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Morgrim7

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Please look at my hand!
« on: May 05, 2012, 09:42:25 am »
0

When would you want your opponent to look at your hand?
Here is one solution:
If you have been keeping very good track of your opponent's deck (which he hasn't been doing) and you know that in his hand he has only one Platnium and 2 Estates, a Witch, and a Venture. In his deck, he has a Copper on top, a Platinum underneath that, and a bunch of VP cards underneath that. In your hand you have a Moat, and a bunch of Gold and Platinum. There is one Curse, and one Colony in the supply, and you are behind. If he plays the Witch, he will draw the Platinum and Copper and win, so you wan't him to see your hand and find out that you have a Moat, so he will play the Venture and only get a Copper. Then, you can buy the last Colony and win. If he doesn't see your hand, then he will play the Witch, give you the Curse, buy the last Colony, and win.
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Schneau

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Re: Please look at my hand!
« Reply #1 on: May 05, 2012, 09:47:51 am »
0

When would you want your opponent to look at your hand?
Here is one solution:
If you have been keeping very good track of your opponent's deck (which he hasn't been doing) and you know that in his hand he has only one Platnium and 2 Estates, a Witch, and a Venture. In his deck, he has a Copper on top, a Platinum underneath that, and a bunch of VP cards underneath that. In your hand you have a Moat, and a bunch of Gold and Platinum. There is one Curse, and one Colony in the supply, and you are behind. If he plays the Witch, he will draw the Platinum and Copper and win, so you wan't him to see your hand and find out that you have a Moat, so he will play the Venture and only get a Copper. Then, you can buy the last Colony and win. If he doesn't see your hand, then he will play the Witch, give you the Curse, buy the last Colony, and win.
This doesn't work. Venture is a Treasure card, so he will play Witch either way and then play Venture.
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Morgrim7

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Re: Please look at my hand!
« Reply #2 on: May 05, 2012, 09:57:50 am »
0

When would you want your opponent to look at your hand?
Here is one solution:
If you have been keeping very good track of your opponent's deck (which he hasn't been doing) and you know that in his hand he has only one Platnium and 2 Estates, a Witch, and a Venture. In his deck, he has a Copper on top, a Platinum underneath that, and a bunch of VP cards underneath that. In your hand you have a Moat, and a bunch of Gold and Platinum. There is one Curse, and one Colony in the supply, and you are behind. If he plays the Witch, he will draw the Platinum and Copper and win, so you wan't him to see your hand and find out that you have a Moat, so he will play the Venture and only get a Copper. Then, you can buy the last Colony and win. If he doesn't see your hand, then he will play the Witch, give you the Curse, buy the last Colony, and win.
This doesn't work. Venture is a Treasure card, so he will play Witch either way and then play Venture.
Replace Venture with Adventurer, pus two coppers on top instead of one, and replace Witch with Torturer.
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eHalcyon

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Re: Please look at my hand!
« Reply #3 on: May 05, 2012, 10:31:26 am »
0

When would you want your opponent to look at your hand?
Here is one solution:
If you have been keeping very good track of your opponent's deck (which he hasn't been doing) and you know that in his hand he has only one Platnium and 2 Estates, a Witch, and a Venture. In his deck, he has a Copper on top, a Platinum underneath that, and a bunch of VP cards underneath that. In your hand you have a Moat, and a bunch of Gold and Platinum. There is one Curse, and one Colony in the supply, and you are behind. If he plays the Witch, he will draw the Platinum and Copper and win, so you wan't him to see your hand and find out that you have a Moat, so he will play the Venture and only get a Copper. Then, you can buy the last Colony and win. If he doesn't see your hand, then he will play the Witch, give you the Curse, buy the last Colony, and win.
This doesn't work. Venture is a Treasure card, so he will play Witch either way and then play Venture.
Replace Venture with Adventurer, pus two coppers on top instead of one, and replace Witch with Torturer.

He wouldn't be able to give you the curse either way.  You have a Moat.

How would you know the order of the top 2 cards in his deck without him knowing it as well?  I can only think of Oracle right now.  I can't remember if there are other Spy-like attacks that let you know the top 2 cards of other players, but I don't think there are any that let you know 3, and I can't think of any that lets you know the order without also informing the others.  So with Oracle, you might know the top two are Copper and his deck only has a Plat otherwise, but you won't know it's the third in the deck.  More importantly, your opponent would know the same -- the next two are copper.  Therefore, he would know that Adventurer would not be helpful and his best shot would be Torturer and hope that he gets his Plat. 

