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Title: Dice probabilities in the Pool
Post by: Paganini on June 19, 2002, 06:53:10 PM
I took the Pool with me on vacation and tore it apart pretty thourghouly. I see a potential problem with the gambling mechanics, and I wondered if anyone has run into this in actual play.

Before I start, let me say that, yes, I do understand that the Pool is not intended for players who want to milk the system to their best advantage. However, the Pool does make a couple of elementry statements about itself: MoVs are desireable, and maximizing the number of dice you roll will help you get MoVs. If there's an obvious, nearly-certain way to win every time you roll, I can't see how taking advantage of it is cheating... it seems more like a system issue that needs addressing.

To make sure I'm not laboring under a misapprehension here, this is how I understand the mechanics of the Pool:

Whenever a player makes a roll the GM gives him 1 - 3 dice. The player then adds any dice from relevant traits, assuming he can role-play them in. Since traits have a really harsh escalating cost scale they will probably fall into the 0 - 3 range. Finally, the player may gamble up to 9 dice from his Pool. This means that the likely range for rolls in the Pool will be 1 - 15 dice. If any one of those dice rolls a "1" the roll is a success, and the player may either take a MoV, or add 2 (or 1) dice to his pool.

The nature of the MoV and pool mechanics are such that players will want to roll as many dice as possible every roll. The nature of trait purchasing system is such that putting dice into traits is undesireable. The advantage gained from traits is in "staying power." Dice in traits aren't lost when a roll is failed. However, this "staying power" has an up-front cost that is quite serious: The higher the trait the more dice are simply "lost" from your pool. Frex, if you buy a trait level of 2 it costs 4 dice... the payment for "staying power" is that 2 dice are completely lost. The severity of this effect increases radically as the trait rating increases. Frex, a trait rating of 3 loses 6 dice, a trait rating of 4 loses 12 (!) dice.

Because of this, players are best served by putting as many dice into their pools as possible, and gambling the entire thing on every roll. Of course, you can never gamble more than 9 dice, so there's no reason to put more than that in your pool. This leaves you 6 dice to buy some traits with - either (1, 1, 1, 1, 1, 1) or (2, 1, 1).

Four dice in a roll gives you a better than 50% chance of rolling a 1. With nine dice to begin with, plus 1 - 3 dice from the GM and whatever traits you might have, you're going to be rolling around 10 - 15 dice every roll. The odds of failing (rolling no 1s) with this many dice is so ridiculously small it's painfull. You might as well not even roll. Players will be calling for rolls all over the place. They basically have the choice of taking a MoV or extra Pool dice whenever they want.

If they go for MoV's, the GM will be in deep bantha Pooldoo (hehe) if he ever wants to narrate again. If they go for dice, their pools will get so insanely large that they won't even need to worry about bombing out once in a seven year's blue moon. They'll also be able to buy up their traits more or less at will.

I see a potential fix for this problem:

Lower the number of dice that may be gambled from the Pool. Players will always have at least 1 die from the GM. Gambling 3 dice from the pool gives them 4 dice - a better than 50% chance of success. If the character has a relevant trait, the edge will be bosted a bit. This means players will be rolling maybe 8 to 10 dice as a maximum (3 from the GM, 3 from the pool, 2 to 4 from a trait), and usually around 4 to 5. If you want players to have a bit more of an edge you could limit the gambling to 4 dice rather than 3 dice.

To me, though, gambling 3 dice feels just right. The mathematical properties make for much more excitement and variation. The "staying power" of traits is more useful, since you can no longer give yourself a sure win by gambling 9 dice. At the same time, a large pool is still an advantage because it means you have soem dice in reserve... you can lose a few gambled rolls and still be in business.

So, what do you think? Have I got the mechanics right, or is there a fundamental error in my thinking?


Title: Dice probabilities in the Pool
Post by: Paul Czege on June 19, 2002, 07:15:34 PM
Hey Nathan,

Three threads you should read if you haven't:

1) This thread is a discussion of the "thrashing at the bottom of the pool" phenomenon that our group experienced. I seriously considered using four-siders instead of six-siders when our play group was struggling with this issue. Mike Holmes does the math for four-siders on the thread. I rather thought when James clarified Trait rolls that the thrashing problem had been mitigated nicely, but I haven't actually played The Pool since he rewrote the Trait roll text.

2) Prompted by my concern with thrashing, Mike Holmes proposed an alternative he called Anti-Pool. Someone should play this thing.

3) And this is a thread about negative return on investment with The Pool. There's some discussion about why it might be generally a good thing.

Paul


Title: Dice probabilities in the Pool
Post by: Paganini on June 19, 2002, 07:49:05 PM
Quote from: Paul Czege
Three threads you should read if you haven't:


<SLASH>

Paul, I have read those threads. I have to say I really don't understand the "thrashing at the bottom of the Pool" thing. The Pool has a clear and simple theme: "Player Power is a Good Thing (TM)!" The Pool also gives players an obvious way to never, ever, relenquish that power. The key to success in the Pool is to maximize the number of dice that you roll. A player's pool can only be depleted if A) he doesn't put enough dice into it in the first place, or B) if he only bets little pieces of it.

To tell you the truth, this seems outright broken to me.


Title: hmm...
Post by: Buddha Nature on June 19, 2002, 09:25:37 PM
Well it might be numerically "guaranteed," but numerical certainty does not exactly figure into human actions (or reality).

For example, look at the stock market: the _vast_ majority of investors sit on their stocks and rarely buy when there is risk involved.  The numbers might say this is the wrong way to do it, but human nature - fear - says otherwise.

I just rolled 15d6 10 times -> on time I had no ones.  That _one_ time (it was the 7th roll) I am SOL.  I lose it all and I lose it big, I am "thrashing" from then on.  The fact is, there is _always_ a chance that you will lose on a gamble no matter how sure the bet is and people are afraid of losing - whether or not they know the odds.  Not everyone is Han Solo.

The numbers say The Pool is broken, but playtests and human nature says it works just fine.

One other note - it is going to be tough to A) always get a trait figured into a roll and/or B) to always weasel a bunch of dice out of the GM.  If you keep doing well those dice may dry up and you may be left with 9-11 dice, which is even scarier than 15.

-Shane

PS: Take a look into Behavioral Economics for more info on people's actions with numbers and money.

[Edited for "getting dice"]


Title: Dice probabilities in the Pool
Post by: Valamir on June 20, 2002, 07:22:21 AM
Quote
Four dice in a roll gives you a better than 50% chance of rolling a 1. With nine dice to begin with, plus 1 - 3 dice from the GM and whatever traits you might have, you're going to be rolling around 10 - 15 dice every roll. The odds of failing (rolling no 1s) with this many dice is so ridiculously small it's painfull. You might as well not even roll.


I think you are underestimating the odds.

The odds of not rolling a 1 on 1d6 are 5 in 6.  5/6 is is 83%.

