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Laura Gerard
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Is it ever worth it for two psychics to guess the same card?

NO!

Here is why.

I'll explain with a simple example. Suppose you are playing 2 player and the non-ghost is controlling 2 psychics (Red and Black). Also you are playing the easy mode and it is the first round. So both psychics are working on a character and there are 4 characters to choose from. Let's say it's the Chef, Nun, General, and Seamstress.

The non-ghost receives two visions (1 for red and 1 for black). He thinks that both visions point to the Chef. He has two options.

Option A: Put both intuition tokens on the chef.
Option B: Put one intuition token on the chef (say red for example) and the other (black) on a second choice (say Nun for example).

In Option A one of two things will happen.
A1) Neither intuition is right; neither is the chef. So both psychics will have 3 characters to choose from in round 2.
A2) One is correct and one is wrong. The correct one advances and the wrong one will have 3 characters to choose from in round 2.

In Option B one of three things will happen.
B1) Neither intuition is right. So both psychics will have 3 characters to choose from in round 2.
B2) One is correct and one is wrong. The one that is correct advances but wrong one will have only 2 characters to choose from in round 2. Both their wrong choice and the other psychic's right choice are eliminated.
B3) Both are correct and both advance.

Comparing A1 and B1 you gain the same amount of information.
Comparing A2 and B2, B2 gains more information than A2 suggesting that option B is better.
And only option B has the possibility of B3 where both psychics advance.

Clearly Option B is always better.

Probability Discussed here
One argument against that I somewhat agree with and my comments here
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Andrew Pillow
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
There is a slight error in your evaluation. If you had no information and you couldn't talk to the ghost this would be the best play. This theory works perfectly for a game like Mastermind.

However you get to talk to the Ghost, you don't have to complete the game perfectly to win and you have two clues you think relate to the Chef.

Lets go through Option A again:

Option A: Put both intuition tokens on the chef. You explain your reason for choosing the chef, and which you think is more likely.

In Option A one of two things will happen.
A1) Neither intuition is right; neither is the chef. So both psychics will have 3 characters to choose from in round 2. However the ghost now knows how you think a bit better and hopefully will help round 2.
A2) One is correct and one is wrong. The correct one advances and the wrong one will have 3 characters to choose from in round 2. The ghost is pretty certain how you think and will select cards which make your future choices better.

The same occurs with Option B but we have a 4th scenario which is worse than both of the options in Option A:

B4) You get the non-chef card correct but get the chef card wrong. The ghost thinks they know how you think, but is incorrect. Even with talking the ghost provide you clues, you should get based on your previous non-chef guess and delay you winning the game. Especially if they use if for the first clue each round.

Towards the end of the game however your idea is correct as when you are running out of time, a joint guess doesn't provide the ghost much more information on how to dish out cards, and wasting a turn on getting one investigator to finish isn't as useful as getting two to finish.
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
But the ghost hears your discussion. The ghost knows that you think both are the chef and you are only choosing nun as a second choice to avoid putting both intuition tokens on the same card.

 
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Andrew Pillow
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
I give you that, and maybe for a two player game that is the best play. The Ghost and the investigator are working together and the best way is for them to

For a 3+ game however you have a problem. Alpha Gaming.

Who should change their card, and why? What if the two possibilities are close? What if the other possibility also causes two players to tie. Who changes then?

Now the ghost has to in future worry about other players changing a players answer. Even when an answer would be perfect for the player they give the card. Now this isn't to say that the other players shouldn't work together. But forcing players to change their mind because you are more right than them...? It could cause problems and more importantly, be less fun.
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Jeff Carter
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
rainbowrose wrote:
Comparing A1 and B1 you gain the same amount of information.
Comparing A2 and B2, B2 gains more information than A2 suggesting that option B is better.
And only option B has the possibility of B3 where both psychics advance.

Clearly Option B is always better.

You forgot about probability. Assuming the ghost is semi-competent, the probabilities for A2 would be much higher than A1, whereas if you change to option B, you made B2 and B3 a crapshoot because you have a 50% chance of changing the wrong one and are making your second guess semi-randomly.
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Victor Lesperance
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
Another thought to consider:

If you're arbitrarily flipping a coin to move one of the players off of the chef, you have a 50% chance that you moved the wrong person off.

Had the correct person remained on the chef, (s)he'd be advancing along the track, making all subsequent choices easier for all other players by (hopefully) reducing their option pool for the remainder of the game.

I think your premise is more applicable for people sitting on the final track. I think I did a similar analysis during our forum game a while back. One of the players was despairing of our chances to win. I was pointing out that we could mathematically assure victory if people with the smaller choice pools guessed in such a way as to "assist" those with the larger choice pools. The various interections either guaranteed or almost guaranteed victory.