If he decides not to do that, it should have little to do with seeing your Moat; rather, it would just be a tactical mistake.  In fact, seeing your hand might even push him to take the risk on the torturer's draw rather than allow you to buy the Colony on your turn, since he'd know that Adventurer would fail.  Then again, if he has no idea of the current score, he might be OK with letting you take the Colony.  But then, seeing your hand makes no difference once again.
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Morgrim7

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Re: Please look at my hand!
« Reply #4 on: May 05, 2012, 10:40:49 am »
0

When would you want your opponent to look at your hand?
Here is one solution:
If you have been keeping very good track of your opponent's deck (which he hasn't been doing) and you know that in his hand he has only one Platnium and 2 Estates, a Witch, and a Venture. In his deck, he has a Copper on top, a Platinum underneath that, and a bunch of VP cards underneath that. In your hand you have a Moat, and a bunch of Gold and Platinum. There is one Curse, and one Colony in the supply, and you are behind. If he plays the Witch, he will draw the Platinum and Copper and win, so you wan't him to see your hand and find out that you have a Moat, so he will play the Venture and only get a Copper. Then, you can buy the last Colony and win. If he doesn't see your hand, then he will play the Witch, give you the Curse, buy the last Colony, and win.
This doesn't work. Venture is a Treasure card, so he will play Witch either way and then play Venture.
Replace Venture with Adventurer, pus two coppers on top instead of one, and replace Witch with Torturer.

He wouldn't be able to give you the curse either way.  You have a Moat.

How would you know the order of the top 2 cards in his deck without him knowing it as well?  I can only think of Oracle right now.  I can't remember if there are other Spy-like attacks that let you know the top 2 cards of other players, but I don't think there are any that let you know 3, and I can't think of any that lets you know the order without also informing the others.  So with Oracle, you might know the top two are Copper and his deck only has a Plat otherwise, but you won't know it's the third in the deck.  More importantly, your opponent would know the same -- the next two are copper.  Therefore, he would know that Adventurer would not be helpful and his best shot would be Torturer and hope that he gets his Plat. 

If he decides not to do that, it should have little to do with seeing your Moat; rather, it would just be a tactical mistake.  In fact, seeing your hand might even push him to take the risk on the torturer's draw rather than allow you to buy the Colony on your turn, since he'd know that Adventurer would fail.  Then again, if he has no idea of the current score, he might be OK with letting you take the Colony.  But then, seeing your hand makes no difference once again.
The curse doesn't matter.
About you knowing the deck order, You played oracle, found out that there were Coppers on top, and because there were no other cards in the deck you knew that the last card was a platinum.
I see what you mean, though. About the Moat and the tactical mistake. Looks like a good puzzle if I can't solve it myself ;)
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I sit here, lost amongst the cloud, that which is the brain of the Morgrim Mod. Perhaps I will learn the inner workings of that storied mind. Perhaps I will simply go mad.

Mad, I tell you.

Maaaaaaaaaaaaad." -Voltgloss
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theory

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Re: Please look at my hand!
« Reply #5 on: May 05, 2012, 11:59:41 am »
+7

He looks at your hand, sees only 1 Copper and 4 Victory cards, and decides to go for buying the second-to-last Colony.  You then take two Platinums out of your Havens and win by buying the last Colony.
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jimjam

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Re: Please look at my hand!
« Reply #6 on: May 06, 2012, 12:53:28 am »
0

There can't really be an answer in a 2 player game with optimal gameplay, since the opponent can just ignore the information given.
In 3 player:
It's the Outpost turn of the player before you. He plays Outpost accidentally through Golem, and has been Rabbled with 3 Provinces on top. There is one Colony left, and he can either play a Saboteur or a Woodcutter, and has $9 in coin. If he buys the Colony, he'll move from third to second place.
The 3rd player has 12 Dukes and 12 Silk Roads, and a decent deck. She's very slightly behind you.
Your deck is pretty much trash so you want to end the game ASAP. The player before you sees that you have a Masquerade , and 4 Duchies in hand. You also have 1 Colony, then 2 Duchies on top of your deck, from Rabble. You also have $11 coming in from duration cards.
Before, your opponent may risk trying to prolong the game, but he sees that if he Sabotages you, you will take his Province and pass a Duchy, which will give a slight lead to the 3rd player. Thus he will be in last place (and you will be in second).
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Schneau

