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For Science!!! game scoring

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simons
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In the game I'm working on now, you play a team of scientists trying to escape a dangerous spaceship without getting killed. The only way to score points in by getting your scientists to the escape pods. Not every scientist will make it, and usually it becomes increasingly difficult to escape as time goes on. Points are scored in the following fashion:

-The first scientist to escape is worth 1 point, the second scientist is worth 2 points, the third is worth 3, and so on.
-Each player has a Head Scientist that is worth double.
-There are 2 cards in the game that temporarily boost the number of points you will earn.

So, in other words, each time one of your scientists escapes, every scientist to follow is worth 1 extra point. In playtesting, this tends to make the early game a game of chicken, as scientists approach the pods, but won't go in until they face a moment of death (such as an alien getting too close, or their lab about to explode). To be honest, I kind of like the feeling this creates.

Here is my worry: the first scientist to escape is worth exactly the amount that every other scientist is boosted because of him. I worry that the optimal strategy is to never be the first player to escape, even if it means loosing your scientist. Because of this, I've considered making the first scientist worth 2, the second worth 3, and so on.

My question is how do you figure something like this out? Is the best way just to reverse-judge the playtests? So far I've only recorded this for one game. Is there a mathematical or logical way of doing it? I considered writing a simulation program, but my computer is being buggy right now (unless there is a good way to do it in Excel).

Also, this might be a stupid question, but are you ever allowed to rely on players not playing optimally? (I think I know the question, but want to hear what you think)

simpson
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Joined: 10/22/2008
A gamer's question (asked

A gamer's question (asked from the gamer-side of me):
Why would a scientist be worth more than another? Logically, I guess I can rationalize the Head Scientist being worth more if the game was about collecting/retaining knowledge and the Head Scientist might know more than others thus making him/her more valuable.

But why would the second, third scientist to escape be worth more points than the first? You just shifted the importance of the payoff -- scoring points by surviving to scoring points by surviving in a particular order.

Quote:
but are you ever allowed to rely on players not playing optimally?

If you want to know how a player will react, then look at the payoff first. If its appropriate and present, a player will always go to their top payoff. Let me give you a scenario to describe payoff and its effects:

First Example:
You are in a room with a black box
The black box has a red button on top
The black box presents itself as a game
(Some players will press the button out of curiosity.)

Second Example:
Same room, same black box with red button
The black box has a note
The note states "PRESS BUTTON FOR $5"
(Some players will press the button for the prospect of gain.)

Third Example:
Same room, same black box with red button
The wall behind the black box has a sign
The sign states "DO NOT PRESS BUTTON ITS A BOMB"
(Some players will not press the button based on self-preservation.)

In each example, the game has remained the same black box but you notice how the expected payoff can alter the player's approach to the game. A player now decides if curiosity, want, or self-preservation will be the best payoff for them.

simpson

simons
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simpson wrote:Why would a

simpson wrote:
Why would a scientist be worth more than another?

Basically, the idea is that the scientists are scrambling to do two things before they leave: gather up research they have done, and test hypotheses that that would normally never pass the ethics board (e.g. "Hmmm... I've never seen a death ray up close before, I wonder what the look like when used? Do they kill with a beam of light, or rather..."). I know it might make a little more sense to be worth the number of turns you stay on board, but I kind of like this idea better. The game is going to be kind of tongue-and-cheek, so I don't worry too much about it making complete sense.

And to your second point, I'm not sure if I understand your example. Do you mean to say that the appearance of optimal play is more important than what is actually optimal? I guess my worry is this: lets say in all those situations, I push the red button. Something happens, game over. But what if I want to play again? I'll now know what the red button does.

Redcap
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What do the points represent?

What do the points represent? I mean why are you getting points for saving scientists, and why is the point value on a scientists life worth more at the end of the game instead at the beginning? If this was an actual situation and it was your job to save scientists and you were being paid on how well you did would you be more highly valued for sacrificing your first scientist just so that you could get your head scientist out later in the crisis?

This non-intuitive scoring method might be what is giving you grief. You would never see this value system in the real world so you have people acting very differently then you expect. In order to maintain your progressive- scoring mechanism though, consider the following:

*Ranking the scientists. The more important the scientist the more points you gain for their escape.
*Losing points for having a scientist die, that way no one wants a scientist to die. Also make the lost points the same for any rank of scientist who dies, that way a rank 6 and rank 1 scientist are worth the same minus points if either die.
*Have higher ranked scientists better equipped to deal with danger. For example rank 1 +5 to their roll, rank 2 +4, rank 3+3, etc.