But as a general rule, yeah, 2 pawns on one target should give the players pause for re-analysis. There's a game theory, of which you're essentially giving an example. At every decision point, you don't promote your best case scenario. You minimize your worst case scenario. In this case, you are playing to minimize your remaining wrong choices for the trailing player, rather than maximizing your chances that the leading player advances...
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
pillinjer wrote:
I give you that, and maybe for a two player game that is the best play. The Ghost and the investigator are working together and the best way is for them to

For a 3+ game however you have a problem. Alpha Gaming.

Who should change their card, and why? What if the two possibilities are close? What if the other possibility also causes two players to tie. Who changes then?

Now the ghost has to in future worry about other players changing a players answer. Even when an answer would be perfect for the player they give the card. Now this isn't to say that the other players shouldn't work together. But forcing players to change their mind because you are more right than them...? It could cause problems and more importantly, be less fun.


I'm saying strategically one should change their vote but if neither decide to do so then that is their decision. If both refuse then they jointly decide to not use this strategy.
 
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
IdleHacker wrote:
rainbowrose wrote:
Comparing A1 and B1 you gain the same amount of information.
Comparing A2 and B2, B2 gains more information than A2 suggesting that option B is better.
And only option B has the possibility of B3 where both psychics advance.

Clearly Option B is always better.

You forgot about probability. Assuming the ghost is semi-competent, the probabilities for A2 would be much higher than A1, whereas if you change to option B, you made B2 and B3 a crapshoot because you have a 50% chance of changing the wrong one and are making your second guess semi-randomly.


I didn't forger probability. I omitted it.

For option A the probabilities in our example are:
A1 6/12 both wrong
A2 6/12 one right

For option B
B1 7/12 both wrong
B2 4/12 one right
B3 1/12 both right
B2 & B3 5/12 at least one right

The probability is a little bit worse for option B but I think that is mitigated by the benefits.

These numbers change with more cards but the difference between A2 and B2+B3 gets smaller.
 
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
vlesperance wrote:
Another thought to consider:

If you're arbitrarily flipping a coin to move one of the players off of the chef, you have a 50% chance that you moved the wrong person off.

Had the correct person remained on the chef, (s)he'd be advancing along the track, making all subsequent choices easier for all other players by (hopefully) reducing their option pool for the remainder of the game.

I think your premise is more applicable for people sitting on the final track. I think I did a similar analysis during our forum game a while back. One of the players was despairing of our chances to win. I was pointing out that we could mathematically assure victory if people with the smaller choice pools guessed in such a way as to "assist" those with the larger choice pools. The various interections either guaranteed or almost guaranteed victory.

But as a general rule, yeah, 2 pawns on one target should give the players pause for re-analysis. There's a game theory, of which you're essentially giving an example. At every decision point, you don't promote your best case scenario. You minimize your worst case scenario. In this case, you are playing to minimize your remaining wrong choices for the trailing player, rather than maximizing your chances that the leading player advances...


If at least one of the psychics has a decent second choice then you are not decreasing the chance of someone advancing nearly as much. But I think you are right that if neither has a decent second choice then perhaps then you would both go on the same card to help improve the change that at least 1 will advance. Also with more psychics, it helps everyone if one player advances as it reduces the number of choices for all who remain behind.

Yours is the first argument that makes me think that in some rare instances, you might be best going on the same card.
 
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Jeff Carter
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
rainbowrose wrote:
The probability is (...) worse for option B but I think that is mitigated by the benefits.

I don't.

...and therefore I also don't think that:
rainbowrose wrote:
Clearly Option B is always better.
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
rainbowrose wrote:
If at least one of the psychics has a decent second choice then you are not decreasing the chance of someone advancing nearly as much. But I think you are right that if neither has a decent second choice then perhaps then you would both go on the same card to help improve the change that at least 1 will advance. Also with more psychics, it helps everyone if one player advances as it reduces the number of choices for all who remain behind.

Yours is the first argument that makes me think that in some rare instances, you might be best going on the same card.

I thought we were talking about when both are "clearly" pointing to the same one since your post said it is ALWAYS better to split them.

I always argue for splitting them when one has a decent second choice.
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
IdleHacker wrote:
[q="rainbowrose"]The probability is (...) worse for option B but I think that is mitigated by the benefits.

I don't.

...and therefore I also don't think that:
rainbowrose wrote:
Clearly Option B is always better.


But the with 9 cards the probabilities are
A2 16/72
B2 and B3 15/72
the difference is less than 1.4%

 
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
IdleHacker wrote:
rainbowrose wrote:
If at least one of the psychics has a decent second choice then you are not decreasing the chance of someone advancing nearly as much. But I think you are right that if neither has a decent second choice then perhaps then you would both go on the same card to help improve the change that at least 1 will advance. Also with more psychics, it helps everyone if one player advances as it reduces the number of choices for all who remain behind.

Yours is the first argument that makes me think that in some rare instances, you might be best going on the same card.