The odds of not rolling a 1 on 10d6 are 83%^10 or 16%
The odds of not rolling a 1 on 15d6 are 83%^15 or 6.5%

16% and 6.5% are low, but not "ridiculously small it's painfull. You might as well not even roll"


Becaue the chance to fail is not so tiny as you suggest, the risk of losing everything become something to be scared of.  To protect yourself from this risk there are two choices 1) keep a reserve...which means not rolling as many dice.  This increases you chance of losing dice but eliminates the chance of losing everything.  2) buy higher Traits...this makes it easier to recover from a loss by guarenteeing more fixed dice.  As you point out buying Traits will reduce the number of dice in your pool also.

So there is a snowball effect...the low chance to fail is just high enough to make it a real possibility.  Fear of that possibility provides motivation to do what is essentially equivelent to buying insurance.  

Like insurance you increase you chance to lose something (the premium for the insurance, if you will) but decrease you chance to be wiped out, or increase your chance to rebuild.

So the odds actually work out pretty well.

If there was one change that I'd make to the Pool (at least to try it out)
I'd be tempted to reduce the price on Traits to encourage more use of Traits and more motivation to play within ones niche.  This would also help players get out from the bottom of the pool if they find themselves there.  To balance out the total number of dice rolled I'd either lower the maximum number of dice that can be gambled to 7, or put an absolute cap on the number of dice for any source.


Title: Re: hmm...
Post by: Paganini on June 20, 2002, 07:28:51 AM
Quote from: Buddha Nature
Well it might be numerically "guaranteed," but numerical certainty does not exactly figure into human actions (or reality).


Sounds like it's time for me to get some actual play. You going to be around on monday at the #indie-netgaming IRC channel? Haven't heard from the other guys, so AFAIK they don't have any other plans. Mebbe we could run some Pool.

Quote

I just rolled 15d6 10 times -> on time I had no ones.  That _one_ time (it was the 7th roll) I am SOL.  I lose it all and I lose it big, I am "thrashing" from then on.


You do realise that this sort of test rolling doesn't really mean much at all? Try rolling the dice 1,000 times (or even better, 10,000 times) and see what the results are. Better yet, figure the probabilities out mathematically. (I stopped when I got to 5 dice, because the numbers were getting big.)

Quote

The fact is, there is _always_ a chance that you will lose on a gamble no matter how sure the bet is and people are afraid of losing - whether or not they know the odds.  Not everyone is Han Solo.


Sure, that's always a risk, but it's not as severe as people seem to think. I dunno, maybe it's just easy for me to see this stuff because I've been fiddling with dice mechanics for years. So, okay, maybe you bombed one of your 15 rolls. How many rolls are you going to make in one session? Say maybe you bomb out once every two sessions. If you make a lot of rolls, maybe once in a session.

So what do you do then? Simple. The GM gets directoral power while you build up your pool. Thrashing players have been gambling little tiny amounts of pool dice, then complaining when they run out. But a soon as they get some back they gamble them again - and, of course, lose them. What you have to do is save the dice. It only takes two successful rolls to get 4 dice in your pool. Based on the frequency of rolls above this should probably take around half a game session from a completely empty pool, less if the GM is nice and helps you out with extra dice. If you have a trait you can use, or the GM feels friendly and gives you 2 or 3 dice, you can roll 6-7 dice right there. That's plenty for a success. Six dice gives you a very good chance of success.

Quote

One other note - it is going to be tough to A) always get a trait figured into a roll and/or B) to always weasel a bunch of dice out of the GM.


Yeah, but think about this: You start out with 15 dice. Put 9 of them in your pool, and gamble them all every roll. Give the other 6 to your traits - giving yourself 6 level 1 traits makes it pretty easy to incorporate one of them into your roll. Even if you can't add a trait to your roll, you still get at least 1 die from the GM. You always roll at least 10 dice!

Just for fun I'm going to do the rest of the math beyond 5 dice and get back with some exact numbers.


Title: Re: hmm...
Post by: Paganini on June 20, 2002, 07:29:50 AM
Quote from: Buddha Nature
Well it might be numerically "guaranteed," but numerical certainty does not exactly figure into human actions (or reality).


Sounds like it's time for me to get some actual play. You going to be around on monday at the #indie-netgaming IRC channel? Haven't heard from the other guys, so AFAIK they don't have any other plans. Mebbe we could run some Pool.

Quote

I just rolled 15d6 10 times -> on time I had no ones.  That _one_ time (it was the 7th roll) I am SOL.  I lose it all and I lose it big, I am "thrashing" from then on.


You do realise that this sort of test rolling doesn't really mean much at all? Try rolling the dice 1,000 times (or even better, 10,000 times) and see what the results are. Better yet, figure the probabilities out mathematically. (I stopped when I got to 5 dice, because the numbers were getting big.)

Quote

The fact is, there is _always_ a chance that you will lose on a gamble no matter how sure the bet is and people are afraid of losing - whether or not they know the odds.  Not everyone is Han Solo.


Sure, that's always a risk, but it's not as severe as people seem to think. I dunno, maybe it's just easy for me to see this stuff because I've been fiddling with dice mechanics for years. So, okay, maybe you bombed one of your 15 rolls. How many rolls are you going to make in one session? Say maybe you bomb out once every two sessions. If you make a lot of rolls, maybe once in a session.

So what do you do then? Simple. The GM gets directoral power while you build up your pool. Thrashing players have been gambling little tiny amounts of pool dice, then complaining when they run out. But a soon as they get some back they gamble them again - and, of course, lose them. What you have to do is save the dice. It only takes two successful rolls to get 4 dice in your pool. Based on the frequency of rolls above this should probably take around half a game session from a completely empty pool, less if the GM is nice and helps you out with extra dice. If you have a trait you can use, or the GM feels friendly and gives you 2 or 3 dice, you can roll 6-7 dice right there. That's plenty for a success. Six dice gives you a very good chance of success.

Quote

One other note - it is going to be tough to A) always get a trait figured into a roll and/or B) to always weasel a bunch of dice out of the GM.


Yeah, but think about this: You start out with 15 dice. Put 9 of them in your pool, and gamble them all every roll. Give the other 6 to your traits - giving yourself 6 level 1 traits makes it pretty easy to incorporate one of them into your roll. Even if you can't add a trait to your roll, you still get at least 1 die from the GM. You always roll at least 10 dice!

Just for fun I'm going to do the rest of the math beyond 5 dice and get back with some exact numbers.


Title: Dice probabilities in the Pool
Post by: Paganini on June 20, 2002, 07:52:06 AM
Quote from: Valamir


The odds of not rolling a 1 on 1d6 are 5 in 6.  5/6 is is 83%.
The odds of not rolling a 1 on 10d6 are 83%^10 or 16%
The odds of not rolling a 1 on 15d6 are 83%^15 or 6.5%

16% and 6.5% are low, but not "ridiculously small it's painfull. You might as well not even roll"


<blink> Turn those numbers around for a second. With 10 dice you have an 84% chance of success. With 15 dice you have a 93.5% chance of success! Those are *really* good numbers. With 10 dice it's like saying you have to beat a 16 with a d20. With 15 dice it's like saying that the only way to fail is to roll a natural 20!

