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76

Feedback / Re: Recommended web hosting for forum.dominionstrategy.com

« on: April 25, 2012, 01:53:14 pm »

If it's a temporary thing, I've had good experiences with https://www.nearlyfreespeech.net/.  They only charge for what you use, so it's good for temporary things where you don't want to prepay for 6 months.

77

Goko Dominion Online / Where's the official app?

« on: April 25, 2012, 01:21:05 pm »

Okay, I know this has been talked about to death, but its been a while since I've seen any news whatsoever.

Donald X. posted in January saying that the Isotropic tournament would get to finish and urging people to hurry up with whatever unofficial things they were doing, which seemed to imply the game would be released imminently.

Previous discussions/news also talked about time frames like "early 2012" and "Q1 2012."

We're now entering mid-2012.  I've been patiently saving up my hard-earned cash (RGG, Mr. Lincoln says "Hello!").  When can I have my official game?

78

Dominion Isotropic / Re: Discussion on non-random game selection and TrueSkill ranking

« on: April 25, 2012, 12:56:06 pm »

Province games are shorter and simple strategies tend to be more competitive.  Big Money + X wins a lot of the time, and a level 0 who goes first and picks the correct X can give a top-ranked player a run for his money on a healthy percentage of boards.

Colony games have a lower percentage of boards where simple Big Money + X wins.  Further, Prosperity contains several cards that would make you favor at least Big Money + X + Y, if not a full-blown engine, so simpler strategies aren't as competitive.  Weaker players have fewer chances to cause an upset, so stronger players would have fewer rank-damaging losses.

That's my guess, at least.

More importantly, though, I think skill comparisons based on level are pretty meaningless among the top players.

79

Dominion General Discussion / Re: Throne Room

« on: April 24, 2012, 09:18:01 am »

It's also useful for situations where you want as many of a particular card as possible and its pile has drained.  You can't have another copy of the card, so it's the next best thing.

Also, cards with high cost have been mentioned, but Scrying Pool bears special mention.  You want a certain density of pools ASAP, which can be hard to get with the Potion cost.  Usually you get one per shuffle max.  Throne Room helps your action density and lacks the awkward Potion cost (even better if Ironworks is around).  Further, with Scrying Pool, you're probably working on action density with your other buys, so even if you don't draw it with a Pool, you probably have something else you'd like to double.

80

Dominion General Discussion / Re: Major Dominion slump

« on: April 23, 2012, 12:39:20 pm »

It's happened to me a couple of times.  It starts with a streak of bad luck, which gets followed up by poor play because the losses mess with my thinking.  Alternately, I tend to lose when I'm stressed or tired.

Also, for whatever reason, I've noticed several low-level players who play way beyond their indicated level, and I lost a game against chwhite who was listed as level 0 at the time.  He said it was probably because he hadn't played in a while.  I'll lump these into the "Bad luck" category as well.

To shake it, you need to refocus, whatever that means for you.  Step away for a few minutes.  You haven't really gotten worse; everyone loses games due to factors unrelated to skill.

81

Dominion Articles / Re: Noble Brigand

« on: April 16, 2012, 11:47:59 pm »

I just finished a Colony game where I was getting smoked by player 1 opening Noble Brigand / Silver and spamming Noble Brigand buys.  I should have lost, but my opponent made some major late-game mistakes.

It forced me to open 3/3 and generally screwed with my early game economy to the point where I was struggling to afford Gold for many turns.

The consensus so far in this thread has been that the card is best in the mid-late game and isn't so hot in Colony games because of Platinum.  Now I'm wondering whether spamming it early on is viable or if that game was just a fluke.

82

Dominion General Discussion / Re: Possession, a poll!

« on: April 16, 2012, 10:02:34 am »

It can be enjoyable when things are roughly equal. Oddly, the reasons I don't like this card are the same reasons I don't like Tournament: it's swingy, it tends to reward the person who is already winning, and it does very little to help end the game.

Your first $6p hand gets possessed, giving your opponent 2 Possessions to your 0.  My blood pressure just skyrocketed thinking about it.

83

Dominion General Discussion / Re: Homage to the Best Card

« on: April 16, 2012, 12:29:32 am »

84

Dominion General Discussion / Re: This card art is wrong!