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Re: Please look at my hand!
« Reply #7 on: May 06, 2012, 08:12:07 am »
+4

There can't really be an answer in a 2 player game with optimal gameplay, since the opponent can just ignore the information given.
Not necessarily. Optimal gameplay can result in a worse decision if the probability of a better decision is quite small. For example:

Let's say there is one Colony left, no other victory cards available, and 2 Curses. You are up by 9 points, so that if your opponent gets the last Colony, he wins, but if he gets the last 2 curses, he cannot win. Your opponent has 2 Golds, 2 Estates, and a Wishing Well in hand, and you have a Village and 2 Witches and 2 Estates. You opponent's deck somehow consists of 10 Lighthouses, 1 Platinum, and the rest are Victory cards; your deck has no other Curse-givers besides the two in hand. If he doesn't see your hand, he plays the Wishing Well, drawing an Estate, and wishes for a Platinum, which he gets to buy the Colony and win the game. This is the optimal decision, since he is unlikely to get the required $11 in his hand again, and since it is unlikely that you have both Witches in your hand. If he looks at your hand, he sees both Witches, which, if you are allowed to play, will make him lose. So, he wishes for a Lighthouse, but finds a Platinum instead. This is the optimal decision, since he is more likely to find a Lighthouse, and since if he doesn't either play a Lighthouse or end the game this turn, he will lose.
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DG

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Re: Please look at my hand!
« Reply #8 on: May 06, 2012, 12:47:54 pm »
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In a three player game both you and the player on turn may want to share victory before another opponent takes a turn and wins. An example might be the player on turn using a governor to trash a silver  to a duchy knowing that you will trash a militia for a duchy too, emptying the duchies as the third pile. If the hands are revealed the player on turn can make that decision.
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blueblimp

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Re: Please look at my hand!
« Reply #9 on: May 06, 2012, 01:27:40 pm »
+1

There can't really be an answer in a 2 player game with optimal gameplay, since the opponent can just ignore the information given.

This is partly true. If you choose to reveal additional information to your opponent and your opponent knows this, then your opponent would obviously be inclined to ignore the information and play normally. After all, why would you reveal information you weren't required to except as a trick?

On the other hand, it can sometimes be helpful to you for your opponent to find out additional information, as long as they still lack some information.

Here is a concrete example. Imagine you are playing a game where you flip a coin, you look at it, and then your opponent tries to guess what it is. Suppose you have already flipped the coin and looked at it: it's tails. Suppose also that (before starting this game, while your opponent wasn't here) the previous 10 flips of the coin were heads. If your opponent knew this, he might think the coin is rigged and guess heads, which would help you, compared to normal play of guessing randomly. But if you chose to tell your opponent that the previous 10 flips were heads, he'd be wise to ignore the information. So if you could somehow trick your opponent into thinking he learned this by accident when actually you intended to reveal it, you would gain an advantage in the game.
« Last Edit: May 06, 2012, 01:29:43 pm by blueblimp »
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jimjam

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Re: Please look at my hand!
« Reply #10 on: May 06, 2012, 10:52:05 pm »
0

There can't really be an answer in a 2 player game with optimal gameplay, since the opponent can just ignore the information given.
Not necessarily. Optimal gameplay can result in a worse decision if the probability of a better decision is quite small. For example:

Let's say there is one Colony left, no other victory cards available, and 2 Curses. You are up by 9 points, so that if your opponent gets the last Colony, he wins, but if he gets the last 2 curses, he cannot win. Your opponent has 2 Golds, 2 Estates, and a Wishing Well in hand, and you have a Village and 2 Witches and 2 Estates. You opponent's deck somehow consists of 10 Lighthouses, 1 Platinum, and the rest are Victory cards; your deck has no other Curse-givers besides the two in hand. If he doesn't see your hand, he plays the Wishing Well, drawing an Estate, and wishes for a Platinum, which he gets to buy the Colony and win the game. This is the optimal decision, since he is unlikely to get the required $11 in his hand again, and since it is unlikely that you have both Witches in your hand. If he looks at your hand, he sees both Witches, which, if you are allowed to play, will make him lose. So, he wishes for a Lighthouse, but finds a Platinum instead. This is the optimal decision, since he is more likely to find a Lighthouse, and since if he doesn't either play a Lighthouse or end the game this turn, he will lose.