There's something else you should keep in mind, also. Let's say that you can make about 8 rolls before bombing out. Everyone of those 8 rolls gives you a choice: take extra dice, or take a MoV. Let's say that you only take MoV's half the time. You've got 4 MoVs, and 8 extra dice! Even if you do lose it all you've got a huge reserve... your net loss is only 1 die!

With these kinds of numbers it's going to take years to deplete your pool! :)

Quote

If there was one change that I'd make to the Pool (at least to try it out)
I'd be tempted to reduce the price on Traits to encourage more use of Traits and more motivation to play within ones niche.  This would also help players get out from the bottom of the pool if they find themselves there.  To balance out the total number of dice rolled I'd either lower the maximum number of dice that can be gambled to 7, or put an absolute cap on the number of dice for any source.


This is more or less the same line I was thinking along earlier. Limiting the number of dice that you can gamble to 3 or 4 gives you better than a 50% chance of success when you're at full power. At the same time, if you lose it all, it only takes a couple of rolls to get back up to full power.

I think that I would remove the "losing dice" element of creating traits. The cost in dice for a trait would simply be the level of that trait. If you wanted, you could put 5 dice into a trait... but it would take 1/3 of your starting pool. Then I would limit the number of dice that may be gambled to 3.

This would do two things: The first one is that it emphasizes traits over the pool. Since no dice are lost when you buy traits, there's no reason not to put dice into them. They have staying power... they're more or less "the safest investment." However, you can only use one trait at a time, so you're still going to want to have pool dice to boost your traits with. The pool will still be important, it just won't break the game. If you lose your gambled dice, it won't be incredibly difficult to get them back. Since the numer of dice is limited, you won't be winning every single roll, either.


Title: Re: hmm...
Post by: Michael Bowman on June 20, 2002, 02:12:05 PM
Quote from: Paganini
So, okay, maybe you bombed one of your 15 rolls. How many rolls are you going to make in one session? Say maybe you bomb out once every two sessions. If you make a lot of rolls, maybe once in a session.

So what do you do then? Simple. The GM gets directoral power while you build up your pool. Thrashing players have been gambling little tiny amounts of pool dice, then complaining when they run out. But a soon as they get some back they gamble them again - and, of course, lose them. What you have to do is save the dice. It only takes two successful rolls to get 4 dice in your pool.


But you forget, the point of rolling in The Pool is not to gain more dice, it's to narrate MoVs. What if I want to gain an MoV in those early rolls? Obviously I'll gamble what I have to get a better chance to do so.

My actions in the game will not be government by mathematics, but by how badly I want an MoV when I roll those dice.

Michael


Title: Dice probabilities in the Pool
Post by: Ron Edwards on June 20, 2002, 02:24:28 PM
Hey,

Michael is absolutely right. One of the keys in the dialogue between Mike Holmes and myself, and it's a key that people always miss somehow until they play the game, is that not all rolls are equal. One cares about some of them more than others. Hence, playing the odds in order to gain the broadest range of successful rolls is not as important as playing the odds in order to gain a particular successful roll.

When playing The Pool, every roll, one must ask, is this scene a big payoff? Is this the time when I do go for the best odds? Or is this one that I don't want to lose out on, so I'll play it safer, so I'll be better off for a big-ass roll when it comes?

Again, until one plays the game, the facts that rolls apply to whole conflicts (rather than actions) and that not all conflicts are equally emotionally important, are crucial to decisions about dice to roll. That throws the "always gamble" rule of thumb straight into the wastebasket.

Best,
Ron


Title: Re: hmm...
Post by: Paganini on June 20, 2002, 02:25:20 PM
Quote from: Michael Bowman

But you forget, the point of rolling in The Pool is not to gain more dice, it's to narrate MoVs. What if I want to gain an MoV in those early rolls? Obviously I'll gamble what I have to get a better chance to do so.

My actions in the game will not be government by mathematics, but by how badly I want an MoV when I roll those dice.


Right. And the mechanics of the Pool are easy to mainpulate so that you have an 85% to 95% chance of getting a MoV on every roll.


Title: Dice probabilities in the Pool
Post by: Mike Holmes on June 20, 2002, 09:35:48 PM
You can't get a 95%, Nathan, that would require sixteen dice. I'm not sure that even fifteen is legal. 8 from pool, 3 from trait, 3 from GM who is being nice, I get fourteen max. Maybe I'm using old rules. Keep in mind that there are different versions, and some previous arguments were made when, for example, you only got one die back on a refused MOV.

Let's say you can roll fifteen consistently somehow. Would you believe that the chance Shane had to accomplish the task of rolling a failure in seven rolls was 37.5%. That's seven rolls or less. Or in other words given three people trying the same test it was most likely that one of them would have this result or one that was even earlier. Not at all what I'd call unlikely. In fact at ten dice, much more reliablly obtained, there is a fifty percent chance of failing by the fourth roll or before (do the math yourself, .85 ^ 4). If you do your alternating tactic there, you'll still end up losing out more than half the time.

And as posted, this all fails to account for human nature, and the vagaries of the nature of each encounter.

So I can't support your findings, Nathan; if you got them from me, you misread me. My point has always been  that, barring great luck, all strategies will fail eventually in the Pool. The only way to not lose dice is not to gamble them. In any case, whatever strategy you try, in the end, it just ends up being an effect on the story line. Even if you play the worst strategy you can concieve, that still can make for a great story. So the system is far from broken.

As soon as people disregard the idea that The Pool is at all supportive of Gamist play, and see how supportive it is of Narrativist play, the sooner we can get past this math problem.

Mike


Title: Dice probabilities in the Pool
Post by: Valamir on June 21, 2002, 05:06:57 AM
Quote
My point has always been that, barring great luck, all strategies will fail eventually in the Pool.


That's a great way to put it.  And actually provides people who realize it with good incentive to go for Traits which they can never lose, than a big early dice pool which they inevitably will...


Title: Dice probabilities in the Pool
Post by: James V. West on July 01, 2002, 06:56:52 PM
Hey, everyone!

This is friggin great thread. I love the fact that The Pool sparks this kind of debate. Well, to be honest, I wish the debate could get past the math at times (as Mike put it). But still, fun stuff.

Just a few quick thougts:

I have thought of altering the costs of Traits, and in fact I'm implementing the changes in The Questing Beast based on a suggestion by Mike. But I'm still not quite ready to make any serious changes to The Pool itself.

