Dominion Strategy Forum

Please login or register.

Login with username, password and session length

Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

Messages - heron

Filter to certain boards:

Pages: [1] 2 3 ... 43
1
Tournament + Herald

Used Herald overpay to topdeck province and tournament. I bought an early province and got 3 prizes with it on my next shuffle.

Something tells me that would have taken multiple shuffles...

Well, not if you keep buying herald, and avoid drawing too many cards.

2
Puzzles and Challenges / Re: Easy Puzzles
« on: March 13, 2019, 08:40:06 pm »
Alternatively, Summon - Mission

3
Puzzles and Challenges / Re: Unbounded scoring in a single action
« on: March 10, 2019, 06:27:40 pm »
Does buying a temple or gaining an estate with wild hunt satisfy the requirements?

4
Fortune could basically be reworded to have a buy restriction if you want... "You can't gain or buy this unless 5 Gladiators have been gained this game". (Yes it's not the same in all cases, but it is in most cases). To me, having 5 cards sitting on top of the card is absolutely a buy restriction.

That's besides the point. If my opponent gains 5 Gladiators, I can buy Fortune for $8D8 without ever gaining any Gladiators.

This isn't the point you are making but also it's very false that you can't get fortune unless 5 gladiators have been gained. A lot of gladiators get trashed from the supply.

5
Instead of comparing Ducat to Candlestick Maker, we should really be comparing it to Market Square.

Isn't that like comparing Gold to Smithy? How does that work?

Well, if you buy it and trash a copper, ducat is like a nonterminal +buy that doesn't take up space in your deck for $3.
Market square is also like that.


6
Dominion League / Re: Season 32 - Signups
« on: January 27, 2019, 11:03:01 pm »
New league player:

Dominion: heron
Discord: @heron#0905
Time Zone: America/New_York

7
According to some stats markus (I think) compiled, black market is still one of the cards that most favors the more skilled player today.
Also, I'm pretty sure that there are no potion cards in the black market unless a potion card is already in the kingdom. Similarly, you don't find travellers and a few other cards (not quite sure which) in the black market.

8
Dominion General Discussion / Re: Are promos worth it?
« on: January 14, 2019, 05:22:18 pm »
I feel like using the randomizer deck and then just grabbing actual copies of whatever cards get bought is a pretty good compromise.

9
Jack / Cathedral
Nothing too special here but it's very fast. I got 6 provinces in 12 turns.

10
Dominion General Discussion / Re: My new Dominion YouTubing Series
« on: December 19, 2018, 10:18:25 pm »
I recently received a message from "Jake". He says he is a fellow dominion tuber and would like to skype/play me for one of my videos. However, I got it as a do not reply email. How would I go about responding?

Maybe look in your "messages" tab near the top of the forum website and you can reply there? If it was a message from this forum anyway. If it's from youtube I don't know.

11
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 12, 2018, 02:13:43 pm »
It seems like the same logic can be used to say that in any game with an auction mechanic, the mechanic doesn't work because the optimal thing is simply for the first player who bids to bid the exact correct amount that the thing is actually worth. If both players know exactly that paying $51 for the up-for-bid power plant reduces your chances of winning, while paying $50 for it increases your chances of winning, then the right move is simply to immediately bid $50. Bidding any less than that allows your opponent the chance to be the one to bid $50 himself.

Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.

Except, these mechanics DO work, because of 3 main factors:

1) Neither player knows exactly the correct amount. While there is some statistical calculation possible to determine the exact dollar amount where your chances go from increasing to decreasing if you win the auction, neither player is capable of actually making that calculation.

2) There is a risk/reward prospect at play. Purchasing the plant for more money may be riskier; but each player may have a different threshold for how much risk they are willing to take.

3) Humans are not robots; there is psychology at play here. The idea that you may want to bid a little bit higher, in hopes that your opponent bids even higher, just to cost him more money, comes into play. The slowly increasing cost of the power plant makes it harder to judge the exact point where it is way too expensive. Bidding on a plant is also egging your opponent on to bid higher.