With that simple point system you would see the following happen.
1)People would have incentive to either save their high ranking scientist first to ensure they received the large points, or they will save a low ranking scientist first to ensure that the better skilled scientists last for the more dire crisis.
2)There will be no game of chicken anymore, people will make a made dash to the escape pod every time, just like you would in real life.

Just my two cents.

metzgerism
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What are all of your point

What are all of your point values?

Let's say that you have three scientists on the board for each player, and there are two players. Possible point values are 1-6, points available are 21.

1-3-6 (10) loses to 2-4-5 (11), which means that if you escape first, you must wait at least two pods to escape again to even have a chance at winning.

What if the values are 2-7 (27)? They actually just end up adding one to the value again. 2-4-7 (13) loses to 3-5-6 (14).

I'd say go through likely scenarios in your head, and playtest the ones that seem the best, or are the least broken in your mind.

It seems to me that late-game proportionality is really the kicker here, to I have some ideas for you:

Fibonacci series: 1-1-2-3-5-8-13-21-34-55... (you could start at 2), all proportions hover around the Golden Ratio (http://en.wikipedia.org/wiki/Golden_ratio).

Triangular series: 0-1-3-6-10-15-21-28-36...(you could start at 2, add 2 to every number).

simpson
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Quote:Do you mean to say that

Quote:
Do you mean to say that the appearance of optimal play is more important than what is actually optimal?

Yes. Payoff is really what goes on in the rationalizing mind. The appearance (of optimal play) is much more profound in rationalizing than logic. Take for example the black box scenario...

Rationally, pressing the button is good because; you either get $5, you die (in which case you don't need $5 anyways), or nothing happens. You can rationalize that the money, or risk of life, or risk of effort are all worth the payoff (something happens).

Logically, not pressing the button is the best option as it does not alter your status in any way. You are no better no worse and have risked nothing.

The key thing to know is that the game introduces new payoffs by showing signs, even conflicting signs. This sparks their game decisions. This helps them rationalize what is most important to them and they move forward in the game.

Gamers (since they are people) will rationalize their game decisions rather than logically break them down. Which means, if you present the right payoff for them, they will always go for it. You job as a game designer is to find out the right payoffs for people that play your game.

Quote:
I guess my worry is this: lets say in all those situations, I push the red button. Something happens, game over. But what if I want to play again? I'll now know what the red button does.

Books are the same re-read, movies are the same watched over and over, and chess will always be white vs. black. That doesn't stop people from play even despite their expectations. Do you know if the red button will produce the same result as last time? Would you be willing to find out?

simpson

Lucas.Castro
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Excel File

Hi Simons,

I created a little excel file that can be used to try out different scenarios with 4 players (and with five scientists per player, including the head scientist). Any idea where/how I can uploaded. To give you an idea, this image shows the scenarios that I tested out.

Overall, I think that:

  1. What happens early on is not of major consequence either way, because getting scientists out late (the head scientist especially) is where the big payoff is.
  2. Losing a scientist is somewhat bad early on, quite bad in the mid-game, and horrible in the late-game (given the potential payoff of getting them out during those stages).
  3. If a player sacrifices a scientist because it would give 1 point to him and 1 point to ALL subsequent scientists, he is missing the point: that scientist gave him 1 point per scientist as well (including the first). Losing a scientist seems more costly.

Of course, seeing a few games play out could change things. And there are other complications to the whole problem (events, cards, etc... correct?).

simons
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Thanks for all of the advice.

Thanks for all of the advice. Let's see...

Redcap wrote:
What do the points represent? I mean why are you getting points for saving scientists, and why is the point value on a scientists life worth more at the end of the game instead at the beginning?

In this game, I refer to the points as "Data Points." And it is not your job to save some external group of scientist. Basically, you are the scientists, and it is your job to get as much of your team's research off the space ship before it implodes (I'm thinking of having a flavor text to the effect of, "Remember, your students may be expendable, but their research is not"). The longer a scientist is on the ship, the more of their own research data they are able to save, the more hypotheses they are able to test, and the more interesting observation they can make, all of which will give them an edge next year when they are writing grant proposals.

Again, this is supposed to be kind of tongue-and-cheek. Does this make sense? Or, at least enough sense to work?

Redcap wrote:
2)There will be no game of chicken anymore,

Honestly, I kind of like the game of chicken. Is that necessarily a bad thing? It's kind of a push your luck mechanic, except other players.

simpson wrote:
Gamers (since they are people) will rationalize their game decisions rather than logically break them down

This might be getting off topic at this point, but what makes someone act rational but illogical? Does there just need to be a lack of information (such as the other player decisions)? Can you think of a game that does this?