No, your situation contradicts itself by both saying the Platinum is on top and that the top card is undetermined. Nor does it demonstrate a situation in which a player who always ignores your information is hurt by seeing your hand.
blueblimp's situation is legitimate but in a game-theoretic perspective, in a 2-player zero-sum game, information can never hurt your expected utility.
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ftl

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Re: Please look at my hand!
« Reply #11 on: May 07, 2012, 11:50:35 pm »
+1

Quote
blueblimp's situation is legitimate but in a game-theoretic perspective, in a 2-player zero-sum game, information can never hurt your expected utility.

It can never hurt your expected utility, but it can hurt your ACTUAL utility.

Speaking abstractly - opponent has two options, X and Y.

Consider the following situation. Suppose you have the following information: your hand, your opponent's hand (maybe they played a Hunting Party?), and extra information your opponent does not have and will not have (content of havens or native village mat, top cards of the deck due to Secret Chamber reaction reveals, knowing which cards are left in the deck, etc.). Knowing this, you know that your opponent will win if they choose X, and lose if they choose Y.

Your opponent starts with the following information: knowing his own hand. With this information, the choice with the highest expected utility for him is X.
Then he plays something (maybe a Bureaucrat?) that gives him the following information: knowing your hand. With this information, the choice with the highest expected utility for him is Y.

In this case, you want your opponent to look at your hand and thus use that information to make the wrong choice.  This is not a contradiction. It may be rare, but it's not impossible.
« Last Edit: May 08, 2012, 12:07:29 am by ftl »
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ftl

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Re: Please look at my hand!
« Reply #12 on: May 08, 2012, 12:04:02 am »
+3

Native village is an example.

Suppose you have bought exactly one scrying pool and one university; you know that both of them are on your Native Village mat.  Your opponent does not know that they are on the NV mat; they may know that you haven't played them, but since there's been a lot of Minions going around, that isn't unusual.  You have lots of stuff in your discard pile, and your deck is empty.

In your hand, you have four coppers and a Native Village. This is a very GOOD hand, since you can play University to gain an inn and shuffle many actions from your huge discard pile into your empty deck, and then play the Pool to draw them.

If your opponent does not look at your hand, they don't have much information about your possible turn at all; they may correctly play it safe, as if you have a good hand (not break PPR, or equivalent.)

However, if they play a bureaucrat and look at your hand, they will see that you have a native village, with only two cards on the NV mat, and four coppers. This is EXTREMELY likely to be a bad hand - for most possible contents of the NV mat, given all the things that COULD be on there, you cannot have a very good turn. The opponent will then play as if you have a bad hand (since, as far as they know, you do.) This will be a mistake, since you actually have an amazing hand and will end the game on a win.
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jimjam

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Re: Please look at my hand!
« Reply #13 on: May 08, 2012, 03:36:23 am »
0

Again, you have not demonstrated that an opponent who always ignores your information is hurt by you giving them information.

If one places the ability to reveal the hand inside the framework of the 2-person game, it does not increase that player's utility under optimal gameplay, because the opponent is able to consider the space of possibilities in which you would choose to reveal your hand.

Theory already gave a good, simple example of where you might "trick" your opponent. The gain in utility stems from a psychological fault (i,e, the opponent is not playing optimally by failing to model the choice to reveal the hand as being part of the game), not a game-theoretic one.

If however, there was a rule that said "During your opponent's turn, roll a dice, if you get a 1, reveal your hand", then yes, there are situations in which you would want a 1 to be rolled.
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GendoIkari

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Re: Please look at my hand!
« Reply #14 on: May 08, 2012, 09:33:19 am »
0

Again, you have not demonstrated that an opponent who always ignores your information is hurt by you giving them information.