« on: April 11, 2012, 11:16:31 am »

The one that always bugs me is Navigator.  It is indeed a picture of a Navigator, so maybe the gripe doesn't belong here, but the proportions of everything are all off, and it's one of the few cartoony cards.  The fact that it's depicting an Asian person with exaggerated proportions looks, well, wrong in a different sense of the word.

I think it's just that illustrator's style, but those cards really jump out.  Compare Pearl Diver to Salvager.  Both depict similar things, but Salvager fits in so much better with the rest of the cards.  Also, Shanty Town looks like a screen capture from The Simpsons when seen at a glance, but it doesn't seem quite as out of place, probably because the people aren't as prominent.

85

Dominion Articles / Re: Promo: Stash

« on: April 06, 2012, 11:25:39 pm »

A $4 price point would also cause interaction with Ironworks, Workshop, and Talisman.

It'd be far too easy to acquire 3 or more Stashes before the 2nd shuffle, which seems broken.  I imagine many games would become Stash races similar to what we see with Fool's Gold, but worse in some ways because it's a no-brainer decision to buy a Stash instead of a Silver.

86

Dominion General Discussion / Re: Early Deck Cycling Revisited

« on: April 06, 2012, 11:00:40 am »

Let's call this "blind cycling" since anything that draws cards (e.g. Smithy) will cycle the deck.

I think the risk of opening with Loan would depend a lot on the kingdom, but my hunch is that the odds of really screwing yourself are pretty low and mitigated by the fact that you're cycling with the Loan, so if you do discard your other opening buy, you'll find it faster.

I say that, but I can't tell you how many times Loan has failed to find a Copper in my early hands.

There's a pretty disgusting case worth noting here, where you draw Loan on turn 4 with an Estate and opening non-treasure in the draw pile.  Either you play Loan and make your other opening buy miss 2 shuffles (and your Loan miss one shuffle) or you treat the Loan as a dead card in your current hand and still miss 1 shuffle with your opening buy.

87

Dominion General Discussion / Re: Let's talk about - the most difficult card in Dominion

« on: March 30, 2012, 09:47:20 am »

Develop

88

Dominion Isotropic / Re: People to avoid on isotropic

« on: March 30, 2012, 09:43:22 am »

As luck is so clearly a big part of this game, you're going to look like an idiot if you're berating the other guy for his good luck.

If I say someone won because they got lucky in hitting the KC + mountebank.  Or they merely opened a 5/2 on a mountebank board, do I look like an idiot?

What if that is me talking about my own win?  Why is this not symmetric?

If you're talking about your own win, you're giving the other guy the benefit of the doubt.  You're saying that he played as well as you did, but lost due to circumstances beyond his control.  It's a gesture of respect.

If you're talking about your own loss, you're saying that the other guy's victory was due (at least in part) to chance.  You're knocking him down a peg by saying he shouldn't have won or shouldn't have won by such a margin.  If it's someone you've played a lot and there's a mutual understanding that you have similar skill levels, that might be an okay thing to say.  Saying it to a stranger is pretty rude, though.

That all said, I'll point out luck events during the game, mostly just to make conversation ("wow," "ouch," "nice hand," or rarely "I can't draw $6 to save my life").

89

Dominion Articles / Re: A theorem about drawing and density

« on: March 26, 2012, 12:47:08 pm »

Clearly Venture improves future hands if cycling improves future hands.  The question was whether Venture has any filtering effect or if it's purely a cycling effect.

I showed on the previous page that when you take into account shuffling, it does have a miniscule filtering effect, however that effect is not always good for your deck depending on what other treasures you have and what your target hand value is.

To sum up the conclusions:
  - Playing Venture adds $1 plus whatever it draws to your current hand, which is good.
  - Playing Venture draws some cards, increasing the rate at which you cycle, which is usually good.
  - Playing Venture has complicated filtering effects which you can safely ignore.  The only tangible impact it has on your draw pile is making it smaller.

90

Simulation / Re: Simulation Challenge: Make Scout useful

« on: March 25, 2012, 10:27:47 am »

I'm betting there are solutions involving Conspirator.  The question is what other support is needed.  Loan and/or Hamlet might work.  Just Scout / Conspirator probably loses bad to big money.  It seems like the simulators would have a hard time playing things correctly, though.

