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Author Topic: For math geeks  (Read 11003 times)
Jeffrey Straszheim
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Posts: 112


« on: January 04, 2002, 10:29:43 PM »

Here are some statistics I've worked up for Questing Beast.  The first table is the odds per the number of dice rolled.

Code:

==========================================================
Dice   MoV    GM     MoF
  0    0.0  100.0    0.0
  1   16.6   66.6   16.6
  2   30.5   44.4   25.0
  3   42.1   29.6   28.2
  4   51.7   19.7   28.4
  5   59.8   13.1   27.0
  6   66.5    8.7   24.7
  7   72.0    5.8   22.0
  8   76.7    3.9   19.3
  9   80.6    2.6   16.7
  10   83.8    1.7   14.4
  11   86.5    1.1   12.3
  12   88.7    0.7   10.4
  13   90.6    0.5    8.8
  14   92.2    0.3    7.4
  15   93.5    0.2    6.2
  16   94.5    0.1    5.2
  17   95.4    0.1    4.4
  18   96.2    0.0    3.6
  19   96.8    0.0    3.0
  20   97.3    0.0    2.5

Percentage chance of each result type based on dice rolled.

MoV  Player gets a Monologue of Victory.
GM   GM narrates.  Players gets a die.
MoF  Player gets a Monologue of Failure.  Loses all dice.
===========================================================


The next table is the average payoff per roll given n dice bet and k dice from other sources (gifted or from traits).  The top row is dice bet, the left column is dice gifted.  I've added columns for 12 and 20 dice bets, which although not allowed do provide interesting statistics.

Code:

==========================================================================
     0     1     2     3     4     5     6     7     8     9    12    20
 0  1.00  0.50 -0.05 -0.55 -0.94 -1.21 -1.39 -1.48 -1.50 -1.48 -1.24 -0.51
 1  0.66  0.19 -0.26 -0.65 -0.94 -1.14 -1.26 -1.31 -1.31 -1.28 -1.05 -0.43
 2  0.44  0.01 -0.37 -0.67 -0.90 -1.04 -1.12 -1.14 -1.13 -1.09 -0.89 -0.35
 3  0.29 -0.08 -0.40 -0.65 -0.82 -0.92 -0.98 -0.99 -0.97 -0.93 -0.74 -0.30
 4  0.19 -0.13 -0.40 -0.60 -0.73 -0.81 -0.84 -0.84 -0.82 -0.78 -0.62 -0.25
 5  0.13 -0.15 -0.38 -0.54 -0.64 -0.70 -0.72 -0.72 -0.70 -0.66 -0.52 -0.20
==========================================================================


What should be obvious is that by betting over one die from your pool will, on average, lose you dice in the long run.  Betting zero dice is the only way to consistently gain dice.  Betting only one die can give you a gain, but only if gifted two or less.

The negative average payoffs are surprising to me.
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Jeffrey Straszheim
James V. West
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« Reply #1 on: January 05, 2002, 01:11:27 PM »

Interesting.

I knew betting low would produce more chances of winning dice, which is the reason I set it up that way. Betting high will of course always get you the best odds for success.

Several people have pointed out in the past that they find that a bit weird. Gambling higher ought to be riskier, in the sense that its a bigger gamble. But that's not really the point. The point of betting more dice is to help ensure you get creative control over a scene or conflict. Betting low is for gaining dice.

By the way, there would never be an instance where no dice are cast and you still get the Guided Event and the extra die for your Pool. To get the award, you have to make a roll. Even if you roll one die, there is a 1 in 6 chance you'll get a MoV.

