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126

General Discussion / Re: Maths thread.

« on: May 02, 2017, 01:06:24 pm »

I get the solution except for the line between t=1/k and t=1/(k+1) being at least 1/k + 1/(k+1) long. Isn't it just/also at least 2 long, since it's sqrt(2² + [1/k - 1/(k+1)] > sqrt(2²) = 2?

No, because the function is t*cos(pi/t), not just cos(pi/t).

More detail: Consider just t=1 and t=1/2. (1,-1) and (1/2,1/2) are two points on the graph. Draw a right triangle between the two points. Clearly the length of the hypotenuse is a lower bound for the  arc length between those two points. The length of a leg of the triangle is also a lower bound. The height of the triangle is 1/2+1. Now consider t=1/2 and t=1/3 giving (1/2,1/2) and (1/3,-1/3). Draw the triangle between the two points. The height of the triangle is 1/2+1/3. Etc. The sum of the heights of all such triangles is a lower bound on the arc length. That sum is at least as large as the harmonic series which diverges.

Edited wording.

127

Dominion League / Re: We need your kingdoms again :)

« on: April 23, 2017, 03:47:51 pm »

How do we find old games? Do we just have to note the number after playing?

128

Dominion General Discussion / Re: Is There an Eventful New Scout in Our Midst?

« on: April 20, 2017, 12:31:30 pm »

Trade and Delve are strange picks for this list, considering you did not add all events.

I didn't want to type all the events out; ten seemed like a nice number, and I saw Trade low on Qvist's list of $5s and a lot of negative talk around Delve in some threads.

Edit: words.

129

Dominion General Discussion / Is There an Eventful New Scout in Our Midst?

« on: April 20, 2017, 10:50:42 am »

I bought Windfall for the first time ever in a game yesterday and it got me thinking that there are some Events that I almost never use. Or want to use. Or really ever think is the best use of a buy. What is the worst Event? Maybe the winner of the poll should be declared The Event Most Likely To Replace Scout As The Butt of Every Joke Because It's Almost Completely Useless?

Here are my candidates:

Windfall -- Very rarely do I draw my deck, want Golds as a payload, and not have a better way of gaining them.

Tax -- Maybe I just don't get it, but it seems like it's only really worth buying when you are playing an engine against a big money-ish player. But how often does that happen anymore?

Raid -- I've bought this in maybe two games. And it just feels like I'm cursing myself.

I haven't played enough games to have a solid feel for Annex, Banquet, or Conquest, but they also strike me as potentially very situational, at best.

What do you think?

130

Dominion General Discussion / Re: Math is hard - questions about chance

« on: March 29, 2017, 06:23:41 pm »

I now get ~1.408 as the answer for the second question.

This is not correct. I confirm Mic's calcs.

Across 8 games you get an average of ~11.593 total landscapes (compared to 11.328 for the easy approximation).

I iterated the formula above to confirm this. Straightforward program, but not a straightforward resulting formula to do by hand.

reproduces your result for ~2.84 as the average total over 2 games.

I confirm this, too.

More details:

Code: [Select]

Prob of 0 wide cards is 4.462e-08
Prob of 1 wide cards is 7.852e-07
Prob of 2 wide cards is 8.423e-06
Prob of 3 wide cards is .00006193
Prob of 4 wide cards is .00034865
Prob of 5 wide cards is .00154516
Prob of 6 wide cards is .00556432
Prob of 7 wide cards is .01641124
Prob of 8 wide cards is .04006905
Prob of 9 wide cards is .08080099
Prob of 10 wide cards is .1345347
Prob of 11 wide cards is .18262003
Prob of 12 wide cards is .19971533
Prob of 13 wide cards is .17028032
Prob of 14 wide cards is .10912924
Prob of 15 wide cards is .04719838
Prob of 16 wide cards is .01171141

Expected Number of wide cards is 11.592913


131

Dominion General Discussion / Re: Math is hard - questions about chance

« on: March 28, 2017, 07:46:31 pm »

Just a question to your remark about the cap making it easier: Without the cap, wouldn't it just be w/t*10?