91

Dominion Articles / Re: Mandarin

« on: March 24, 2012, 10:34:35 am »

I think Mandarin works better as a mid-late game card than an early game accelerator.  It's a terminal Gold, give or take.  Not a bad card to play if you can spare the action/card.  The problem is its on-gain effect.

In the early game, if you see $6, you probably want a Gold.  If you see $5, your treasure quality is probably very poor (5 Coppers, 3 Coppers + 1 Silver, etc).  Top-decking those treasures makes you wait an extra turn to cycle, which is a big penalty in the first two shuffles.  Most of the time, it's probably not worth it.

In the mid-late game, the on-gain effect can work to your advantage, because (a) you probably don't care about buying another Gold with $6 and (b) you're much more likely to see $5, $6, or $7 (or higher in Colony games) with high-quality treasure.  Play 2 Golds, buying a Mandarin and top-decking 2 Golds, hoping to line them up with Province- or Colony-buying treasure next turn.  The down-side here is that you're missing out on a Duchy, so it's a bit situational.  Like Courtyard and Haven, its effect is also quite good at smoothing out hands in the late game (though not as good as Courtyard and Haven).

I still haven't quite figured out the card, but my sense is that it's usually a trap in the early game and situationally nice in the mid-late game.

If you have sources of extra +buy available, I imagine the on-gain could be quite nice with Vineyards as well.  Buy Mandarin + Vineyards, top-decking your Potion for Vineyards next turn.

92

Dominion General Discussion / Re: Is resigning considered rude?

« on: March 22, 2012, 11:15:47 am »

I'm starting to wish people would resign more often.  I've had a couple of games recently where I had won mathematically, but either I was too green or my opponent was too slow so I had to make both of us miserable by playing it out for another dozen turns.  I'd feel like a jerk asking someone to resign, but I wish it were possible to show that someone was not catchable on boards where this can be determined.

On the flip side, I will automatically resign if I notice that I'm in that position, unless I expect my opponent to win within about 30 more seconds of playing.

93

Dominion General Discussion / Re: Is resigning considered rude?

« on: March 15, 2012, 04:29:48 pm »

I'm fine with people resigning.  It's maybe a little annoying when it's a quick game, but whatever.

However, I think it's very rude when people resign in a way that forces me to wait around for 3 minutes to click the "make soandso resign" button.  Wait until your turn starts, click "end turn", click "resign", then click "resign" again.  People say just clicking "exit" works as well, though I've not tested it.  Definitely don't just close the tab.

94

Dominion Articles / Re: A theorem about drawing and density

« on: March 13, 2012, 11:09:27 am »

It was a long thread, but I think it's important to understand what cards really do.  For me, it doesn't impact when I'd play Venture.  I'd play it nearly 100% of the time.  It may impact when I'd choose to gain Venture, though.  It'd have a much bigger influence on when I'd choose to play or gain Farming Village.

95

Dominion General Discussion / Re: What is your favorite Dominion Downer?

« on: March 13, 2012, 01:58:25 am »

Having just experienced it... $2P on a Familiar board on turn 5

96

Dominion Articles / Re: A theorem about drawing and density

« on: March 12, 2012, 10:22:01 pm »

Ok, as promised...

I started simulating what happens at the reshuffle.  Since we're interested in testing the filtering effect of Venture, I only shuffled in cards that were in the original draw pile.  I didn't shuffle in Venture itself, whatever was in the Venture hand, or any buys or previous hands.  All of that stuff would be there in reality, but it seems irrelevant when looking for a filtering effect.

Let T be the number of treasures, and D be the number of non-treasure draws (dead cards).  The expected number of cards that Venture draws is (T + D + 1) / (T + 1).

I construct a deck with 3 treasures and 8 dead cards.  We expect Venture will draw 3 cards in this case.  Because of this, we'll compare it to a Smithy when running the numbers.

That math has been eating at me for a while.  Let's say all the treasures are Copper.  We expect that Venture's draw has a value of $1/3 per card, but the deck's average card value is $3/11.

On to the experiments:

First, we take a deck containing a Platinum, a Gold, a Copper, and 8 dead cards.  We look at the next two hands in if we draw them normally, if we play a Smithy this turn, and if we play a Venture this turn.