I thought we were talking about when both are "clearly" pointing to the same one since your post said it is ALWAYS better to split them.

I always argue for splitting them when one has a decent second choice.


I've never come across a situation where I didn't think there was a decent second choice for at least one of them. But "decent" is subjective.
 
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
rainbowrose wrote:
But the with 9 cards the probabilities are
A2 16/72
B2 and B3 15/72
the difference is less than 1.4%

I let it slide the first time, but your numbers are if you're picking at random. Since you're getting clues, the chances that one of you is interpreting correctly is a lot higher than both of you being wrong.
 
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
IdleHacker wrote:
rainbowrose wrote:
But the with 9 cards the probabilities are
A2 16/72
B2 and B3 15/72
the difference is less than 1.4%

I let it slide the first time, but your numbers are if you're picking at random. Since you're getting clues, the chances that one of you is interpreting correctly is a lot higher than both of you being wrong.


Yes my numbers are at random. Not sure how to quantify the effect of clues. Maybe you could give it a go.
 
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Jeff Carter
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
rainbowrose wrote:
IdleHacker wrote:
rainbowrose wrote:
But the with 9 cards the probabilities are
A2 16/72
B2 and B3 15/72
the difference is less than 1.4%

I let it slide the first time, but your numbers are if you're picking at random. Since you're getting clues, the chances that one of you is interpreting correctly is a lot higher than both of you being wrong.


Yes my numbers are at random. Not sure how to quantify the effect of clues. Maybe you could give it a go.

Sure, here it is: "better than random." And since you don't know which one to change, B stays with the random numbers, making the difference greater.
 
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
rainbowrose wrote:
IdleHacker wrote:
rainbowrose wrote:
If at least one of the psychics has a decent second choice then you are not decreasing the chance of someone advancing nearly as much. But I think you are right that if neither has a decent second choice then perhaps then you would both go on the same card to help improve the change that at least 1 will advance. Also with more psychics, it helps everyone if one player advances as it reduces the number of choices for all who remain behind.

Yours is the first argument that makes me think that in some rare instances, you might be best going on the same card.

I thought we were talking about when both are "clearly" pointing to the same one since your post said it is ALWAYS better to split them.

I always argue for splitting them when one has a decent second choice.


I've never come across a situation where I didn't think there was a decent second choice for at least one of them. But "decent" is subjective.


More thoughts on this....

Because one of them must not be the chef, then one of them must have a decent second choice no matter how slim it is.

If you aren't sure which one to put on the chef and which to go with a second choice, I recommend that the person who got there vision first go on the chef. The person who got there version later goes with a second choice. The reason is, as ghost, this is how it most likely happened. ...

I had a good vision for chef so I gave the player who has chef their vision. Then I draw back up and get another good vision for chef. But I don't have a good vision for the second psychic. My best card is the second chef clue which has a secondary clue for what I need. This is the best I have and I give it to the second psychic.

If I had both cards in my hand to start, I would have given them both the the player who should guess chef.

And I would not give the first chef clue to the non-chef psychic first off; I only do it in the end as a last ditch effort.
 
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Laura Gerard
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
I wanted to thank everyone for their contributions. Keep them coming.
 
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Re: Is it ever worth it for two psychics to guess the same card? NO! Here is why.
I wouldn't use the word "always" (for reasons I mentioned above), but as a "general rule" I agree with you.

With my forum games, I usually move to a free spot for this very reason. I recall one game where people were sitting on my #1, #2, and #3 picks. So, rather than go with my #4 pick or cause a huge scramble with possibly long reaching bad effects, I joined someone on my #1 pick.

Now, to support your arguement...my #4 pick was the correct one! Doh!
To my defense, every player thought my #1 was spot on, and when that was wrong, thought my #2 was right. And so on.

But the point being, call it a corner case, but I'd never intentionally skip my top 3 guesses and go with #4.
 
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Laura Gerard
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Okay, you have convinced me to change "never" to "almost never".
 
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Martin Lester
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I've only recently played Mysterium (7 player) and was looking for some cluing tips.

One thing missed on these comments. There is an advantage for all other players for 2+ people choosing the same card. One of you is definitely wrong so everyone else can put a wrong token on it guaranteeing they will all get a point on the clairvoyance track (do they get 2 if you are both wrong? Probably not).

Not sure its much of a bonus as you don't get to use it unless you all get to the end.
 
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Dave Rathbun
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wookieontheweb wrote:
There is an advantage for all other players for 2+ people choosing the same card. One of you is definitely wrong so everyone else can put a wrong token on it guaranteeing they will all get a point on the clairvoyance track

If by "it" you mean a person, you're playing correctly. If my "it" you mean on the card, that's not the way it works. Your intuition token has to be assigned to a specific player, not the card in general.

Yes, if two people guess the same card, one of them is guaranteed to be wrong. But you only get credit for a "Wrong" vote if you indicated the proper person.
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