This isn't what they are trying to demonstrate. Of course if the opponent ignores the information, then they can't be hurt by it. But in the first example of the Wishing Well / Platinum / Cursers, ignoring the information is not optimal play. Without having that information, optimal play is wishing for Platinum. With that information, optimal play is wishing for Lighthouse. Yes, if you ignore the information you can still wish for Platinum and still win, but once you know that your opponent has 2 Cursers in hand, doing so is a bad decision.

Quote
If however, there was a rule that said "During your opponent's turn, roll a dice, if you get a 1, reveal your hand", then yes, there are situations in which you would want a 1 to be rolled.

This is basically what they seem to be saying. And there is such a rule; with things like Bureaucrat. They aren't talking about you just saying "hey, look at my hand!"
« Last Edit: May 08, 2012, 09:38:28 am by GendoIkari »
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DStu

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Re: Please look at my hand!
« Reply #15 on: May 08, 2012, 09:45:29 am »
0

I'm not sure if you can really generally model this metagame things. It should depend on the personality of the players.

In which situations will my opponent show his hand? Of course I could ignore it and don't be hurt, but I could also infer that he wants to hurt me, so I should do the opposite of what his hand suggest, to even improve my chances. Or I could know that he knows me to know that. Where is the recursion most likely to stop? I might be thinking that I can win this mindgame...

And can I really choose to ignore information? If I have two possibilities, one say high risk high reward, one low risk low reward, and I happen to get some information, can I really make the same decision as without this information? Which of these ways to go might depend a lot on intuition, and this might be contanimated.
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GendoIkari

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Re: Please look at my hand!
« Reply #16 on: May 08, 2012, 09:55:13 am »
+3


In which situations will my opponent show his hand? Of course I could ignore it and don't be hurt, but I could also infer that he wants to hurt me, so I should do the opposite of what his hand suggest, to even improve my chances. Or I could know that he knows me to know that. Where is the recursion most likely to stop? I might be thinking that I can win this mindgame...

So I CLEARLY cannot choose the glass in front of me!
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Re: Please look at my hand!
« Reply #17 on: May 08, 2012, 10:25:41 am »
0

I'm not sure if you can really generally model this metagame things. It should depend on the personality of the players.

In which situations will my opponent show his hand? Of course I could ignore it and don't be hurt, but I could also infer that he wants to hurt me, so I should do the opposite of what his hand suggest, to even improve my chances. Or I could know that he knows me to know that. Where is the recursion most likely to stop? I might be thinking that I can win this mindgame...

And can I really choose to ignore information? If I have two possibilities, one say high risk high reward, one low risk low reward, and I happen to get some information, can I really make the same decision as without this information? Which of these ways to go might depend a lot on intuition, and this might be contanimated.
This isn't the point. I don't think we're talking about someone "tipping their hand on purpose". I think we're talking about situations where it would be better if the opponent played a card that makes you reveal your hand (Cutpurse, Bureaucrat, etc.), and by doing so makes them play worse than they would have otherwise. At least, that is what I was interpreting the questions as. With this interpretation, you don't have to think about metagame or personality - it is all about optimal play given your current knowledge.
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DStu

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Re: Please look at my hand!
« Reply #18 on: May 08, 2012, 10:38:22 am »
0

Then I think the answer is already given: After revealing your hand you still need to have more (or at least different) information than your opponent on the state of the game. If he has at least the information you have, he can know at least as much as you, so he also knows that it was a benefit for you to reveal your hand, so he knows the information he gets would trick him into the wrong decision. So he takes an other decision.

If you have more information, that does not need to be the case. Situations where you have more information might be (... I remember to have written that before, but it's not in the thread ...) Haven, Native Village, small discard pile. And in hope to win the "most ridiculous construction award", you can also have information on the next card if you played and Outpost (only redrawing 3 cards) and an Apothecary/Scout (inspecting 4 cards) in the last Outpost-turn.

:eApothecary and Scout reveal to public knowledge, so they don't work. Navigator would.
« Last Edit: May 08, 2012, 10:43:58 am by DStu »
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theory

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Re: Please look at my hand!
« Reply #19 on: May 08, 2012, 10:55:57 am »
0

Well, it is different if you are "choosing" to reveal your hand.