Code: [Select]

Deck: 1x Platinum, 1x Gold, 1x Copper, 8x dead

Percentage of hands by coin value (500000 trials):

          Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10
   Next hand, normal | 12.17% | 15.09% |  0.00% | 15.14% | 12.16% | 15.06% | 12.23% |  0.00% | 12.11% |  6.03% |  0.00%
 Second hand, normal | 12.14% | 15.11% |  0.00% | 15.23% | 12.09% | 15.11% | 12.14% |  0.00% | 12.11% |  6.07% |  0.00%
  Next hand, Venture | 12.07% | 15.25% |  0.00% | 15.09% | 13.79% | 15.12% | 13.76% |  0.00% | 13.74% |  1.18% |  0.00%
Second hand, Venture | 16.91% | 16.95% |  0.00% | 17.12% |  9.59% | 17.05% |  9.68% |  0.00% |  9.64% |  3.07% |  0.00%
   Next hand, Smithy | 12.16% | 15.17% |  0.00% | 15.21% | 12.07% | 15.13% | 12.15% |  0.00% | 12.09% |  6.02% |  0.00%
 Second hand, Smithy | 12.00% | 15.11% |  0.00% | 15.17% | 12.13% | 15.19% | 12.22% |  0.00% | 12.11% |  6.07% |  0.00%

The normal hands and Smithy hands all have comparable coin values.  The next Venture hands are significantly worse.  I strongly suspect that it's only the reshuffle hand that's worse on average.  Note that the hand after Venture is almost as good, and that hand is also the least likely to trigger a reshuffle.

In a normal game, though, having a crappy hand at the reshuffle is a good thing.  Let's try a different experiment.  This time, we'll construct two decks.  The first deck contains 6 Coppers, 14 dead cards, and 1 Silver.  The second is the same, but it contains a Venture instead of the Silver.  Note that the Venture will always be worth as much as the Silver.  We'll run through those decks a bunch of times and check the distribution of hand values drawn.

Code: [Select]

Deck 1: 14x dead, 6x Copper, 1x Silver
Deck 2: 14x dead, 6x Copper, 1x Venture

Percentage of hands by coin value (5000000 turns):

Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7
    Deck 1 |  9.84% | 29.51% | 31.74% | 19.68% |  7.75% |  1.41% |  0.07% |  0.00%
    Deck 2 |  9.87% | 29.35% | 31.49% | 19.82% |  7.93% |  1.46% |  0.08% |  0.00%

Those numbers are interesting.  With that many trials, I think the percentages indicate a legitimate difference that can be chalked up to Venture's filtering; however, it's imperceptibly small.  Venture gets ever so slightly better hands.

Let's try it again, this time with a 20-card deck so that nothing misses the shuffle in the Silver deck:

Code: [Select]

Deck 1: 6x Copper, 13x dead, 1x Silver
Deck 2: 6x Copper, 13x dead, 1x Venture

Percentage of hands by coin value (5000000 turns):

Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7
    Deck 1 |  8.28% | 27.69% | 32.29% | 21.13% |  8.79% |  1.72% |  0.10% |  0.00%
    Deck 2 |  8.37% | 27.55% | 31.91% | 21.16% |  9.10% |  1.81% |  0.10% |  0.00%

Similar results.  Venture gets ever-so-slightly better hands.

Finally, let's look at a more realistic deck, where Venture has an average value of $3 and replaces a Gold.

Code: [Select]

Deck: 3x Copper, 5x dead, 4x Gold, 3x Silver
Deck: 5x dead, 3x Copper, 3x Gold, 3x Silver, 1x Venture

Percentage of hands by coin value (5000000 turns):

Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15
    Deck 1 |  0.03% |  0.50% |  1.51% |  4.01% |  8.00% | 11.46% | 16.47% | 16.57% | 15.49% | 12.41% |  7.19% |  4.20% |  1.57% |  0.50% |  0.10% |  0.00%
    Deck 2 |  0.04% |  0.51% |  1.56% |  4.13% |  7.88% | 11.69% | 15.86% | 16.59% | 15.38% | 12.06% |  7.78% |  4.10% |  1.80% |  0.52% |  0.11% |  0.00%

That one is more complex.  Venture is beneficial depending on your target treasure value.

Before anyone says it, I've run these trials multiple times with a few different parameters, and the results are consistent with one another to the point that I'm convinced we're not looking at statistical noise.