I absolutely love Mikes statement here: "all strategies will fail eventually in the Pool.". That's classic. Of course, he does give the disclaimer "barring great luck". In my experiences playing the game, luck (blind, dumb, and unmotivated by any higher powers) is the single most powerful element of a session.

The numbers. I still don't get into them. Math was never my strong suit. All I know is that when the dice are thrown, you can never friggin tell what's going to happen. I've seen players win on a roll of just 2 dice. I've seen them blow the whole wad and lose. And both instances happen all the time.

The Pool is about weighing the importance of every scene against what might come next as Ron (sort of) put it.

Now, what people might be most interested in seeing happen is for me to get the shit all lined out real nice and neat-like, huh? It's been a crazy roller-coaster ride of creativity this year, but I'm giving it my best shot!

Please take care of yourselves, and thanks so much!

James V. West
www.randomordercreations.com


Title: Dice probabilities in the Pool
Post by: Paganini on July 01, 2002, 07:42:41 PM
Quote from: James V. West

Now, what people might be most interested in seeing happen is for me to get the shit all lined out real nice and neat-like, huh? It's been a crazy roller-coaster ride of creativity this year, but I'm giving it my best shot!


Yes, James! I want an "official" Pool. In spite of how I might have come across in this thread, I *love* the Pool. I'm seeing problems with the numbers (which people are saying don't bear out during play), but man, the idea of the game rocks.


Title: Dice probabilities in the Pool
Post by: Paganini on July 01, 2002, 09:16:23 PM
I finall got around to running those numbers:

Code:

Dice    Percentage
----    ----------
  1     16.67% (17%)
  2     30.56% (31%)
  3     42.13% (42%)
  4     51.77% (52%)
  5     59.81% (60%)
  6     66.51% (67%)
  7     72.09% (72%)
  8     76.74% (77%)
  9     80.62% (81%)
 10     83.85% (84%)
 11     86.54% (87%)
 12     88.78% (89%)
 13     90.65% (91%)
 14     92.21% (92%)
 15     93.51% (94%)


Not actually as bad as I thought. (Cue 'I-told-you-so' from Mike.) Although, it is a bit worse than some made it out to be. (Cue 'I-told-you-so' from Pag. :)

Assuming you do what I said you did (9 dice in the Pool, gamble them all every time). Worst case: you roll 10 dice (if the GM only gives you 1, and you don't have any traits). You can figure that you'll make about 8 rolls before you fail. When you fail, you lose your entire pool. Now, I'm assuming that you're not going to take a MoV on every one of those 8 successes (anyone who is aware of this line of reasoning will make sure that he doesn't!). Let's say that you take 4 MoVs (which means that you're exercising directoral power 1/2 the time that you make rolls). This seems like plenty to cover personally important scenes. So, when you fail your roll, you've built up around 8 reserve dice in your pool to gamble. The odds are that you will get *another* 7 or 8 rolls before you fail. Let's say you fail on the 7th roll, and you have 6 reserve dice in your pool. You're still not going to fail for another 6 or 7 rolls.

It evens out right around here. With 6 dice in your pool you can expect to make around 6 rolls before you fail. If you take dice from three of those rolls, you've maintained your status. This is assuming that the GM *never* gives you more than a single die, and it's assuming that you have *no* traits to use. So, in other words, these are worst case numbers.

OTOH, if you decide to take a MoV every time, then it gets very bad. After around 6 rolls you start to thrash.

So, basically, this post is a line of reasoning with this conclusion: never have fewer than 6 extra dice in your pool, if you can help it. People have been saying "yeah, but this isn't how the Pool is played." The point I'm making is that, if you understand the numbers, this is *exactly* how the Pool *must* be played. There's no reason to ever play it differently. The Pool is primarily a resource that determines *player* effectiveness... it's designed that way. The more you have, the more effective you are. If said resource was unimportant, people wouldn't complain about thrashing. So, if you don't want to thrash, keep an eye on the numbers. It's easy to keep from thrashing, all you have to do is leave a certain amount of directoral control with the GM.


Title: Dice probabilities in the Pool
Post by: Valamir on July 02, 2002, 06:52:39 AM
definitely a case for going back to 1 die per passed up MOV instead of 2.


Title: Dice probabilities in the Pool
Post by: Paganini on July 02, 2002, 07:41:41 AM
Quote from: Valamir
definitely a case for going back to 1 die per passed up MOV instead of 2.


Good point, Valamir. That would change things drasticaly. That might just be the solution.


Title: Dice probabilities in the Pool
Post by: Ron Edwards on July 02, 2002, 09:56:42 AM
Hey,

I always liked the one-die rule better.

Best,
Ron


Title: Dice probabilities in the Pool
Post by: hardcoremoose on July 02, 2002, 11:23:08 AM
No fair to bust on James when he's out to lunch, but I liked the one-die rule better as well.  There was a simple elegance to it, which was the hallmark of The Pool in general.

And is one of the reasons I never really dug the MoD.  But that's just my personal cross...

- Scott


Title: Dice probabilities in the Pool
Post by: Mike Holmes on July 02, 2002, 12:47:50 PM
Quote from: Paganini

Assuming you do what I said you did (9 dice in the Pool, gamble them all every time). Worst case: you roll 10 dice (if the GM only gives you 1, and you don't have any traits). You can figure that you'll make about 8 rolls before you fail.


No, no, no, no, no. I refuted this before. Everyone makes that superstitious assumption that you'll roll on average 8 times before you Fail. Actually there are two problems here. Even if you were exepcted to always get through a full set of rolls before failing (which you are not) your math would be off. At 84% that logic would give you one in 6 failure. One in 8 would be 87.5%.

In any case, the fallacy is that your assumption is about expected value. That is, yes, it is true that if you roll the ten dice six times that you'll likely get one failure somewhere in that set of rolls. But it says nothing about where you are likely to fail. It is as likely that the failure will occur on the first roll as the last. So what are the odds? The chart below shows the chance that you have starting out of getting past a certain number of rolls using a certain number of dice.

Code:
     Dice
Rolls 10       11       12       13       14
1     83.85%   86.54%   88.78%   90.65%   92.21%
2     70.31%   74.89%   78.82%   82.17%   85.03%
3     58.95%   64.81%   69.98%   74.49%   78.40%
4     49.43%   56.09%   62.12%   67.53%   72.30%
5     41.45%   48.54%   55.15%   61.21%   66.66%
6     34.76%   42.01%   48.97%   55.49%   61.47%
7     29.14%   36.35%   43.47%   50.30%   56.68%
8     24.44%   31.46%   38.59%   45.60%   52.27%
9     20.49%   27.22%   34.26%   41.33%   48.20%
10    17.18%   23.56%   30.42%   37.47%   44.44%


You'll note that even at 14 dice that it's even odds that the character will fail at some point before 9 rolls. At ten dice the same can be said of just 4 rolls. And only a 24.44% chance of actually getting to 8 rolls. Not something I'd count on.