Let's say that sometimes you are randomly forced to reveal your hand.  There are absolutely situations where your opponent will then make a different "optimal" move that is nevertheless worse in hindsight.  It is not hard to think of a situation where opponent can do choice A for 70% chance of winning or choice B for 30% chance of winning, but given X, opponent can do choice A for 30% chance of winning or choice B for 70% chance of winning.  Switching from A to B is the correct choice, but not always the best in hindsight.
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GendoIkari

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Re: Please look at my hand!
« Reply #20 on: May 08, 2012, 11:25:16 am »
+2

Then I think the answer is already given: After revealing your hand you still need to have more (or at least different) information than your opponent on the state of the game. If he has at least the information you have, he can know at least as much as you, so he also knows that it was a benefit for you to reveal your hand, so he knows the information he gets would trick him into the wrong decision. So he takes an other decision.

Not necessarily. Going back to the example with Lighthouse / Platinum / Wishing Well / Witches. In that case, you don't have any information that your opponent doesn't have. If he doesn't see your hand and plays optimally, he wins. If he does see your hand and plays optimally, he loses.

The big difference being that in this case, you don't have enough knowledge to determine that you want your opponent to see your hand! In fact, before everything goes down, you should be hoping that he doesn't see your hand, because you want him to try for the Platinum and fail. You have no way of knowing that if he doesn't see your hand, he tries for the Platinum and succeeds. So it doesn't literally fit the theme of "please look at my hand," because you don't "want" him to look at your hand. But, in the end, you will be glad if he did.
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Schneau

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Re: Please look at my hand!
« Reply #21 on: May 08, 2012, 02:21:59 pm »
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Then I think the answer is already given: After revealing your hand you still need to have more (or at least different) information than your opponent on the state of the game. If he has at least the information you have, he can know at least as much as you, so he also knows that it was a benefit for you to reveal your hand, so he knows the information he gets would trick him into the wrong decision. So he takes an other decision.

Not necessarily. Going back to the example with Lighthouse / Platinum / Wishing Well / Witches. In that case, you don't have any information that your opponent doesn't have. If he doesn't see your hand and plays optimally, he wins. If he does see your hand and plays optimally, he loses.

The big difference being that in this case, you don't have enough knowledge to determine that you want your opponent to see your hand! In fact, before everything goes down, you should be hoping that he doesn't see your hand, because you want him to try for the Platinum and fail. You have no way of knowing that if he doesn't see your hand, he tries for the Platinum and succeeds. So it doesn't literally fit the theme of "please look at my hand," because you don't "want" him to look at your hand. But, in the end, you will be glad if he did.
The is really well explained. My example highlights a case where you will do better if your opponent sees your hand, but you do not know it at the time. So, yes, it doesn't really fit the "please look at my hand" idea in that you wouldn't hope your opponent sees your hand during the game.
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jimjam

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Re: Please look at my hand!
« Reply #22 on: May 08, 2012, 04:53:14 pm »
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I'm not sure if you can really generally model this metagame things. It should depend on the personality of the players.

In which situations will my opponent show his hand? Of course I could ignore it and don't be hurt, but I could also infer that he wants to hurt me, so I should do the opposite of what his hand suggest, to even improve my chances. Or I could know that he knows me to know that. Where is the recursion most likely to stop? I might be thinking that I can win this mindgame...

And can I really choose to ignore information? If I have two possibilities, one say high risk high reward, one low risk low reward, and I happen to get some information, can I really make the same decision as without this information? Which of these ways to go might depend a lot on intuition, and this might be contanimated.
Under the expectimax algorithm (i.e. you assume both players have really powerful computers and can calculate every single decision they could make), what happens is that the player will try to decide what % of the time he will reveal his hand and when he won't, for each different scenario where he could reveal his hand,
such that his opponent will not be able to ascertain the player's intentions well enough to gain an advantage in expected utility. However, the opponent's strategy of choosing to ignore performs at least as well when he has nonzero %s as when he has 0 %s, and there might be even more benefits if he selectively doesn't ignore the information. So choosing to never reveal his hand is an optimal strategy.
I haven't played bridge (though I've played Napoleon, which is similar), but that is also a game that can be modeled under expectimax. Even things like playing conventions and metagame behavior can be modeled, because those are either artifacts of non-optimal gameplay, or, if they aren't, will be settled upon by expectimax, which doesn't understand the notion of communication, but simply sees that it's the best way to go.
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