Conclusion:

Because of the expected value formula, we expect Venture to draw cards that are worth more than the average value from the draw pile.  Simulations show this to be the case.  Venture is sending better-than-average cards to the discard, filtering in the wrong direction.  You don't notice the effect until you reach the end of the draw pile, though.  At the reshuffle, you tend to draw a slightly worse hand.

There's another side of this.  Venture, being a card that draws, is more likely to miss the reshuffle.  It's also a better than average treasure by definition. 

In Dominion, it's a good thing to have bad hands miss the reshuffle.  It's a bad thing to have better than average treasures miss the reshuffle.  These effects nearly cancel each other out if you always play Venture.  There is an slight difference in hand values that you'd never notice in practice.

I'd be really interested in someone explaining the math of what happens near the reshuffle point.  It's been way too long since I've done any statistics work.

97

Dominion Articles / Re: A theorem about drawing and density

« on: March 12, 2012, 05:35:02 pm »

I still haven't really understood the term "unchanged". "Unchanged" with respect to what? To not playing the Venture?

It seems that can not really be, because the Venture does not stop at a random card, but at a Treasure. So if you have an empty discard, a Venture in hand and a draw-deck of 99 Estates and a Gold, the probability that you will draw a Gold next turn without playing the Venture is 5%. When you play the Venture, the probability of drawing the Gold is a lot smaller, because if you don't reshuffle during drawing your next hand, it's exactly 0%. And even if you reshuffle, which has a probability of 5% (namely if your ventured Gold is on positions 96-100) it's smaller than 5% (namely if your Gold in the next reshuffle is on positions 1-5 [it's smaller because depending on which position the ventured Gold was, you have fewer spots).
So the probability of drawing the Gold next turn, given you play the Venture this turn is smaller than 0.05*0.05 = 0.25%

And that's not because I just have on treasure, you could do the same thing with 98 Estates, 2 Golds and the probability that you draw 2 Golds next turn:
Without Venture probability of drawing 2 Golds next turn is 5/100*4/99.
With Venture to draw 2 Golds, I need to trigger a reshuffle, that is both Golds have to be behind position 95, which has prob 5/100*4/99. Then after the Venture, I'm guaranteed to have the second Gold in hand, but I also need to redraw the first Gold again, which again has probability smaller than 5/100, which gives probability 5/100*5/100*4/99 to this event.

So the "thing" that didn't change (given you don't reshuffle) is the distribution of your cards minus a random Treasure.

And to rate if you want to play an unneeded Venture, these are the two important things: a) Which non-treasure cards are left in my draw, and do I want to play them? b) Which treasure cards are left in my draw deck, and do I want to play them?

Ok, that sounds like it's only thing, and maybe it is. Of course Treasures and non-Treasure act differently, because the less Treasures in my deck, the more other cards I skip (on average).

Edit: Or, what (an unneeded and uninformed) Venture does is to move you a random number of positions forward in your deck, at the cost of a random Treasure. Otherwise it does not change the distribution.

I ran some tests, and it turns out that Venture is actually quite bad for hands on the shuffle boundary in a greening deck.  I'll try to put together a write-up of the results later (no time now), but basically what DStu says here is correct.  Venture hurts your chances of seeing two treasures in the same hand.

I'm sure this will all be further complicated by the fact that bad hands on the shuffle boundary are a good thing in Dominion.

98

Dominion Articles / Re: A theorem about drawing and density

« on: March 12, 2012, 03:32:43 pm »

Here's the decks you asked for.  This time it's 500,000 trials because the big decks were taking a while, so it's slightly less accurate, though still good enough to get the idea.

Code: [Select]

Deck: 3x Platinum, 3x Gold, 3x Silver, 3x Copper, 10x dead

  Total hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15 |     16 |     17 |     18 |     19 |     20 |     21 |     22
    Next hand, no Venture |   4910 |  11976 |  18861 |  33175 |  35123 |  48489 |  53351 |  49353 |  58999 |  42756 |  43098 |  32980 |  21911 |  20212 |   9686 |   7867 |   3947 |   1557 |   1219 |    302 |    174 |     54 |      0
  Second hand, no Venture |   4685 |  11874 |  18897 |  33359 |  35226 |  48361 |  53826 |  49372 |  58633 |  43043 |  43187 |  33054 |  21746 |  19800 |   9550 |   7742 |   4162 |   1714 |   1247 |    308 |    162 |     52 |      0
       Next hand, Venture |   4757 |  12013 |  18746 |  33118 |  35163 |  48185 |  53475 |  49626 |  58436 |  42796 |  43446 |  33492 |  21825 |  20020 |   9707 |   7755 |   4021 |   1599 |   1288 |    291 |    177 |     64 |      0
     Second Hand, Venture |   4874 |  12164 |  18826 |  33891 |  35000 |  48310 |  53463 |  49301 |  58660 |  42887 |  43169 |  33022 |  21613 |  20201 |   9635 |   7576 |   3989 |   1661 |   1234 |    296 |    170 |     58 |      0