Do you see the problem? If you don't believe me try rolling a d6 and try to get to six rolls without getting a 1. Very similar to the 10 chart above. You'll find you only do it about one in three times. The rest of the time you fail at some point earlier than that. Not what I'd call a winning strategy. Then again, as I point out, the only winning strategy is to risk no dice.

I can get much more in depth with this too. This all says nothing about the game theory of continuing odds, and expected rewards. For example, if you look at it from an expected reward view point, then one die is your best bet in all cases. That is, assuming that a win is worth 2 dice at least (as you can use it as that), then the risk of 1 die to 2 dice won tips the scale well versus 9 to 2 (from between a two to one ratio with few additional dice to a four to one ratio). It's not even close; of course by that ratio, risking no dice is a huge advantage. Many gamblers play these sorts of odds.

In any case, I'd suggest playing it and seeing what happens. No use speculating what sorts of strategies it will produce until you actually play.

Mike


Title: Dice probabilities in the Pool
Post by: Jeffrey Straszheim on July 02, 2002, 02:29:46 PM
There are two situations that I want to avoid

    That a player will flounder around too long with an empty pool
    after a big hose

    That a player will find a "winning" strategy that will allow them to
    bet lots of dice, but win dice enough to keep growing their pool.
    This would reward an "always bet lots of dice" strategy that I think
    would be bad.
    [/list:u]

    Now, I ran a simple simulation that rolled dice.  I found that if a
    player followed a strategy of always betting their entire pool (or 9
    dice), and always took the bonus dice, the following happened:

    If they received 3 dice from gifts and/or traits, then with a two dice
    reward their pool would eventually grow unbounded.  With only one
    reward die, it would fluctuate, but often grew into triple digits
    before it came back down.

    If they consistently received 5 gift/trait dice (assume an experienced
    character with large traits), then both the single and two dice
    options quickly grew unbounded.
    [/list:u]

    I think this is undesirable because it can reward an uninteresting
    strategy (always bet hight).  Obviously a character's taking MOV's
    would lessen the effect, but not eliminate it for a character skilled
    at probability.

    I would suggest a cap on the size of the pool to counteract this problem.

    As a side note, a tried a strategy that rewards dice based on the
    current size of the pool.  I used this scheme

Code:

empty pool   :  3 dice
1 - 9 dice   : 2 dice
10 - 15 dice : 1 die
16 + dice    : none


The advantage here is that the pool stays capped, so that it cannot
run away, but also players who are hosed will not flounder around with
zero dice for too long.


Title: Dice probabilities in the Pool
Post by: Paganini on July 02, 2002, 05:46:54 PM
Mike, you're right... darn it! (Note to self: always use calculator!)

However, the main point I was making still stands... it doesn't matter how soon you fail if you can replenish your pool before doing so.

[edit: That is, if you know you're going to fail sometime in the first 8 rolls, then you're going to do your darndest to make sure that you minimize the consequences of that failure. You're going to take dice instead of MoVs until you have enough backup dice in your pool not to worry about it. If you can get as many or more dice into your pool by doing so failure is trivialized. Standard thinking assumes that the failure will come in the middle of the tries you make. (That is, if you're brute-forcing a crypto system with 100 keys in a random order, you assume that you'll have the correct key after about 50 tries.) So, if you've got 8 to 1 odds, statisticaly, yes, that one failure could occur on any of your nine rolls. But for the purpose of strategy you can assume that you'll get at least 3, possibly 4 rolls before failing. With the current rules, that means 6 - 8 dice added to your pool. Like I outlined below, this ability to regenerate is not trivial. It will effect your approach to deciding whether to take dice or MoVs. So, summary: I like the one-die option better than the two-die option. :)]

Stimuli, You pretty much nailed it from my perspective. I don't think your proposed fix fits with the philosophy of the Pool though. Two points: The number of dice that you can gamble is already limited to 9. From your post I'm not sure you took that into account. The other thing is, if you can only get one die back from a successful roll, things are much different.

So, anyway, Mike, I disagree with you when you talk about the pool not being Gamist. Or rather, I see it as a bit of a non sequitir. The Pool gives you a resource, and it makes it valuable. This encourages skillful management of the resource, *without* implying any sort of inter-player competition.  If a way exists to maximize returns, then there is absolutely no reason not to take advantage of it. The design of the system encourages this sort of thinking: "How can I use my dice most effectively?" Not "more effectively than everyone else," just "how can I get the most out of them?" They're a resource... that's what they're for. :)

What it comes down to, IMO, is how much you want to risk on a "put up or shut up" basis. How much are you willing to risk in order to gain an extra die or a MoV? In order for the game to work this has to be meaningful - you have to be able to evaluate the worth of the rewards and weigh their value against the value of the stakes.

This is why the system is so cool... on the one hand you have a resource (dice) that can be quantitatively evaluated. On the other hand, you have a resource (directoral control in the form of MoVs) that can not be objectively quantified. The player has to decide how much risk a MoV is worth in terms of the quantifiable component of the system.[\i] You can't just say "oh, I think a MoV here is worth three dice to me." You have to decide what your reward dice are worth in terms of success chances (which correspond directly to the reward dice you would get by forfeiting a MoV). Consider this:

Quote from: Mike

For example, if you look at it from an expected reward view point, then one die is your best bet in all cases. That is, assuming that a win is worth 2 dice at least (as you can use it as that), then the risk of 1 die to 2 dice won tips the scale well versus 9 to 2 (from between a two to one ratio with few additional dice to a four to one ratio).


This isn't true *unless* your chance of success is 50%. If you have an 80% chance of success (8 dice from the pool, plus 1 die from the GM), then the odds are 4 to 1 in favor of success. So risking 8 dice against 2 dice is fair odds. So the question then becomes, how does the MoV you stand to get compare to the 2 dice that you'll have to give up. It will depend on your reserve dice, and on how badly you want the MoV. :)


Title: Dice probabilities in the Pool
Post by: Jeffrey Straszheim on July 03, 2002, 05:01:47 AM
Quote

 Stimuli, You pretty much nailed it from my perspective. I don't think your proposed fix fits with the philosophy of the Pool though. Two points: The number of dice that you can gamble is already limited to 9. From your post I'm not sure you took that into account. The other thing is, if you can only get one die back from a successful roll, things are much different.


I did, in fact, use the 9 die limit in my tests; and using 1 die did help.  But it was still possible to build up pools in the triple digits, which would allow for gratuitous trait purchases, which in turn would only worsen the problem.


Title: Dice probabilities in the Pool
Post by: Paganini on July 03, 2002, 06:19:31 AM
Quote from: stimuli

I did, in fact, use the 9 die limit in my tests; and using 1 die did help.  But it was still possible to build up pools in the triple digits, which would allow for gratuitous trait purchases, which in turn would only worsen the problem.


Hmm. Next question. Did you take the reward die after every success, or did you account for some MoVs in there? I suggest taking the reward die every other time.