All 3 of these reasons should apply just as well to Bottle Imp.

Thanks for bringing up an actually reasonable argument.
Here are some reasons I disagree (first overall, and then corresponding to each of your three points). It basically boils down to, for bottle imp the bidding goes the wrong way (the less you pay, the bigger your reward).

In auction games, I believe that bidding tends to go around in a circle increasing. Maybe player A can bid 5, then player B bids 7, then player C bids 8, then player A goes again and bids 9. Why didn't player A bid 9 to begin with? The answer is that the gamestate has changed. Since their first bid, player A has learned what the other two players think they should bid, and has updated their bid accordingly.

On the other hand, if for some reason player A already knew that for all players it was good to purchase the auction prize for 9 or less and bad to purchase it for 10 or more, then yes player A should immediately bid 9. Cursed bottle does not have this circular bidding mechanic (although even if it did, you would always want to fold or bid min amount).


1. In the case of cursed bottle, the correct amount is either the minimum amount or not to take cursed bottle. So in fact it is very possible to compute the exact amount.
2. This does not come into play with cursed bottle. Paying more for the bottle imp is both a higher cost and a lower reward. On the other hand, if you had to pay more than the previous time, it could work very nicely.
3. Again, this doesn't apply to cursed bottle because of how you have to underbid. Like, am I going to buy bottle imp for 6 hoping that my opponent will spend 5 on it? That's nonsense; they are losing less than me, and regardless they can still just buy it for min amount.
You could also do something silly like pay a lot for bottle imp on a board where it is bad to have (if such a board even exists!), hoping that your opponent will take it away from you. This is kind of nonsense also, clearly ignoring psychology this is just worse than not getting bottle imp, and if you allow psychology your opponent should be suspicious the moment you pay more than min amount.







Holunder:
I think that you are trolling, sorry if you aren't, I won't respond to you anymore.





12
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 12, 2018, 01:04:50 pm »
By your own admission, you did not answer my challenge:
"Not at the very moment I have to make the choice, then I am pissed."

Your chess analogy is irrelevant. I make no claims about number of options available. Only about when the options available in one state are a superset of the options available in another state.


13
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 12, 2018, 02:43:20 am »
Ok, to anyone who believes paying minimum amount is not optimal, I offer a challenge:

Assume that $1 is the minimum amount you can pay for bottle imp.
Construct ANY scenario where your opponent has bottle imp, you have played cursed bottle, and would be happier if your opponent had paid $1 for bottle imp than if they had paid >$1.

Hard mode: Same as the above, but you are playing open-hand dominion, where you can always see your opponent's hand.

I believe normal mode to already be very difficult and to have no solutions which are not extreme edge cases. Prove me wrong.

Actually, I believe both modes to be impossible without assuming that you are a bad player

14
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 12, 2018, 02:05:28 am »
I guess where I still see value in the card is that Dominion is not a perfect information game. Even if it's true that every decision can only increase the chances of winning for a single player; there are many times when it is not really possible to calculate which decision increases the chances for you. In that way, it's quite possible for both me and my opponent to want my opponent to take Bottle Imp from me. Throughout much of the middle of the game, it will not be clear whether it is better to have Bottle Imp or not. I may easily think that the best way to use Bottle Imp is to have it for a few turns and then lose it; while my opponent, having seen that I've taken it; may think that taking it away from me is still the better play.

In other words, it's not counting on your opponent to act irrationally. It's counting on them to simply have a different risk threshold than you do, or to have a different analysis than you do.

No matter what, you still would never want to pay more than the minimum amount for bottle imp.
Suppose that there are two gamestates of dominion which are almost identical. In state 1, you are deciding whether you want to do choice A, choice B, or choice C. You have no other choices. State 2 is exactly the same, except that for some reason you only have the options to do choice A and choice B.

Which state would you rather be in? Obviously it is state 1, since the options available to you are a superset to the options in state 2.

