. If wrong, I then guess A-B-C. Am I not supposed to know what X-Y-Z was before I guess A-B-C? (and in parallel we are also guessing D-E-F off your teams clue)

In RL, we would write our guess on a sheet of paper and so would you. So neither we would be allowed to see A-B-C nor you would be allowed to see X-Y-Z before the correct answer is revealed.
To play the game by forum, we can make slight adjustments to make the game faster. Because you have more information than us (you know the codewords), us seeing A-B-C has a major impact on the game (hence posting it in the QT). In contrast, you seeing X-Y-Z does not have the same urgency, because if you have to rely on our guesses to figure out what Watno meant, you are probably in trouble anyway. Still you should try to make your guess without seeing our attempted encryption, hence the spoiler tags.

91

Non-Mafia Game Threads / Re: Decrypto

« on: January 09, 2020, 03:30:52 pm »

In the first round it doesn't really matter, because we will not guess anyway. In the future, it might happen that you post before us. If we accidentally read uncover the spoiler tags or you forget to use them, it can ruin the game.

The discussion with your teammate still happens in 4 player games, because you can discuss the clues of the other team.

Btw. search engines allowed or not?

92

Non-Mafia Game Threads / Re: Decrypto

« on: January 09, 2020, 03:11:53 pm »

I created the codewords and the quicktopic for faust and me. I let him confirm that he can access it and then start with our first clues.

Anyone know how to move the thread?

In the very bottom of the page, above quickreply.

93

Non-Mafia Game Threads / Re: Decrypto

« on: January 09, 2020, 06:55:58 am »

I would suggest the following modification

1) Cluegivers generate a code using the same site, make clues and post them to the game thread.
2) Guessers guess their own teams code. Starting round 2, teams simultaneously discuss about the opponent's clue and try to guess their code.
3a) If you guess the clue of your own team, you post it in the team quicktopic.
3b) If you guess the clue of the opposing team, you post it in spoilers in the game thread.
4) Once all guesses are ready, the cluegivers state their partner's guess, reveal the correct codes and tokens are assigned.
5) Start new round with switched cluegivers.

This avoids accidentally spoiling the code of the team with the keywords. You can still accidentally spoil the guess of the team without the keywords, but that is less critical.

Do we need time limits or do we just play as fast as we can?

94

Non-Mafia Game Threads / Re: Decrypto - 1 more player needed

« on: January 07, 2020, 06:42:14 am »

/in

How do we adjust the rules for playing it online?

95

Puzzles and Challenges / Re: Asymptotic analysis of kingdoms puzzle

« on: April 19, 2019, 09:52:11 am »

Treasures solution(?) 1.17^T

Cards used:
* Will-o-Wisp (WoW) - source of card draw
* Idol (Id) - source of WoW via Boons
* Contraband (CB) - source of Buys
* Crown (Cr) - double Id, CB and WoW
* Bank - source of Coin
* Loan - trash Silver from Boon
* Royal Seal - put the Silver on top of the deck, so Loan finds them
* Copper - source of discard for Boon
* Quarry - reduce cost of Crown
* Talisman - enhance the number of gains
* Castles - for cash-out
The limiting factors are WoW, Id, CB. Because the coins grow quadratically in the number of Banks, Banks are not limiting. All other cards used in the build-up phase can be gained via Talisman so that again only a square-root of buys needs to be spend on those cards and Talisman.

Action phase: Play Cr + WoW, draw Cr, Id, Loan, or CB and WoW or Copper. The net draw is the same as the number of WoW + a sufficient amount of copper.
Buy phase: Consider the Boons first: 9 of them can be played more than once; 3 of them are helpful (+1 card, +2 card/discard 2, gain WoW), 1 is harmful (+1 silver), 5 do nothing. So for every 9 boons I get 3 cards, 1 WoW, and need to trash 1 silver. I play Cr for every odd Id (gaining boons) and only Id for every even one (distributing curse).
For a set of 9 Cr, 18 Id, 2 Loan, I play 18 boons gaining 2 WoW, drawing 6 cards, and gaining/trashing 2 Silver. The 6 cards are of course more of these sets; the geometric series converges to sum_n (6/(9+18+2))^n = 29/23.

Assuming, I use my WoW to draw A of these sets and B CB. I use the buys for a ratio R of Id and (1 - R) CB. Because I can use Cr on the CB, I need to buy only half of the buys. I require then that all three limiting cards grow at the same rate
1 = 29 A + B
1 + 29/23 * 2A = [29/23 * 18 A + R B] / [29/23 * 18 A] = [B + 2(1-R) B] / B
Solving this leads to
A = 0.0323, B = 0.0624, R = 0.959
and a growth rate of 1 + 29/23 * 2A = 1.082. By using castles, I can increase the growth rate to the square of this.