Title: Dice probabilities in the Pool
Post by: Mike Holmes on July 03, 2002, 06:37:18 AM
OK, first Nathan, using your strategy, you will not often have MOVs. Which would be really boring. Sure, you can do it, but since you can't spend these points on a porsche, it seems silly to hoard them. In play, you are probably going to want to take an MoV from time to time. If you want to play it as a Gamist exercise where you are just trying to accumulate points, you can "win" going home with the most points at the end of the night (heck, you can just roll your base dice and gamble nothing, and most certainly increase in points). But that's hardly the point of play in The Pool. Ron pointed this out before, and you have yet to rebut in any way.

The converse argument is also true. That is, given that you cannot buy a porsche with the points, what's the downside to having a small pool? The character has a period of negative results that he has to sort of climb back from. Isn't that good for making a story? Isn't failure an important part of Protagonism? Do you really want your character to succeed all the time? If so, then, once again, you miss the point of the game. What changing strategies does for you is to alter the flow of the game back and forth. Which could be fun (a lot more fun than a game about accumulating dice from rolling them).

Both you and Jeff are also assuming an enormous number of rolls, as well. What if there are six rolls per game for your character, and the game goes for only six sessions. Sounds about right. You'll never grow to triple digits because the story won't last that long. If you won every roll and never took an MoV you'd only have 72 dice; at which point the story would be over. You are going to squander the vast majority of your rolls on successes without MoVs. Let's say you take one in eight as MoVs to keep your pool high. That gives you maybe one a session, and only four in the character's whole existence. And in order to keep the strategy you must at times forgo the MoV when you might really want to take one.

Your arguments about when you expect to come across a random event are just wrong, Nathan. You do not assume half. You run a limit summation based on the odds of the original chance that it happens each try. Again, this is more voodoo statistics. In any case, such an argument does not allow for waht happens if the odds happen to go against you. Wherin you have to resort to other strategies. So you can start out with such strategies, but the game might just not allow you to use them (the obvious example is what do you do if you fail that first roll, and go straight to the bottom?).

Again, you refuse to actually play and see what happens. If you did it might change your opinion. I defer to Ron who has played. This is not D&D, its not about acumulating dice. It's a Narrativist system. Yes, if you play it Gamist, it will suck. So don't do that.

Mike


Title: Dice probabilities in the Pool
Post by: Jeffrey Straszheim on July 03, 2002, 06:52:16 AM
Quote from: Paganini

Hmm. Next question. Did you take the reward die after every success, or did you account for some MoVs in there? I suggest taking the reward die every other time.


No, I assumed they always took the reward.  What I wanted to find out was if it was possible for a pool explosion.  Now, assuming the cusp between bounded and unbounded behavior is rather narrow (which I haven't checked, but is the norm for such recursive functions) there will be some fraction where the player can take MoV's and still get the unbounded behavior.  I'm not sure where this lies, but it wouldn't be too hard to find.


Title: Dice probabilities in the Pool
Post by: Mike Holmes on July 03, 2002, 07:13:35 AM
Quote from: stimuli
No, I assumed they always took the reward.  What I wanted to find out was if it was possible for a pool explosion.  Now, assuming the cusp between bounded and unbounded behavior is rather narrow (which I haven't checked, but is the norm for such recursive functions) there will be some fraction where the player can take MoV's and still get the unbounded behavior.  I'm not sure where this lies, but it wouldn't be too hard to find.


I totally agree. The point is that the point of taking MoVs is far enough apart that it's not a very interesting stratey to play. It assumes that charcter success is the only thing a player wants, and that the Gm will not be able to tempt them into taking MoVs more often. Something that's impossible to calculate.

Mike


Title: Dice probabilities in the Pool
Post by: Jeffrey Straszheim on July 03, 2002, 07:23:33 AM
Quote from: Mike Holmes

OK, first Nathan, using your strategy, you will not often have MOVs. Which would be really boring. Sure, you can do it, but since you can't spend these points on a porsche, it seems silly to hoard them. In play, you are probably going to want to take an MoV from time to time. If you want to play it as a Gamist exercise where you are just trying to accumulate points, you can "win" going home with the most points at the end of the night (heck, you can just roll your base dice and gamble nothing, and most certainly increase in points). But that's hardly the point of play in The Pool. Ron pointed this out before, and you have yet to rebut in any way.


Speaking for myself, my only goal was to discover whether is was possible to abuse the system.  Also, I'm interested in finding a good balance between slow pool growth, and a statistical explosion.  I doubt there is a perfect balance, but it is worth knowing the tradeoffs.


Quote from: Mike Holmes

Both you and Jeff are also assuming an enormous number of rolls, as well. What if there are six rolls per game for your character, and the game goes for only six sessions. Sounds about right. You'll never grow to triple digits because the story won't last that long. If you won every roll and never took an MoV you'd only have 72 dice; at which point the story would be over. You are going to squander the vast majority of your rolls on successes without MoVs. Let's say you take one in eight as MoVs to keep your pool high. That gives you maybe one a session, and only four in the character's whole existence. And in order to keep the strategy you must at times forgo the MoV when you might really want to take one.


But who says the game should only go for six sessions?  Who says there will only be a few rolls?  It is certainly possible for a player to choose to roll very often.  And it might all seem perfectly valid while it's happening.


Quote from: Mike Holmes

Again, you refuse to actually play and see what happens. If you did it might change your opinion. I defer to Ron who has played. This is not D&D, its not about acumulating dice. It's a Narrativist system. Yes, if you play it Gamist, it will suck. So don't do that.


I know you weren't talking to me here; however, I'll respond anyhow.  I have played The Pool and found it a profoundly interesting system.  We played a very short game, and never ran into any pool explosions.  In fact, we had quite the opposite problem; players who'd lost their pool ended up floundering around with no dice for too long.  This was not fun.  We were, at the time, using the single die reward system.

I am still concerned, however.  I think the system can, over longer term play, reward some undesirable strategies.  The fact that we all agree (I think we do) that these strategies aren't the best way to play doesn't stop that they are rewarded.  I wonder if there aren't some small tweaks that can be made to mitigate this problem?

It occurs to me that there, perhaps, shouldn't be one single According-to-Hoyle The Pool.  Just as James tweaked the resolution mechanic in QB to make the flow more predictable, I believe that perhaps some aspects of The Pool (as a generic entity) can be tweaked by various play groups to match the flow they desire.  I'm thinking of such aspect as
    The number of reward dice
    The presence or absence of a MoD
    The cost for traits
    ... and so forth ...
    [/list:u]
    but it seems I'm drifting from the topic.


