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Citadels» Forums » Rules

Subject: When playing with the Witch rss

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Rex Ford
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If I had first pick in the draft why would I ever choose anything OTHER than the witch? She can't be assassinated, she can't be stolen from... yet she's automatically as powerful as the highest numbered card? I don't get it.

 
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ackmondual
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RexGoodheart wrote:
If I had first pick in the draft why would I ever choose anything OTHER than the witch? She can't be assassinated, she can't be stolen from... yet she's automatically as powerful as the highest numbered card? I don't get it.

There are only a few reasons, and because of that, with my games, I refuse to play with the Witch with 6 or more players, and even then, things do end up "devolving" into what you mentioned... that, and she's one of the exp char and people would also like to try them out since base game ones are more commonly used.

Otherwise...
--She can only build when she bewitches someone, so she probably won't be able to get the "first to 8" bonus, and settle for the 2pts instead. IIRC, somene mentioned that her being able to "pass" on her power was bogus and that this was not the case.
--if she names a char not in play, then she's hosed (though rare).

--FWIW, the designer stated he prefers the Assassin over the Witch. The former is much more meaner
 
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Rex Ford
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Thank you for your reply. We're fairly new to the Citadels experience and tried the Witch after a few games... each of us felt that it was so out of whack that we kept going back to the rule book to make sure we were playing it correctly. I think maybe I'll give some consideration to using the Witch while always denying her the power to build... she would still be a pretty tempting choice for a "1".
 
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Grarrrg Grarrrgowski
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Citadels » Forums » Rules
Re: When playing with the Witch
RexGoodheart wrote:
If I had first pick in the draft why would I ever choose anything OTHER than the witch? She can't be assassinated, she can't be stolen from... yet she's automatically as powerful as the highest numbered card? I don't get it.


First off, she can't be assassinated because there IS NO ASSASSIN, the Witch replaces the Assassin (unless you're using some kind of house-rule).
And she's automatically as powerful as the character she wants to be IF that Character is IN PLAY, and the Witch must wait until the Victim's turn, but the Victim still gets to take 2-Gold/1-Card.

The Witch is a fine swap if you want a 'friendlier/faster' game, but is pretty much strictly weaker than the Assassin.

If guessed right, the Assassin gets a Full Turn (+1), and the Victim loses a Full Turn (+1). If wrong, the Assassin still gets a Full Turn (+1).
If guessed right, the Witch gets (effectively) a Full Turn (+1), and the Victim gets Half a Turn (+.5). If wrong, the Witch still gets Half a Turn (+.5).
Assassin +3, Witch +2.
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mumu shanshi
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grarrrg wrote:
The Witch is a fine swap if you want a 'friendlier/faster' game, but is pretty much strictly weaker than the Assassin.

If guessed right, the Assassin gets a Full Turn (+1), and the Victim loses a Full Turn (+1). If wrong, the Assassin still gets a Full Turn (+1).
If guessed right, the Witch gets (effectively) a Full Turn (+1), and the Victim gets Half a Turn (+.5). If wrong, the Witch still gets Half a Turn (+.5).
Assassin +3, Witch +2.

A gross oversimplification, of course. One may debate the exact value of "Half a Turn"; but more importantly, not all Full Turns are created equal. An Assassin's Full Turn is worth a lot less than a Merchant or an Architect's Full Turn.
Further, the quoted assumes an equal probability of guessing right or wrong, which is only true in worst-case scenarios.
 
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Chris Berger
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I'm gonna try to work this by induction.* For sake of argument, every role has an equal chance of being taken. If you are good at guessing what roles people will pick, then that will adjust the percentages quite a bit.

Let's take a 5p game. Hopefully I remember the 5p rules correctly - one role face-down, one face-up to start. At the end of the round, one more role goes face-down. (Right?)

Player 5 has the Witch and another role in his hand. If he takes the Witch, there are 5 roles he can't see, 4 of which were taken by somebody. So he has an 80% chance of picking the right role and getting a full turn. If he guesses wrong, he doesn't get a full turn (if someone has no cards or low gold, it will influence the decision), but let's assume he takes the witch if it gets to him. As player 1, you have a 20% chance of being picked, or an 80% chance of getting a full turn if player 5 takes the Witch.

If player 4 took the Witch, he could either pick one of the two roles left in his hand, giving him a 50/50 chance of getting a full turn, or he could pick one of the 4 roles he can't see, giving him a 75% chance of a full turn. Let's say he picks a role he can't see (better odds), so as player 1 you have a 25% chance of being picked, or a 75% chance of getting a full turn if player 4 takes the Witch.

If player 3 took the Witch, he could either pick a role in his hand, giving him a 67% chance of getting a full turn. Or he could pick one of the 3 roles he can't see, giving him, again, a 67% chance of getting a full turn. Flip a coin. If player 3 takes the Witch, he will choose the role that he needs the most. As player 1, you have a 1-in-6 chance of being picked, or an ~83% chance of getting a full turn. If you know which role 3 is likely to want, this can change the odds.

If player 2 took the Witch, he could either pick a role in his hand, giving him a 75% chance of getting a full turn, or a role he cannot see, giving him a 50% chance. Assuming he is playing reasonably, you don't expect him to pick a role he cannot see. If you know the role that 2 is most likely to want and avoid picking that, you can influence this, but let's assume that p2 will choose a role in his hand. You have a 0% chance to get picked. (This might seem unfairly generous, but remember we assumed that p4 would definitely pick a role he can't see... it balances out.)