I don't think so, no. 55/330*10=1.67 would be with replacement (you can draw the same card twice) and drawing exactly 10 cards (not 10 necessarily tall cards).

Also, sorry for the confusion, I was using t for the number of cards not including events and landmarks (not the total number of cards including events and landmarks). Mic has corrected me on the number above.

132

Dominion General Discussion / Re: Math is hard - questions about chance

« on: March 28, 2017, 06:44:15 pm »

Maybe you already know this, but Polk's t is just the number of kingdom cards, not the total, so if you're interested in the 275 kingdom, 55 landscape case, t needs to be 275. This will give an average number of landscapes of ~1.416. I did sim this as well and got ~1.416.

Lol. That's  correct. I guess I am already anticipating the next expansion! ... or I just don't know how many cards there are anymore!

133

Dominion General Discussion / Re: Math is hard - questions about chance

« on: March 28, 2017, 05:57:46 pm »

Next question:

Say that the number from the first question is x. Say that we select a number of kingdoms, let's say 8 kingdoms, and no cards (including E/L) are allowed to be repeated across kingdoms. On average, how many L/E would show up in total? I think the answer is just x times 8, but I'm not sure.

I think we need more information here. What exactly happens to events/landmarks you pass over if you hit the cap of 2 in a kingdom? Discarded or mixed back in for drawing of the second kingdom?

134

Dominion General Discussion / Re: Math is hard - questions about chance

« on: March 28, 2017, 05:42:17 pm »

First question:

The cap of 2 Events or Landmarks per kingdom actually makes this easier. Consider drawing 10 cards then looking to see if you have 0, 1, 2, etc. events/landmarks. If you've drawn 0, you are done. If you have exactly one event/landmark, draw one more card. If it's an event/landmark, you max out at 2; if it's not, you've filled the kingdom and have 1. If you have drawn 2 or more, you max out at 2 and discard all events/landmarks until you fill out the 10 cards for the kingdom.

Let t = number of kingdom cards (not including events and landmarks) and let w = number of events and landmarks. (I am thinking "tall"/portrait orientation cards and "wide"/landscape orientation cards)

The expected number of events or landmarks in a 10 card kingdom is equal to ....
        0 TIMES Probability of drawing 10 tall cards
PLUS 1 TIMES Probability of drawing 9 tall cards and 1 wide card, then 1 more tall card
PLUS 2 TIMES Probability of drawing 9 tall cards and 1 wide card, then 1 more wide card
PLUS 2 TIMES Probability of drawing at most 8 tall cards

In math, that becomes:
       0 * C(t,10)*C(w,0)/C(t+w,10)
    + 1 * C(t,9)*C(w,1)/C(t+w,10) * (t-9)/(t+w-10)
    + 2 * C(t,9)*C(w,1)/C(t+w,10) * (w-1)/(t+w-10)
    + 2 * (1 - C(t,10)*C(w,0)/C(t+w,10) - C(t,9)*C(w,1)/C(t+w,10))

Simplifying, the expected number of event or landmarks is
       2 - 2 * C(t,10)/C(t+w,10) - C(t,9)*w/C(t+w,10) * (t-9)/(t+w-10)

For t = 330 275 and w = 55 we get approximately 1.273 1.416.

C(n,k) is "n choose k".

--

Note: When sampling n cards without replacement from a deck with two types (of size t and w), the probability of drawing exactly k of the first type is C(t,k)*C(w,n-k)/C(t+w,n).

Edit: Correct number of kingdom cards not including landmarks and events is evidently 275. Also, the probability on the last line, probability of at most 8 tall cards, is just 1 minus probability of exactly 10 tall cards minus the probability of exactly 9 tall cards, as Mic mentions below. That shortcut is what the formula above reflects.
Edit 2: Simplified formula.