Title: Dice probabilities in the Pool
Post by: Paganini on July 03, 2002, 08:33:03 AM
[Note: This message was originaly posted by accident... so I'm clearing it out and using to append something I forgot in my other post. :)]

Mike, I forgot to mention that my comments about expecting results were not "just plain wrong." As I said, what I described is a *common method.* I've seen it in many texts, including several of notable authorship (for example, Bruce Schnier's Applied Cryptography). I'm sure that there are more accurate and more complex methods of prediction. Citing the exitence of such, however, in no way detracts from the validity of my point.


Title: Dice probabilities in the Pool
Post by: Paganini on July 03, 2002, 08:51:08 AM
I'm feeling that you've missed the point of the game, and this thread, Mike. Let me say it right now in big, blod letters:

I do not think the Pool is a Gamist game.

Satisfied?

Now, let me back that up: The Pool is not a Gamist game, because it is *not* about competition of any sort. However, it *is* about player effectiveness. You asked: "Do you really want the character to succeed all the time?" For the Pool, the answer is, "who cares?" The Pool is not about character success, it's about *player* success. James has even said that in another thread, IIRC. The answer is, yes, if you're a player, you want to succeed all the time. Success is your goal, as defined by the system itself. If you win rolls, you get a MoV or extra dice - desireable rewards. If you lose rolls, you lose dice and story power.

What does success entail in a narrativist game? It's not "winning a contest with other players," it's "influencing or controling on the story." Your pool is the means to that end. No one here is talking about "hoarding" dice. The point I've been making all along is that if you can bloat your pool up to 60 dice you don't have to worry. You can take a MoV whenever you want, you can buy whatever traits you want. You *own* the game.

So, in the Pool, buying a porcshe is exactly what you *can* do with accumulated dice, in an in-game sense. The player's pool is an exact measure of his effectiveness... Whatever a porsche happens to be in the game in question, if you get enough dice in your pool you can have it.

Now, a couple of places where it seems you've misunderstood what I was saying:

Quote from: Mike Holmes
OK, first Nathan, using your strategy, you will not often have MOVs.


No, Mike, you'll have MoVs exactly half the time that you succeed. I ran the 30,000 roll test about 10 times, tracking minimum and maximum values for the pool. On success I alternated between MoVs and reward dice.

With +2 reward dice and 30,000 rolls, the pool often rises to 60+ dice.

With only +1 reward die, the numbers are much more reasonable. The highest pool was 20 dice.

Since you were complaining about the number of rolls that we've been using I also ran the test using 36 rolls. With +2 reward dice, the pool still climbs significantly, up to 25 dice. With only +1 reward die, it tends to hover right around where it starts.

Quote from: Mike Holmes

In play, you are probably going to want to take an MoV from time to time. If you want to play it as a Gamist exercise where you are just trying to accumulate points, you can "win" going home with the most points at the end of the night (heck, you can just roll your base dice and gamble nothing, and most certainly increase in points). But that's hardly the point of play in The Pool. Ron pointed this out before, and you have yet to rebut in any way.


Well, no I haven't. There was quite a bit in my last post devoted to that subject. Please reread this section from my previous post:

Quote from: Paganini

So, anyway, Mike, I disagree with you when you talk about the pool not being Gamist. Or rather, I see it as a bit of a non sequitir. The Pool gives you a resource, and it makes it valuable. This encourages skillful management of the resource, *without* implying any sort of inter-player competition. If a way exists to maximize returns, then there is absolutely no reason not to take advantage of it. In fact, the design of the system encourages this sort of thinking: "How can I use my dice most effectively?" Not "more effectively than everyone else," just "how can I get the most out of them?" They're a resource... that's what they're for. :)


Title: Dice probabilities in the Pool
Post by: James V. West on July 05, 2002, 03:16:26 AM
I regret I haven't been able to devote more time and energy to playtesting so that I can respond to some of the statistical predictions with real experience.

I find it very difficult to concive a group playing the same characters long enough to run into a bloated pool scenario. Certainly never in the 30,000 rolls range. I average 4-6 rolls per session in my games so far (usually around 3 hours of playing).

Although I can understand the concern for abuse, I don't think it is necessary to mitigate the potential for it by adding any new rules. I like to think that people can police their own actions.

Once you start playing I doubt you'd want to horde dice and give up your story power. Plus, as it has already been expressed, you don't start with a slew of dice, just a few. Its very difficult to build them up significantly. It seems to me you'd have to play a very boring strategy in order to do it--something I'd have a hard time with as a GM.

I want the rules to express that a "success" for the player means the ball is in his court, whereas a "failure" puts it back in the GMs court. Nothing more or less. If you opt out of a MoV, you essentially put that ball back into the GM's court. I can't imagine someone having so little interest in the story that's happening to their character that they would give up MoVs regularly for dice--unless their pool was dangerously low.

I see there are several supporters of the original one-die-reward system. It doesn't irk me whatsoever if people tweak the rules to their own taste and use either method of rewarding successes. But I still prefer two dice as a reward for no other reason than to help curb the rapid loss of dice that can happen when pools are small. I agree with Moose that one die is more elegant and I'd prefer it that way if I knew it would work better over time. Again--more urgency for playtesting an extended game.

There was also mention of scaling the rewards to the size of the pool. While I like the idea that this will help those with very small pools while keeping large pools at bay, I don't like the add-on nature of it.


Title: Dice probabilities in the Pool
Post by: Paganini on July 05, 2002, 06:50:44 AM
Quote from: James V. West

I find it very difficult to concive a group playing the same characters long enough to run into a bloated pool scenario. Certainly never in the 30,000 rolls range. I average 4-6 rolls per session in my games so far (usually around 3 hours of playing).


Oh, certainly! Hehe... The tests aren't supposed to say "this is what happens when you make 30,000 rolls." It's just that a large number of rolls are required to demonstrate the nature of the probabilities. If you just make one or two rolls it's difficult to tell anything about the system (unless you're figuring things out with math). OTOH, 4-6 rolls in a 3 hour session is really quite low by some standards, so even if you were running a "I wonder what will happen next session" kind of a test I think you'd want to do more.

Quote

I want the rules to express that a "success" for the player means the ball is in his court, whereas a "failure" puts it back in the GMs court. Nothing more or less. If you opt out of a MoV, you essentially put that ball back into the GM's court. I can't imagine someone having so little interest in the story that's happening to their character that they would give up MoVs regularly for dice--unless their pool was dangerously low.


You see, this is the crux of what I was saying. You've got a couple of key phrases and concepts here. Number one is the idea that story power bounces back and forth as determined by the dice. You have that built into the game - boy, do you ever! And that's a Good Thing (TM). It's part of what makes the Pool so cool.

Your next statement: "I can't imagine someone having so little interest in the story that's happening to their character that they would give up MoVs regularly for dice--unless their pool was dangerously low."