So, if you don't take the Witch as p1, and have no idea what roles anyone else might pick to allow you to better gauge the probabilities, you would estimate that you have a (0% + 17% + 25% + 20%) / 4 = ~15.5% chance of not getting a full turn. Or an 84.5% chance of getting a full turn vs. 80% chance of getting a full turn if you chose the Witch yourself. That is assuming that the Witch definitely gets picked by someone. (In which case, the turn "stolen" from another player doesn't really play into it because in each situation, someone will lose half their turn.)

Now, I'm not saying that you always have an 84.5% chance of getting your full turn if you don't pick the Witch vs. 80% chance if you do pick her. But I am saying that there are going to be situations where these probabilities make sense and in those situations, you might choose to pick the role you want instead of choosing the Witch. On balance, if you assume every role is as likely to be taken as any other, and every player will play for the highest chance of stealing a turn when choosing the Witch, then not taking the Witch as p1 is a perfectly viable option. In fact, if p5 is playing for the highest chance of getting a full turn (and discounting the value of costing someone else a turn), then he'll discard the Witch and take a different role, meaning your odds just went up.

(edit: fixed some math... hopefully it's right now)
*(edit again: I had intended to figure out what p5's expected choice would be and then factor that into the value and decision-making for the other players - that's why I went in reverse. But then it turned out to be too much work and I don't think it matters that much in the end.)
 
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Grarrrg Grarrrgowski
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mumushanshi wrote:
grarrrg wrote:
If guessed right, the Assassin gets a Full Turn (+1), and the Victim loses a Full Turn (+1). If wrong, the Assassin still gets a Full Turn (+1).
If guessed right, the Witch gets (effectively) a Full Turn (+1), and the Victim gets Half a Turn (+.5). If wrong, the Witch still gets Half a Turn (+.5).
Assassin +3, Witch +2.

A gross oversimplification, of course. One may debate the exact value of "Half a Turn"; but more importantly, not all Full Turns are created equal. An Assassin's Full Turn is worth a lot less than a Merchant or an Architect's Full Turn.
Further, the quoted assumes an equal probability of guessing right or wrong, which is only true in worst-case scenarios.


It is an oversimplification, but that doesn't really affect the results.

The ratio of Right/Wrong doesn't really matter (and keep in mind whether Assassin or Witch, your odds of guessing correctly are about the same).
Right: Assassin +2, Witch +1.5
Wrong: Assassin +1, Witch +.5
In either case, the Assassin comes out ahead.
 
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Rex Ford
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Let's see...

Case 1: In a five player game, P1 takes the witch:

- He knows two cards for sure that won't be in play: the original face down card and the face up.

- So, of the eight cards, three are accounted for, one is unknown, four are in the hands of his opponents. He has an 80% chance of bewitching somebody.

- Each of his opponents has a 80% x 25% chance of being knocked out, or 20% for each. So, P1's chance of having a full turn is precisely equal to each of the cards he's passed along, with the added benefit of safely choosing the best available role he wants.

- Conclusion: why would P1 take anything other than the witch?

Case 2: In a five player game, P1 takes something else and passes the witch to his left, and P2 takes the witch.

- P2 knows two cards for certain, and one half certain. If P2 wished to target P1, he has a 50% chance of success. P1's chance of having a full turn is 50%.

- Conclusion so far: by passing the witch, P1 has placed himself in a mere 50% chance of taking a full turn if the player to his left targets him. If he had taken the witch he would have had an 80% chance of a full turn, with the added benefit of safely choosing the best available role.

I won't take this any further... I think I've convinced myself that it's craziness to take anything other than the witch as P1... just as our actual playing experience reinforced.











 
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Chris Berger
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RexGoodheart wrote:
- P2 knows two cards for certain, and one half certain. If P2 wished to target P1, he has a 50% chance of success. P1's chance of having a full turn is 50%.

- Conclusion so far: by passing the witch, P1 has placed himself in a mere 50% chance of taking a full turn if the player to his left targets him. If he had taken the witch he would have had an 80% chance of a full turn, with the added benefit of safely choosing the best available role.


Why would P2 accept a 50% chance of success? Unless P1 is about to win, or P2 is P1's wife, that's just a stupid play.
 
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Rex Ford
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OK, let's take it further then.

P2 passes four cards and knows three will be taken. So if P2 chooses not to target P1 his chances of success are only 75%, anyway.

This is fun.





 
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Chris Berger
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RexGoodheart wrote:
OK, let's take it further then.

P2 passes four cards and knows three will be taken. So if P2 chooses not to target P1 his chances of success are only 75%, anyway.


In which case I'd rather take the 75% chance, or not take the witch, instead of a 50% chance (unless I need to target P1).

Anyway, this part of the probabilities, I already addressed in my previous post. If you don't agree with the math, let me know where I'm wrong.
 
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Rex Ford
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Assuming your math is correct, it just doesn't make much sense to take an 84.5% risk with some card other than the witch, when the next players can then have a pretty good idea on what you've taken, versus taking the witch and safely having any role you want, including the best available for your personal game situation, with 80% success.

Not only that, we think the game discombobulates a bit with the Witch. Makes it a bit cumbersome.
 
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Chris Berger
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RexGoodheart wrote:
Assuming your math is correct, it just doesn't make much sense to take an 84.5% risk with some card other than the witch, when the next players can then have a pretty good idea on what you've taken, versus taking the witch and safely having any role you want, including the best available for your personal game situation, with 80% success.


I dunno, having an 85% chance to get the role I want vs. 80% chance to get the role I want is better. Not better in the sense of I would never take the Witch, but in the sense of, I might not take the Witch if I think those probabilities are accurate for the current game situation.

As to players having a pretty good idea what I've taken - it's only 50/50. And there are a lot of situations in the game where you know 50/50 what someone else has taken. And if you're taking the Witch because you expect someone else to try and target you, then you almost have to steal the Magician (if he's in play).
 
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