96

Puzzles and Challenges / Re: Asymptotic analysis of kingdoms puzzle

« on: April 12, 2019, 08:40:37 am »

I figured the Debt cards out. The key is to gain estates while you are building up the Engineer and City Quarters.

In build-up phase: Gain X En, X CQ, and X^2 Es. Then cash-out by gaining Estate + Triumph for several turns. For X = R T the total victory points are
VP = (R T)^2 + 2 * (1 - 2 R)T * R T = (2R - 3R^2) T^2
This is optimal for R = 1/3 leading to VP = 1/3 T^2.

97

Puzzles and Challenges / Re: Asymptotic analysis of kingdoms puzzle

« on: April 11, 2019, 03:06:03 am »

And here is my solution for the Artisan, ... puzzle

Card draw and actions are not an issue, because of Champion and Counting House/Cellar. If I have N Copper, I just need log_N(deck size) CH/C to draw my entire deck.

Strategy:
-buy Artisan every other turn ~T^2
-gain Vampire for every Artisan ~T^3 (gain a few Ill gotten gains with vampire to provide trashing fodder for the Bats)
-gain Cobbler for every Vampire ~T^4
-gain Page/Gardens with the Cobbler ~T^5
-exchange Page to Heros ~T^5
-gain Bank with every Hero ~T^6
-coin grows quadratic in the number of banks ~T^12
-buy Masterpiece - gain silver with overpay ~T^13
total points #garden * #silver ~T^18

98

Puzzles and Challenges / Re: Asymptotic analysis of kingdoms puzzle

« on: April 11, 2019, 02:20:03 am »

In the meantime, I worked also on the 6+ cards. I found that using Hunting Grounds and Expand, you can improve on my previous solution, because you can gain more cards that you can play on your current turn. The general idea is to Expand Hunting Grounds into more King's Courts and Expands gaining the Duchies in the process required to Expand into more Hunting Grounds
A * KC Ex(3HG) Ex(3D) -> 3KC, 3HG, 3D
B * KC Ex(3HG) Ex(3D) -> 3Ex, 3HG, 3D
C * KC Ex(3HG) Ex(3D) -> 6HG, 3D
D * KC HG HG -> draw 24
In every loop you will play a few less of each card (X KC, Y Ex, Z HG) leading to
24 D = 9 (A + B + C)
3 A = A + B + C + D - X
3 B = 2 (A + B + C) - Y
3 C = 2 D - Z
The optimal solution to this is for A = 88, B = 128, C = 48, D = 99, X = 99, Y = 144, Z = 54. Per loop this leads to gain of 3A / (3A + X) = 8/11 of the cards I already have. The geometric series converges to 11/3.

In the cashing out phase I add Goons to square the number of points ~13.444^T. There maybe a chance to optimize this further, because you have some excess draw from the previous turn (the number of HG is optimized to draw the action cards and the Duchies, but the Duchies don't remain in the deck). However, I didn't find a way to put this in an equation.

99

Puzzles and Challenges / Re: Asymptotic analysis of kingdoms puzzle

« on: April 10, 2019, 03:29:34 am »

I verified your solution and checked whether adding Weddings would bring a benefit
Normal turn: A * TF + Ex, B * TF + Qu, C * TF + Cu
Mission turn: X * TF + Ex, Y * TF + Qu, Z * TF + We
A ratio R of my total cards are Gold the rest are Curses

I find the optimal values A = 0.526, B = 0.044, C = 0.009, X = 0.551, Y = 0.048, Z = 0.002, R = 0.912. This leads to a growth rate of (1 + C/(1-R))^T = 1.103^T. Including the cubic cashing-out, we get 1.341^T.

Here are the equations

Code: [Select]

5 A + 2 B + 2 C = 3 R
2 B = (1 - R)
2 A = 1 + B + C
5 X + 2 Y + 9 Z = 3 (R + B)
2 Y = (1 - R) + C
2 X = 1 + B + C + Y + Z
(1 - R) * (B + Y + Z) = R * C

100

Non-Mafia Game Threads / Re: Self-referential quiz

« on: April 09, 2019, 10:46:22 am »

If you suppose there's 0 correct answers, then that answer isn't correct, because you don't answer 2: so the answer (5, 5, 10, 1111, 0, 0) seems to be the best we can take, since if N's more than 0 then your reasoning suggets there's more than N correct answers. Am I right? Just doing it intuitively.

Yeah, you need to modify the answers a bit once N < 5, because the median is not formed by N and 5 anymore. But the tuple (5, 6, 11, *, 1, 0) would also work. In general, because the answer to question 4 is directly related to itself if there is at least one 0 in any of the other questions, you can vary that number to produce infinitely many answers.

I think you would still get a paradox, if you modified 4 to ask only about the range of the other questions, but I'm not sure.