I think its funny how this system seems to spark the attention of the mathematical folks when in fact I'm a mathematical lummox :)

Thanks for the breakdowns. Now where's Mike Hall?
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Jeffrey Straszheim
Member

Posts: 112


« Reply #2 on: January 05, 2002, 07:39:51 PM »

One issue comes up, however.  If my math is correct, then on average players will lose dice rather than gain them.  Over the long haul I can see this being an issue.  How has this worked out in playtesting?
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Jeffrey Straszheim
James V. West
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« Reply #3 on: January 05, 2002, 08:58:17 PM »

Playtesting The Pool (same system, minus the MoD) revealed that gambling low often means losing your shirt. I haven't had the opportunity to put the TQB version of the system through the ringer. Because this is such a heavily narrativist game its more difficult to find players who are 1) willing to play it and 2) capable of playing it right.

But its a draft, and I have plenty of time to test it. I don't think I'll need to make any major rules changes (based on The Pool playtesting), but you never know.

Thanks!
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Blake Hutchins
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Posts: 614


« Reply #4 on: January 06, 2002, 07:48:07 PM »

When the X-Games group playtested the Pool, there were a lot of losses, but only one of the players bet a lot of dice (and he lost that one).  Everyone else stayed pretty conservative.  Over a long run story, our expectation was that big gambles would risk losing more dice, and that a player was statistically better off to hoard dice and build up Traits.

Best,

Blake
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Jeffrey Straszheim
Member

Posts: 112


« Reply #5 on: January 07, 2002, 07:41:58 PM »

For fun, I've worked up an alternate set of statistics that seems nice to me.  These haven't been playtested, but I think they would work.  It is based on using a D10 instead of a D6.  Ones are still victory, and tens failure.  I've changed the assumption on how dice are won, which gave a better distribution.  When you get neither an MoV or an MoF (GM narrates), you win all the gift dice and trait dice for your pool.  If there were no gift dice or trait dice you win at least one.  An MoV still entitles you to no extra dice; an MoF loses all dice bet.

For example, if you are playing with a +2 trait, and 2 gift dice, and you bet 3 dice, you roll 7 dice.  A one gives you an MoV, and you keep your 3 dice; a ten (with no one) give you an MoF and you lose the 3 dice; anything else wins you the four dice, plus you keep the three you bet.

Anyhow, here are how the odds work out:

Code:

Dice   MoV    GM     MoF
  1   10.0   80.0   10.0
  2   19.0   64.0   17.0
  3   27.1   51.2   21.7
  4   34.4   41.0   24.6
  5   41.0   32.8   26.3
  6   46.9   26.2   26.9
  7   52.2   21.0   26.9
  8   57.0   16.8   26.3
  9   61.3   13.4   25.3
 10   65.1   10.7   24.1
 11   68.6    8.6   22.8
 12   71.8    6.9   21.4
 13   74.6    5.5   19.9
 14   77.1    4.4   18.5
 15   79.4    3.5   17.1
 16   81.5    2.8   15.7
 17   83.3    2.3   14.4
 18   85.0    1.8   13.2
 19   86.5    1.4   12.1
 20   87.8    1.2   11.0

     1     2     3     4     5     6     7     8     9    10    11    12
 0   0.7   0.3  -0.0  -0.5  -0.9  -1.3  -1.6  -1.8  -2.0  -2.2  -2.3  -2.4
 1   0.5   0.1  -0.2  -0.6  -1.0  -1.3  -1.6  -1.8  -2.0  -2.1  -2.2  -2.2
 2   0.8   0.3  -0.0  -0.5  -0.8  -1.1  -1.4  -1.6  -1.8  -1.9  -2.0  -2.0
 3   1.0   0.5   0.0  -0.3  -0.7  -1.0  -1.3  -1.5  -1.6  -1.7  -1.8  -1.8
 4   1.0   0.5   0.0  -0.3  -0.6  -0.9  -1.2  -1.3  -1.5  -1.6  -1.6  -1.7
 5   1.0   0.5   0.1  -0.2  -0.6  -0.8  -1.1  -1.2  -1.3  -1.4  -1.5  -1.5
 6   1.0   0.5   0.0  -0.2  -0.5  -0.8  -1.0  -1.1  -1.2  -1.3  -1.4  -1.4
 7   0.9   0.4   0.0  -0.2  -0.5  -0.7  -0.9  -1.0  -1.1  -1.2  -1.2  -1.2
 8   0.8   0.4   0.0  -0.2  -0.5  -0.7  -0.8  -0.9  -1.0  -1.1  -1.1  -1.1


As before, the top line of the second table is the dice bet, the left most collumn is the dice from traits and gifts.  The number in the chart is the average payoff per play.