Now consider that you have just played cursed bottle. Your opponent currently has the bottle imp, and paid N for it. What options are available to you?
You could not take the bottle imp, or you could pay 1 to take the bottle imp, or you could pay 2, or ..., or you could pay N-1 to take the bottle imp.
If your opponent had instead paid N+1 for the bottle imp, you would have the exact same choices, plus the choice to pay N to take the bottle imp.
So, your options are a superset of the options from the original situation.
Therefore, you always prefer that your opponent pays N+1 for bottle imp rather than N.

Conversely, you should always pay N for bottle imp rather than N+1; i.e. you should always pay the minimum amount.

15
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 10:59:50 pm »
The point that many people seem to be ignoring is that if it is good for me to have my opponent take the bottle imp away from me, then it is bad for my opponent to take it away.

It's not necessarily that simple. Consider Governor: It's usually better for you if your opponent chooses +3 cards instead of Gold, because +1 card for you is usually better than a Silver. Does this mean your opponent should always choose Gold over +3 cards? No, because the +3 cards usually helps them more as well. It's the same with Bottle Imp: taking it away from you can be good for you and them at the same time.

This is flawed reasoning. Only one player can win, every decision decreases one player's win% and increases the others. In this sense no decision can help both players.

So you're saying there's only one Governor option that should always be picked? Which is it?

No, that is not exactly what I am saying. I am saying that each time you play governor, there is only one Governor option that should be picked. It might not be the same every time. Assuming you could see your opponent's hand, it is not possible for both you and your opponent to want you to pick draw cards. Because the small amount of hidden information in dominion has a fairly large effect on what you should pick for governor, I have to hedge and assume you can see your opponent's hand. For bottle imp the effect of hidden information is much smaller.

16
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 09:31:09 pm »
The point that many people seem to be ignoring is that if it is good for me to have my opponent take the bottle imp away from me, then it is bad for my opponent to take it away.

It's not necessarily that simple. Consider Governor: It's usually better for you if your opponent chooses +3 cards instead of Gold, because +1 card for you is usually better than a Silver. Does this mean your opponent should always choose Gold over +3 cards? No, because the +3 cards usually helps them more as well. It's the same with Bottle Imp: taking it away from you can be good for you and them at the same time.

This is flawed reasoning. Only one player can win, every decision decreases one player's win% and increases the others. In this sense no decision can help both players.

17
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 09:06:58 pm »
"If you pay $2 you always have the option of getting rid of Bottle Imp."

No.... you cannot get rid of bottle imp unless your opponent takes it from you.

18
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 07:59:08 pm »
My mistake. The general point still stands though, you ignore time and the very real possibility of high initial prices for Bottle Imp because nobody wants to end up with those -13VPs. The strength of Bottle Imp changes over time, from being very valuable early in the game towards being progressively worse and then sharply becoming a very bad card at the end of the game. This means that strength evaluation changes over the course of the game and thus will its ownership.

You are simply wrong about this being good/bad in a particular Kingdom. It is like pretending that Hireling is always good/bad in Kingdom ABC while ignoring time, while ignoring that it is much stronger early on.

Note that my hypothetical scenario where one player has the option to take the bottle imp is true at any point in time.

It is true that in many games I would like to have the bottle imp at the beginning in order to build, and then I would probably like to get rid of it towards the end of the game. The point that many people seem to be ignoring is that if it is good for me to have my opponent take the bottle imp away from me, then it is bad for my opponent to take it away.

Or like Jimmmmmmm said, giving your opponent a choice is always worse than not giving them a choice.
If my opponent can choose to take the imp away for $1, $2, or $3, or not take the imp, that is better for them than being able to take the imp away for either $1 or $2 (or not taking it), which is better than only being able to take the imp away for $1 (or not), which is better for them than not being able to take the imp.