  Percentage of hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15 |     16 |     17 |     18 |     19 |     20 |     21 |     22
    Next hand, no Venture |  0.98% |  2.40% |  3.77% |  6.63% |  7.02% |  9.70% | 10.67% |  9.87% | 11.80% |  8.55% |  8.62% |  6.60% |  4.38% |  4.04% |  1.94% |  1.57% |  0.79% |  0.31% |  0.24% |  0.06% |  0.03% |  0.01% |  0.00%
  Second hand, no Venture |  0.94% |  2.37% |  3.78% |  6.67% |  7.05% |  9.67% | 10.77% |  9.87% | 11.73% |  8.61% |  8.64% |  6.61% |  4.35% |  3.96% |  1.91% |  1.55% |  0.83% |  0.34% |  0.25% |  0.06% |  0.03% |  0.01% |  0.00%
       Next hand, Venture |  0.95% |  2.40% |  3.75% |  6.62% |  7.03% |  9.64% | 10.70% |  9.93% | 11.69% |  8.56% |  8.69% |  6.70% |  4.37% |  4.00% |  1.94% |  1.55% |  0.80% |  0.32% |  0.26% |  0.06% |  0.04% |  0.01% |  0.00%
     Second Hand, Venture |  0.97% |  2.43% |  3.77% |  6.78% |  7.00% |  9.66% | 10.69% |  9.86% | 11.73% |  8.58% |  8.63% |  6.60% |  4.32% |  4.04% |  1.93% |  1.52% |  0.80% |  0.33% |  0.25% |  0.06% |  0.03% |  0.01% |  0.00%


Deck: 300x Platinum, 300x Gold, 300x Silver, 300x Copper, 1000x dead

  Total hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15 |     16 |     17 |     18 |     19 |     20 |     21 |     22 |     23 |     24 |     25 |     26
    Next hand, no Venture |   9547 |  14433 |  23064 |  34667 |  34385 |  49469 |  48603 |  47921 |  50568 |  38480 |  39471 |  31090 |  22561 |  20317 |  11385 |   9813 |   5845 |   3284 |   2716 |    909 |    852 |    373 |    115 |    108 |      0 |     24 |      0
  Second hand, no Venture |   9502 |  14636 |  23216 |  34279 |  34366 |  49279 |  48874 |  47579 |  50784 |  38572 |  39768 |  30530 |  22699 |  20116 |  11323 |  10024 |   5992 |   3312 |   2689 |   1018 |    856 |    334 |    127 |    103 |      0 |     22 |      0
       Next hand, Venture |   9558 |  14412 |  23231 |  34478 |  34525 |  49298 |  48560 |  47603 |  50959 |  38541 |  39699 |  30776 |  22642 |  20174 |  11285 |   9901 |   5988 |   3316 |   2694 |    912 |    824 |    380 |    111 |    112 |      0 |     21 |      0
     Second Hand, Venture |   9623 |  14626 |  23087 |  34725 |  34343 |  49423 |  48484 |  47678 |  50740 |  38078 |  39770 |  30644 |  22816 |  20093 |  11506 |   9971 |   5968 |   3292 |   2742 |    936 |    873 |    325 |    106 |    120 |      0 |     31 |      0