135

Dominion General Discussion / Re: Rules mess ups you've seen?

« on: March 06, 2017, 02:40:16 pm »

Playing treasures then playing Watchtower to draw. This happened in a real life tournament. There was no Black Market or Villa. Do not even try to justify this, dude.

136

Dominion Online at Shuffle iT / Re: How do we like the new version of Dominions n online?

« on: March 02, 2017, 10:15:27 am »

I actually wonder why Gladiator is the only case where you can pretend to think. With stuff like Fool's Gold, it's still revealing the contents of your hand.

Related: http://forum.shuffleit.nl/index.php?topic=442

Stef responds:

The value of having "done pretending" on gladiator is a bit higher then having it on moat, because with gladiator the person playing it actually has a choice, and could "peek" for multiple cards or key cards to determine turn bootstrapping (like peeking for the only village on the board)

137

General Discussion / Re: Other forums

« on: February 28, 2017, 10:38:48 am »

Oh, you meant not-Dominion forums? Then, no.

138

General Discussion / Re: Other forums

« on: February 28, 2017, 10:38:04 am »

http://forum.shuffleit.nl/

139

Variants and Fan Cards / Re: Dominion: Antiquity (WIP! Please help!)

« on: February 27, 2017, 10:08:55 am »

When we are talking about theme already, is "archeology" really that Dominion-y? I know many good themes are taken, but I can think of at least 2 major ones that are still available.

Don't leave us hanging! What are they?

140

Variants and Fan Cards / Re: Dominion: Antiquity (WIP! Please help!)

« on: February 24, 2017, 01:42:24 pm »

I also like Ancient Waterways, Artifact, and Archaeologist the best of the first set of 6. The other three I wouldn't really keep around -- Cursed Idol especially.

Re: Cursed Idol. Here's my thinking.

Cache is probably your closest comparison. That card gives you a one time penalty of two Coppers on gain. Then the card is just a Gold for the rest of the game. You can play it as many times as you like without slowdown (i.e. waiting for others to potentially reveal), which is a plus, or additional potential penalty. And Cache is still a very weak card. 

So, I'm not excited by Cursed Idol and wouldn't likely ever buy it, so that leaves the whole pile to you! Yay! That's a "yay for me!". Gold is a weak card. Often, taking a $5 kingdom card over Gold even when you have $6 is the right move. It has to be this way for the game to be varied and interesting. Kingdom cards have to compete with and beat out Gold. This calculus wouldn't change even if Cursed Idol was a straight up Gold priced at $5. Think about how events like Delve and Wedding change (or more usually, don't change!) the game.

So I would focus my energies on the wheat (Ancient Waterways, Artifact, and Archaeologist) and cut the chaff (Cursed Idol).

Edit: word.

141

Dominion Online at Shuffle iT / Re: How do we like the new version of Dominions n online?

« on: February 23, 2017, 10:29:37 am »

It's not about disagreeing, I'd say. Apparently, both MF and ShIT have (had) some issues running smoothly on various PCs. I never had a lot of issues with MF.

I guess I'm just unlucky or something.

I think that's about right. Almost all of the speed, networking, and reconnect problems of MF have been fixed for me. However, one of my friends has had a noticeably worse experience on SiT versus MF. That friend and I both were using Chrome on a Mac playing together and we couldn't figure out why things just weren't working for him. He didn't want to bother with the forum and asking for help. He's a busy guy and will try again in a month or two to see if they got the kinks worked out. No real loss to him.

Mobile devices are generally worse because of the lack of an app.

Additionally, the UIX is still arguably worse on SiT. That is currently my opinion, but it depends on who you ask.

142

Dominion General Discussion / Re: Semi-Interesting Dominion Moments Thread

« on: February 21, 2017, 12:31:56 pm »

-img-

Looks like a fun kingdom. My opening move would be to square up those piles.