Oh, and a maximum of 8 dice would be allowed from traits and gifts, and a maximum of twelve from the player's pool.
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Jeffrey Straszheim
Ron Edwards
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« Reply #6 on: January 07, 2002, 08:31:02 PM »

Hi there,

I am a big statistician-dude and I absolutely love probability curves in role-playing system design. Understanding them is really crucial.

I said that because discussions of this matter are a bit funky when it comes to the Pool; always have been. That's because it is not the object of play to keep one's Pool as high as possible.

Pool dice aren't hit points, experience points, skill levels, or anything like them ... they are perhaps unique in role-playing mechanics in being valuable only relative to the next at hand. In other words, if your current action (let's call it Action 1) is really important relative to Action 2 (which you have no idea what it will be!), then your Pool dice are "worth losing." But if Action 2 (whatever it might be, emphasis on might) might possibly, possibly be more important than Action 1, then losing those Pool dice is a big problem.

This means one is always trading off the current situation with the next one to face, and this is a "gamble" specifically because that next situation (and hence its importance) is unknown. That's the issue in playing the Pool, and it needs to be understood when checking out the probability curves.

If one takes the attitude that "now is now," and each Action is pretty much worth any other action, then yes, keeping one's Pool as high as possible is the goal, and strategies such as the ones in this thread do apply. But since Action 2 is always unknown, and since it might be overwhelmingly important or trivial relative to Action 1, the decision to conserve or not conserve is based on more than "keep it high" strategizing.

Best,
Ron
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James V. West
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« Reply #7 on: January 07, 2002, 09:07:25 PM »

You know, I actually love it when people get under the hood of The Pool and do stuff to it. Really. Its one of the coolest things I've ever seen happen. I'd like to someday make a booklet featuring the original game, plus all the alternate versions I've seen.

But in the end, I'm still partial to the original game. As Ron pointed out, the flavor of the game really comes out when you don't know what's coming next and you just lost your last die.

This is a good time to note for the record that the system I chose for The Questing Beast was based on specific needs I felt could not reliably be met by The Pool in its pure form. I guess time will tell.

By the way, I'm diving into a new playing group some time this week. I plan to just play for a few sessions, then I hope to start running TQB or just The Pool. Then....Sorcerer! (as soon as it arrives)
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Paul Czege
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« Reply #8 on: January 09, 2002, 07:46:14 AM »

Hey Jeffrey, Ron, James,

The negative average payoffs are surprising to me.

This was certainly borne out for our group when I ran The Pool. Read the "http://indie-rpgs.com/forum/viewtopic.php?t=689&start=0&highlight=thrashing">no islands in the pool" thread in Actual Play for details. It left an amazingly big footprint on game events and player and GM decisions, so much so that we reacted as if the mechanics were broken and tweaked things to increase the rate of dice replenishment to the pools.

That's because it is not the object of play to keep one's Pool as high as possible.

Pool dice aren't hit points, experience points, skill levels, or anything like them ... they are perhaps unique in role-playing mechanics in being valuable only relative to the next at hand. In other words, if your current action (let's call it Action 1) is really important relative to Action 2 (which you have no idea what it will be!), then your Pool dice are "worth losing." But if Action 2 (whatever it might be, emphasis on might) might possibly, possibly be more important than Action 1, then losing those Pool dice is a big problem.


This is a good point. And interestingly, although it was hugely frustrating to the players, the big footprint I mentioned, I'm increasingly becoming a fan of this aspect of The Pool, the mechanics as is. Let me see if I can explain why.