Lucas and metzgerism, I basically ended up doing a combination of your methods. I found that, as Lucas said, when you get a scientist to escape, it also boosts all of your characters as well. What this means: the only time it will be better to let your first scientist die is if your opponents get more of their scientists to escape than you do. However, it seems near impossible that your first scientist could be worth 1 data point, AND you could have fewer scientists than any other player, AND despite all this you still have as many data points as your top opponent. And I did actually find situations where letting that first scientist die could cost one the game. (although, yes, often it doesn't make a difference)

And Lucas, thanks for the advice. The only thing I would say is that your numbers are a good bit off. In my last game, there were 5 players with 3 scientists each, at the end of the game only 5 had actually escaped. As far as I can tell all your observations are still valid though. And honestly, I like that what happens at the end is more important, at least I think it makes things more exciting (since it keeps it that any player has a chance of winning through to the end).

simpson
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Joined: 10/22/2008
Quote:This might be getting

Quote:
This might be getting off topic at this point, but what makes someone act rational but illogical?

Rational means that you use the information in front of you to act in your own BEST INTEREST. Logical means that you use the information in front of you to come to a PREDICTED CONCLUSION. Similar paths of thought but they often yield vastly different results.

An easy way to remember rational vs. logical is star trek -- the rational mind would be Capt. Kirk (always fighting, willing to cheat, competitive to get the results he wants), the logical mind would be Spock (distant, reflective, sacrifice for the greater good).

Now what makes someone act rational but illogical (i'm assuming erratic or unpredictable?) would be a priority shift. The rational is always seeking priority with his actions leading towards what is most important to him (top priority) at the time. Let's look at an example of how priorities would shift for a person...
=====================
Setup: Europe, during the Arthurian Legends. In the middle of the woods is a dark wizard's tower. A knight has just defeated the wizard and the tower is crumbling around him...

Knight's Priority = self-preservation
Knight's Action = escape the tower

As the knight escapes, huge rocks tumble from the tower's top. He's not sure but he thinks he might have heard a woman screaming...

Knight's Priority = curiosity of environment
Knight's Action = cautiously approach the danger

A princess is trapped on the top floor of the tower!

Knight's Priority = protect others
Knight's Action = rush back into the tower to rescue
=====================

From the example, we can see how quickly a shift in a priority can cause actions, even immediate actions seem to contradict each other. At first the knight runs from the tower, then approaches, then runs right back in. Rationally it makes sense...logically not so much.

Quote:
Does there just need to be a lack of information (such as the other player decisions)?

Short Answer: Yes & No. Not lack of information but more control of how/when a player gets it.

Long Anwser:
Rational/Logical decisions (which is what a player's turn is - he is deciding how to engage the game environment) are all based on information presented to the player. The game environment is constantly spitting out information to the player, as is other players. So, the player is taking the information on two levels - as a gamer (from the game) and as a player (from outside the game).

A game designer can't really control much of the information coming from outside the game but they can control every part of information inside it.

Quote:
Can you think of a game that does this?

Video games make heavy heavy use of information "cues". Players will pickup on these cues as *important info* and adjust their priorities if need be. Examples of info cues; glowing when you are invincible or little chime noises when you collect a gold coin or life bar appears over a mini-boss.

Video games also make heavy use of information masking. A player doesn't see the calculations for most situations (combat resolution, vector clipping for maps, base value of a soldier's gun), seeing instead what is relevant for them to enjoy the game.

For board and card games, you are dealing with more manual player-driven systems that most designers leave wide-open for information-gathering. A small amount of information masking can drastically shift player priorities...

simpson

RobKing
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Joined: 08/11/2009
Might it thus be more logical

Might it thus be more logical to have the score of the scientist based on the number of turns it's on the board. An alternative is to have 'data' scattered around the lab which they have to collect. This could be on every sqaure, to make it more worthwhile. So, do you just get your scientists off as quickly as possible, collecting whatever data you have on the way, and using up all the escape pods, causing problems for others. Or, do you try and collect as much as possible in the hope that the ones you do get off will win you the game.

On players. I think that you can almost always rely on them to play the best move as they see it. If they see the optimal strategy, then they will play that, if they see another strategy which they think is optimal, they they will play that. The only reasons this might not happen is when parents 'go easy' so that their kids get the satisfaction of winning, and beating 'mommy and daddy'. Another option is that players might take a risk, and try out another strategy, just to see how it affects the game. This can actually work, as it forces other players to think, and to question and to possibly change their own strategy.

Another possibility might be a change of scenario. Maybe it's a futuristic extreme sport, the current generation of teenagers standing in the middle of the main road for as long as possible. Or it could be a gameshow, with families competing against each other. Thus you could have granny and baby going slowly to the exits, but being worth loads of points, or whatever.

Just my ideas.

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