  Percentage of hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15 |     16 |     17 |     18 |     19 |     20 |     21 |     22 |     23 |     24 |     25 |     26
    Next hand, no Venture |  1.91% |  2.89% |  4.61% |  6.93% |  6.88% |  9.89% |  9.72% |  9.58% | 10.11% |  7.70% |  7.89% |  6.22% |  4.51% |  4.06% |  2.28% |  1.96% |  1.17% |  0.66% |  0.54% |  0.18% |  0.17% |  0.07% |  0.02% |  0.02% |  0.00% |  0.00% |  0.00%
  Second hand, no Venture |  1.90% |  2.93% |  4.64% |  6.86% |  6.87% |  9.86% |  9.77% |  9.52% | 10.16% |  7.71% |  7.95% |  6.11% |  4.54% |  4.02% |  2.26% |  2.00% |  1.20% |  0.66% |  0.54% |  0.20% |  0.17% |  0.07% |  0.03% |  0.02% |  0.00% |  0.00% |  0.00%
       Next hand, Venture |  1.91% |  2.88% |  4.65% |  6.90% |  6.91% |  9.86% |  9.71% |  9.52% | 10.19% |  7.71% |  7.94% |  6.16% |  4.53% |  4.03% |  2.26% |  1.98% |  1.20% |  0.66% |  0.54% |  0.18% |  0.16% |  0.08% |  0.02% |  0.02% |  0.00% |  0.00% |  0.00%
     Second Hand, Venture |  1.92% |  2.93% |  4.62% |  6.95% |  6.87% |  9.88% |  9.70% |  9.54% | 10.15% |  7.62% |  7.95% |  6.13% |  4.56% |  4.02% |  2.30% |  1.99% |  1.19% |  0.66% |  0.55% |  0.19% |  0.17% |  0.07% |  0.02% |  0.02% |  0.00% |  0.01% |  0.00%


Deck: 2x Platinum, 10x Copper

  Total hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14
    Next hand, no Venture |      0 |      0 |      0 |      0 |      0 | 158923 |      0 |      0 |      0 | 265084 |      0 |      0 |      0 |  75993 |      0
  Second hand, no Venture |      0 |      0 |      0 |      0 |      0 | 159042 |      0 |      0 |      0 | 265094 |      0 |      0 |      0 |  75864 |      0
       Next hand, Venture |      0 |      0 |      0 |      0 |      0 | 158997 |      0 |      0 |      0 | 265351 |      0 |      0 |      0 |  75652 |      0
     Second Hand, Venture |      0 |      0 |      0 |      0 |      0 | 158954 |      0 |      0 |      0 | 265035 |      0 |      0 |      0 |  76011 |      0

  Percentage of hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14
    Next hand, no Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 31.78% |  0.00% |  0.00% |  0.00% | 53.02% |  0.00% |  0.00% |  0.00% | 15.20% |  0.00%
  Second hand, no Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 31.81% |  0.00% |  0.00% |  0.00% | 53.02% |  0.00% |  0.00% |  0.00% | 15.17% |  0.00%
       Next hand, Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 31.80% |  0.00% |  0.00% |  0.00% | 53.07% |  0.00% |  0.00% |  0.00% | 15.13% |  0.00%
     Second Hand, Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 31.79% |  0.00% |  0.00% |  0.00% | 53.01% |  0.00% |  0.00% |  0.00% | 15.20% |  0.00%


Deck: 200x Platinum, 1000x Copper

  Total hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15 |     16 |     17 |     18 |     19 |     20 |     21 |     22 |     23 |     24 |     25 |     26
    Next hand, no Venture |      0 |      0 |      0 |      0 |      0 | 200453 |      0 |      0 |      0 | 201531 |      0 |      0 |      0 |  80374 |      0 |      0 |      0 |  16024 |      0 |      0 |      0 |   1555 |      0 |      0 |      0 |     63 |      0
  Second hand, no Venture |      0 |      0 |      0 |      0 |      0 | 200667 |      0 |      0 |      0 | 201323 |      0 |      0 |      0 |  80491 |      0 |      0 |      0 |  15867 |      0 |      0 |      0 |   1593 |      0 |      0 |      0 |     59 |      0
       Next hand, Venture |      0 |      0 |      0 |      0 |      0 | 200165 |      0 |      0 |      0 | 201823 |      0 |      0 |      0 |  80386 |      0 |      0 |      0 |  15991 |      0 |      0 |      0 |   1570 |      0 |      0 |      0 |     65 |      0
     Second Hand, Venture |      0 |      0 |      0 |      0 |      0 | 200995 |      0 |      0 |      0 | 201436 |      0 |      0 |      0 |  80013 |      0 |      0 |      0 |  15977 |      0 |      0 |      0 |   1507 |      0 |      0 |      0 |     72 |      0

  Percentage of hands by coin value:

               Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13 |     14 |     15 |     16 |     17 |     18 |     19 |     20 |     21 |     22 |     23 |     24 |     25 |     26
    Next hand, no Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 40.09% |  0.00% |  0.00% |  0.00% | 40.31% |  0.00% |  0.00% |  0.00% | 16.07% |  0.00% |  0.00% |  0.00% |  3.20% |  0.00% |  0.00% |  0.00% |  0.31% |  0.00% |  0.00% |  0.00% |  0.01% |  0.00%
  Second hand, no Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 40.13% |  0.00% |  0.00% |  0.00% | 40.26% |  0.00% |  0.00% |  0.00% | 16.10% |  0.00% |  0.00% |  0.00% |  3.17% |  0.00% |  0.00% |  0.00% |  0.32% |  0.00% |  0.00% |  0.00% |  0.01% |  0.00%
       Next hand, Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 40.03% |  0.00% |  0.00% |  0.00% | 40.36% |  0.00% |  0.00% |  0.00% | 16.08% |  0.00% |  0.00% |  0.00% |  3.20% |  0.00% |  0.00% |  0.00% |  0.31% |  0.00% |  0.00% |  0.00% |  0.01% |  0.00%
     Second Hand, Venture |  0.00% |  0.00% |  0.00% |  0.00% |  0.00% | 40.20% |  0.00% |  0.00% |  0.00% | 40.29% |  0.00% |  0.00% |  0.00% | 16.00% |  0.00% |  0.00% |  0.00% |  3.20% |  0.00% |  0.00% |  0.00% |  0.30% |  0.00% |  0.00% |  0.00% |  0.01% |  0.00%


99

Dominion Articles / Re: A theorem about drawing and density

« on: March 12, 2012, 02:18:25 pm »

I *do* want to be really awesome!

5 million trials.  Draw deck was what you posted, except with 6 coppers to guarantee no reshuffles.

Here's the histogram twice.  The first contains the total number of hands at each coin value.  The second contains the percentage of hands at each value.

Code: [Select]

             Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13
  Next hand, no Venture |   4861 |  72618 | 278339 | 558143 | 860531 | 974781 | 912324 | 683080 | 392355 | 186457 |  61022 |  14700 |    789 |      0
Second hand, no Venture |   4862 |  72079 | 278714 | 558022 | 860659 | 973645 | 914068 | 683957 | 392132 | 185692 |  60838 |  14512 |    820 |      0
     Next hand, Venture |   4833 |  72559 | 279492 | 556025 | 860684 | 975051 | 912807 | 683532 | 393007 | 185622 |  60953 |  14640 |    795 |      0
   Second Hand, Venture |   4682 |  72674 | 278416 | 558581 | 860605 | 974627 | 912308 | 683844 | 392206 | 185923 |  60838 |  14557 |    739 |      0

             Coin value |      0 |      1 |      2 |      3 |      4 |      5 |      6 |      7 |      8 |      9 |     10 |     11 |     12 |     13
  Next hand, no Venture |  0.10% |  1.45% |  5.57% | 11.16% | 17.21% | 19.50% | 18.25% | 13.66% |  7.85% |  3.73% |  1.22% |  0.29% |  0.02% |  0.00%
Second hand, no Venture |  0.10% |  1.44% |  5.57% | 11.16% | 17.21% | 19.47% | 18.28% | 13.68% |  7.84% |  3.71% |  1.22% |  0.29% |  0.02% |  0.00%
     Next hand, Venture |  0.10% |  1.45% |  5.59% | 11.12% | 17.21% | 19.50% | 18.26% | 13.67% |  7.86% |  3.71% |  1.22% |  0.29% |  0.02% |  0.00%
   Second Hand, Venture |  0.09% |  1.45% |  5.57% | 11.17% | 17.21% | 19.49% | 18.25% | 13.68% |  7.84% |  3.72% |  1.22% |  0.29% |  0.01% |  0.00%


100

Dominion Articles / Re: A theorem about drawing and density

« on: March 12, 2012, 01:03:59 pm »

:e @ecq: It looked at the variance, and while it may not change, it is nevertheless important. Because as WW said, if it is low, average coin value is a good measure, if it is high, it is not.

What's a better measure?  Number of $8 hands?  Could you give me a sample draw pile containing at least 6 treasure cards and a metric?