We played Chalk Outlines last night.¹  And in it, players have power over both scene framing and the details of conflict resolution. The way it works is the GM selects the core conflict for a scene from among conflicts the player identified for the character on his sheet, and then asks the player to frame a scene based on that conflict. And when it comes down to a dice roll, the player interprets the result and narrates the outcome. It played out and felt very similar to the last session of the scenario I ran for The Pool. With that game I had experimentally ceded an increasing amount of power over scene framing to the players over the course of the four sessions. And because we had also tweaked the mechanics of the game to increase the rate of dice replenishment to their pools, players were pretty consistently able to take MoV's during that last session. So the session was pretty much a double-whammy of player controlled scene framing and conflict resolution. And I have to say, from the Chalk Outlines experience and from the way we played The Pool, I'm starting to formulate some fairly strong opinions about the right ingredients for really electric narrativism, and that particular combination has been kind of a let down. It's hard for me to pinpoint why exactly, but it's as if the player has too much control over what protagonizes the character. The dice were with Tom during that last session of the scenario, so he took a lot of MoV's, and subsequent to the game has said that he pretty much framed and resolved scenes exactly the way he wanted to during that session. But he and the other players have also all commented that the audience interest component of character protagonism was pretty low for them across the board during that session. I'm coming to think that it's pretty important to character protagonism to have the GM, or at least another player, creating and delivering conflict to the character if you're going to give players power over conflict resolutions. It just hasn't worked for us in situations where players both create and resolve conflicts for their own characters.

Which is why I'm re-assessing the significance of the negative average payoffs to gambling in The Pool. What I did as GM in early sessions of the scenario was to sometimes frame scenes and to sometimes ask players if there was a scene they wanted to have. And sometimes as I was getting ready to frame a scene the player would ask for a different scene and we'd do that instead. It kind of worked to deliver control over the direction of the narrative to the person who felt most strongly about things going a specific way. It worked great. And I'm thinking the negative average payoffs to gambling would achieve a similar dynamic for conflict resolution as players got better settled into managing their pools. As it is, the players behaved like the family dog left for longer than usual, with a larger bowl of food to tide him over for the duration. They consumed it all right away, in one glorious event, with legs trembling. And if they got more, they consumed it all as well. But that's what dogs do because they evolved that way. When you're a scavenger and you find a carcass, you never know how much time you have before another scavenger is going to come and try to take it from you. Directorial power is as rare to an unhappy nascent Narrativist as a meaty carcass all to himself is to a scavenger, and they've evolved the eating habits of a starving scavenger in relation to it. But ultimately, players aren't dogs, and I'm coming to think a negative average payoff might actually be a good thing. I think The Pool's newer mechanic for Trait rolls that deliver a little more power to the player (without penalties for failed rolls) probably nicely mitigates the difficulty of recovery from the valleys of negative average payoff by giving the player a way of flowing dice into the pool. And I'm thinking the resulting system ends up with a nice balance between player scene requesting and conflict outcome determination powers and the GM's scene framing, delivery of conflict, and outcome determination powers, where the negative average payoff works to force player pool management behavior that delivers outcome determination to the GM, and undercuts what otherwise might be a consistent and undesirably deprotagonizing double-whammy of player creation of and resolution of conflict.

Any adjustments to the mechanics like we made that provide too much opportunity for player MoV's should, in retrospect, have been accompanied by a cut back on allowing player scene requests in order to compensate. And The Pool would be much less of what makes it great if that were done to it officially.

Paul

1. Vincent, I'm going to post about our Chalk Outlines game in Actual Play and include this same stuff.
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My Life with Master knows codependence.
And if you're doing anything with your Acts of Evil ashcan license, of course I'm curious and would love to hear about your plans
Ron Edwards
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« Reply #9 on: January 09, 2002, 07:51:43 AM »

Ladies and gentlemen,

I give you Paul Czege. That was a brilliant post.