143

General Discussion / Re: Random Stuff Part III

« on: February 20, 2017, 04:32:31 pm »

yeah, playing dominion online kills the game for casual offline purposes.

Play with three or more players per game and volunteer to go last every game.

144

Dominion Online at Shuffle iT / Re: Naming cards

« on: February 13, 2017, 11:36:02 am »

"fixed"

Functionality has been minimally implemented, I'll give them that.

145

Game Reports / Re: May I resign on turn 0?

« on: February 09, 2017, 10:14:45 am »

My opponent bought Mine. Fool's Gold is in the Kingdom.

When you said Mine, did you mean Mint?

The one and only time on this forum this is a legitimate question and not a joke.

146

Dominion General Discussion / Re: Interview with Donald X.

« on: January 31, 2017, 10:44:59 am »

Do you ever go to game nights hosted by friends or family for fun? Or do you almost exclusively play to playtest?

147

General Discussion / Re: Random Stuff Part III

« on: January 26, 2017, 03:20:15 pm »

I haven't had reason to view this thread in its entirety on one page, but it's just a matter of time.

I have. I was searching for f.ds high scores for 2048. I found it in one of the earlier Random Stuff threads (was it really that long ago?). I recently achieved a high score of 120,424. Not surprisingly, I had indeed fallen short of Stef's high score.

148

Dominion General Discussion / Re: Favorite Dominion Expansions - 2017 Edition

« on: January 25, 2017, 09:35:41 am »

1. Hinterlands
2. Intrigue (2nd ed)
3. Seaside

These three expansions are Dominion to me. When I play with friends (which is much less often than it used to be -- people are moving on) I now prefer to randomize among these three expansions (plus a few select cards from base Dominion). Intrigue 2nd edition removed what I disliked about Intrigue and made it even better.

4. Cornucopia
5. Guilds

Both of these small expansions have grown on me. Cornucopia because Tournament is no longer as much of an outlier when stacked against the new crazy from the recent few expansions. Guilds because I initially hated the idea of more tokens, but the cards are just so well implemented and so smooth to play. Coin tokens add enough to win me over. And Masterpiece is great! I love overpay.

6. Empires
7. Prosperity
8. Dark Ages
9. Dominion (2nd ed)

Pluses and minuses in each of these. The novelty of Colony/Platinum has worn off. I have grown to greatly dislike VP tokens and almost never play with them IRL. Dark Ages has some of my least favorite cards and I have cooled to the trashy theme. Dominion 2nd ed still doesnt have a ton of replay value alone. However, there are some great cards in each expansion.

10. Adventures

Gah. Just no. I greatly dislike the tokens, most of the events, and the Travellers. Only a handful of cards appeal to me. This expansion will likely never land on my shelf. I even avoided buying it on MF and would have avoided it on SiT if it wasn't packaged with Empires. 

11. Alchemy

If you've ever played this in person, you know how slow and generally not fun most of these cards are to play. Online it's better, but this is another expansion I have zero desire to own.

149

General Discussion / Re: Maths thread.

« on: January 16, 2017, 04:33:10 pm »

summing them up:

I reading into things and thinking you might need this: Remember, if you have two sets A and B, the number of elements in A or B = number of elements in A + number of elements in B - number of elements in A and B.

150

Dominion Online at Shuffle iT / Re: The Dominion online 2017 thread

« on: January 06, 2017, 07:50:06 pm »

I also was under the impression that Donald X played with Inheritance on some version of the new client, and yet it's not available when the client is released.  Did something in Empires break it, was that implementation completely separate from what you came up with later, or was it actually not implemented very well originally?

I am wondering that, too.

Well if it does anything for you, I'd played with Inheritance on Stef's program before I played with it on MF's.

Does Stef's Inheritance actually work properly with Reserves?

I don't remember, and am not checking, but note that he had the advantage of starting the project knowing about the existence of all of the trickiest Dominion cards.