19
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 07:17:37 pm »
The paradox is based on humans behaving irrationally. If humans behaved rationally, then there is no paradox. It is just obviously correct to never take the bottle in the story. I expect good dominion players to also behave rationally if they are trying to win the game.
You ignore time and player interaction:
Paying a lot for Bottle Imp can prevent the opponent from going for Cursed Bottle at all respectively make it temporarily unable (depending on how good his economy is) for him to get Bottle Imp while you could later pay for it again, but then e.g. $0.

No... paying a lot for Bottle Imp makes it easier, not harder for the opponent to get the imp.

20
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 06:35:31 pm »
I think you guys are mostly missing my point.

Suppose my opponent has bottle imp, and I have the opportunity to take it. Doing so will affect my win probability by delta. If delta is positive, then I will happily take the bottle imp. My opponent will say, "Darn! I should have paid the minimum amount for bottle imp to prevent this from happening!".

Suppose delta is negative. Then I will not take the bottle imp. My opponent will say, "Hm. I guess it didn't matter how much I paid for bottle imp."

Since there is some tiny amount of hidden information in dominion, it is possible for two optimal opposing players to disagree on the sign of delta, but that seems exceedingly rare. The true win probability is zero-sum.

This is why the original Bottle Imp story is a paradox. You can show through induction that it is never good to take it (or in the Dominion case, that if it is good to take it, it's best to take it for . And yet at the same time, taking it for can seem perfectly reasonable.

The paradox is based on humans behaving irrationally. If humans behaved rationally, then there is no paradox. It is just obviously correct to never take the bottle in the story. I expect good dominion players to also behave rationally if they are trying to win the game.

21
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 05:49:46 pm »
I think you guys are mostly missing my point.

Suppose my opponent has bottle imp, and I have the opportunity to take it. Doing so will affect my win probability by delta. If delta is positive, then I will happily take the bottle imp. My opponent will say, "Darn! I should have paid the minimum amount for bottle imp to prevent this from happening!".

Suppose delta is negative. Then I will not take the bottle imp. My opponent will say, "Hm. I guess it didn't matter how much I paid for bottle imp."

Since there is some tiny amount of hidden information in dominion, it is possible for two optimal opposing players to disagree on the sign of delta, but that seems exceedingly rare. The true win probability is zero-sum.

22
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 10, 2018, 02:41:53 am »
I don't really see many situations where you would pay more than 0 for this. Either it's good to have so why would I want to pay more for it / let my opponent take it or it's bad so why would I take it at all.

Because it's better to have it for a while and then lose it than it is to have it forever.

I don't really see it. When would it be good to buy bottle imp for 1? Either my opponent will take it from me very soon because bottle imp is good, and I will never get it back, or I should never have bought bottle imp at all.

In other words, if it is good for my opponent to take bottle imp for 0, why wasn't it good for me?

23
Variants and Fan Cards / Re: Cursed Bottle / Bottle Imp
« on: December 09, 2018, 03:42:26 pm »
I don't really see many situations where you would pay more than 0 for this. Either it's good to have so why would I want to pay more for it / let my opponent take it or it's bad so why would I take it at all.

24
Solo Challenges / Re: Win without reshuffling.
« on: December 08, 2018, 11:16:50 am »
If Inn effect is allowed you can do it with just Inn and Mandarin (21103487).

25
General Discussion / Re: Maths thread.
« on: November 24, 2018, 04:25:13 pm »
The classic solution is to

Draw a graph where the vertices are the interiors of the triangles (and also there is a vertex for the outside), and there is an edge between any two triangles separated by a side with both red and green end points. Then a vertex has odd degree iff if is a trichromatic triangle or the outside vertex. The property that the sum of the degrees of the vertices is twice the number of edges finishes the proof, since that means the number of vertices of odd degree must be even.

Edit: note that this solution also shows the existence of trichromatic triangles in more general configurations.

Also bonus problem, using the result of the triangle problem, prove that every continuous function from the closed disk to itself must have a fixed point.

Pages: [1] 2 3 ... 43

Page created in 0.079 seconds with 18 queries.