Best,
Ron
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hardcoremoose
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« Reply #10 on: January 09, 2002, 11:54:19 AM »

Quote
Ladies and gentlemen,

I give you Paul Czege. That was a brilliant post.


Think about how cool I am.  I get to game with him every Monday.

Ego inflating aside, Paul cuts to the very heart of some important stuff.  There's stuff in that post for game designers, for players, and for GMs.  

And here's the question I have:  If the Pool is so well balanced as is, how does TQB's addition of the Monologue of Defeat affect it?  Does it remove too much of the GM's ability to deliver adversity (and protagonism) to the player, causing it to slip back towards the double whammy?  Or does simple preservation of scene framing power keep this from being a problem?  

Note that I'm not just talking about the effect a MoD has on the feel of the game as it's being played, but the actual statistical opportunity for a GM to deliver events to the players, and how that affects the level of player interaction in the game.

- Scott
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Blake Hutchins
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Posts: 614


« Reply #11 on: January 09, 2002, 12:15:13 PM »

Having played The Pool using the MoD, I found this placed plenty of power in the hands of the players, but that they used it to deliver far more conflict than I would have.  Since large dice-pool rolls frequently produced a 1 or a 6, my three players narrated over 50% of the game events.  I didn't find it overused, but the players tended to see the Monologue of Defeat as a critical fumble kind of result.  With further play to refine our technique, I think the feeling of swinging between extremes would even out nicely.

Personally, I loved the MoD, and my players enjoyed it too.

Best,

Blake
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hardcoremoose
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« Reply #12 on: January 09, 2002, 12:50:38 PM »

Blake,

And here I thought James would be the only one to comment on that question.  I had forgotten that you guys used the MoD in your sessions of The Pool.

I'll tell ya', I would've liked it alot better a few months ago.  Paul's ravenous dog metaphor describes me perfectly - things like director's stance were like new toys to me, and I couldn't get enough of them.  But recent experience has shown that much of the joy of roleplaying, much of what makes it a game I think, comes from the synergy of creating stuff with other people.  And without having tried it, it seems to me that the MoD may place too much power in a single players' hands, to the exclusion of all other participants (potentially decreasing their interest in the narrative).

This sounds funny coming from me.  At least two people in the last two weeks have expressed utter disbelief when I say "I think we need to give the GM some more power."  And don't get me wrong; I believe player empowerment is the absolute best way to guarantee player engagement.  But, as engaged as you may be in what's going on in the beautiful little scene your describing, there's nothing guaranteeing the other players (including the GM) will be if they have nothing to do and no way to effect it.  And when the audience isn't engaged, it'll be readily obvious to you, and you'll be left wanting and unsatisfied.

It's a tough line to draw, and I have no idea if the MoD does a good job of it or not.  The play's the thing, and if your players only narrated 50% of the outcomes, I'd say you still had your work cut out for you, which is a good thing.

- Moose
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James V. West
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« Reply #13 on: January 09, 2002, 07:44:48 PM »

What a fantastic exchange of posts. There are so many points in these comments that I want to talk about, and damn it if I don't have the time to do it. This overtime crap is killing me!

Anyway, thanks Paul for that excellent post. Moose is right when he said there's stuff in there for all. And it makes sense to me. I know as a player I like being surprised, and if I had full control over conflicts and resolutions I'd probably not enjoy it as much as I would if the GM or another player were intensifying things for me. Thus the "game" part of rpgs. Its a social activity.

And you guys nailed The Pool perfectly! I remember the night I wrote it I was imagining how it would play out and in that rough imagining I thought the game would have these wild swings from player control to GM control. I like that in a game.

As far as the MoD goes, it seems the only people who have actually used it in play enjoyed it. I have yet to try it out. In TQB, since the only purpose of playing is to write a story (albeit a shared one, at least to a great degree), I felt like more control was needed by players. However, I'm not beyond thinking the game might give too much. I don't know. Finding a good group to play any game with is hard enough...finding one to play TQB with is proving nearly impossible.

More later. Gotta run.
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