(emphasis added, of course)

Aha! This is what I was getting at: A player who understands the system is not going to be irresponsible with his resource (dice), because the high value of that resource is made clear by the rules. A person who understands the math will not *wait* until his pool is dangerously low to start giving up MoVs. He'll give up MoVs whenever he can[1], because he knows that if he waits until his pool is low he'll be *involuntarily* giving up MoVs and reward dice - he'll be failing rolls. This is the situation that the player wants to avoid at all costs. So, he'll only take MoVs whenever there's something that he particularly wants, and use the others to build up his pool. I could imagine this being only once in a while (not even every other success, which was the way I ran it in the tests).

[1] Meaning, in situations that he doesn't particularly care about, or in situations where he feels that the GM will do just as well as he will. Remember, for years game systems have given the GM *all* the power. Me, I can't imagine a player alive who wouldn't be willing to sacrifice superflouous story power to make sure that he's got it when it really counts.

Of course, after you play this way for a while (I'm not talking 30,000 rolls here, I'm talking 20 to 30 rolls) you'll have so many dice in your pool that you'll have "security." As long as you leave enough dice in your pool to cushion a serious failure, you'll be able to do *whatever you want.* You want a MoV every time? You can do that. You want to pump up your traits? You can do that. If you do have a catastrophic failure (which you will eventually) you just start playing the way you did initially until your pool is built back up.

This bothers me the most when you use two reward dice, because over 36 rolls the pool will often shoot up to 60 or more dice.


Title: Dice probabilities in the Pool
Post by: Jeffrey Straszheim on July 05, 2002, 09:25:30 AM
I agree with Paganini here.  It doesn't require thousands or rolls for a problem to occur.  Moreover, once the problem begins, positive feedback takes over and a runaway situation begins, especially with two reward dice.

That being said, this problem does not occur with only a few dozen rolls, so it probably won't occur in the normal course of playtesting.  But over long term play, particularly if a clever player begins buying ever increasing trait levels (which becomes possible).  Imagine what happens when a player buys up his "fighting" trait to +8 -- which only costs a measly 64 dice.

Obviously no one is suggesting that we add a bunch of obtuse rules, but perhaps some sort of optional "if you're playing long term perhaps apply this limit" sort of thing.  For instance, in Sorcerer there is a similar sort of problem with banish abuse.  Positive feedback exists between a character's humanity score and banishing demons.  Ron adds no special rules for this, but does provide some suggestions on how to deal with the issue if it arises.


Title: Dice probabilities in the Pool
Post by: Buddha Nature on July 05, 2002, 12:40:20 PM
Okay, I think stimuli is heading in the right direction here, namely - make changes as you feel they are needed/warranted to your own game, don't ask James to make them canon.  If someone out there wants to write up a webpage of tack-on rules, by all means do it--I am all for that kind of thing--heck if James really likes it he might link off his main site.

Suffice to say, none of this really is going to come into play (at least as far as I can tell).  I don't think people are _really_ going to get into the 60+ roll area, and I seriously doubt any normal player is going to grow their pool beyond 20 dice.  I just don't see it happening, A) because the game is about the MoV's--they are what you want! B) I have done some rolling of my own, and you will lose sooner rather than later. C) Why play wussy?  Play it fast and loose and have fun--you are playing a Narrativist game so stop thinking about the dice so much and think about the story--taking dice over MoV's is good for the player (and maybe the character) but not for the story.

Don't try to play a Narrativist game like a Gamist, it is just not going to be fun for anyone.

-Shane


Title: Dice probabilities in the Pool
Post by: Paganini on July 05, 2002, 01:19:54 PM
Quote from: Buddha Nature
Okay, I think stimuli is heading in the right direction here, namely - make changes as you feel they are needed/warranted to your own game, don't ask James to make them canon.  If someone out there wants to write up a webpage of tack-on rules, by all means do it--I am all for that kind of thing--heck if James really likes it he might link off his main site.


Yow, I agree totally. The point of this is not to get James to add rules. Ack! I love elegant simplicity.

To paraphrase Gandalf, "This thread has grown long!" Originaly this thread was something like this: "Hey, I love the idea of player directoral control, but I see some potential problems with the numbers. How do you handle this?" This is still more or less the core of the thread (so far I've gotten one answer that I like... use only +1 reward die instead of +2) but it also got derailed a bit, since a fair amount of the thread has become discussion of whether or not the problems I notifced actually exist. :)

Quote

Suffice to say, none of this really is going to come into play (at least as far as I can tell).  I don't think people are _really_ going to get into the 60+ roll area, and I seriously doubt any normal player is going to grow their pool beyond 20 dice.


Please note that the second set of tests I did was with 36 rolls - not 30,000. With a +2 reward dice scheme, the pool regularly (as in, more than half the time) grows to 20 or more dice. The highest it went was 25 dice. With only +1 reward die, it doesn't do this. Also note that this is taking reward dice every other success. However many successes were rolled, half of them were taken as MoVs.

Quote

I just don't see it happening, A) because the game is about the MoV's--they are what you want! B) I have done some rolling of my own, and you will lose sooner rather than later. C) Why play wussy?  Play it fast and loose and have fun--you are playing a Narrativist game so stop thinking about the dice so much and think about the story--taking dice over MoV's is good for the player (and maybe the character) but not for the story.


This is a fallacy along the lines of "System Doesn't Matter. So check out the rant that follows. :)

Quote

Don't try to play a Narrativist game like a Gamist, it is just not going to be fun for anyone.


ARRRRGH! Stop it with this! I see it's time for me to rant:

<begin rant>
In order for Gamism to exist, competition is required. Period. Exploitation of system is not in itself sufficient for Gamism to exist. If system exploitation is happening *in order to compete with other players* then Gamism exists. If system exploitation is happening as a natural continuation of the system (i.e., following the implications of the system to their logical conclusion) then there is no Gamism.

There is no Gamism in the Pool. There can not be Gamism in the Pool without some sort of conflict being established among the players. If the game starts off with "Okay, the winner is the player with the most dice in his pool," *then* you have Gamism. The Pool does not do this. The Pool must be drifted manually by something like the above in order for Gamist play to exist. This does not mean that system exploitation is in any way out of place. System exploitation and Gamism are not one and the same. One does not imply the other.

System exploitation simply means taking advantage of the rules in order to recieve the greatest possible returns from them. If your goal is to "win," then system exploitation can do that. If your goal is to drive the story (as it is in the Pool) then system exploitation can do *that.*
<end rant>


Title: Dice probabilities in the Pool
Post by: James V. West on July 05, 2002, 08:45:07 PM
Shane: Hell yeah I'd link to anyone with something cool for The Pool or TQB.

Paganini: Just wanted to say I totally understand where you're coming from and I appreciate your concern about the numbers. Its been a most helpful discussion.

So, it seems that some people like the one-die reward better than the two-die reward. Let me clarify why I changed it in the first place: There were a couple of discussions about "thrashing", as Paul pointed out earlier in the thread. I wanted to help the problem by giving players a slightly higher reward. Because you tend to start with few dice, you tend to lose them fast. Getting two dice in stead of one helps with this problem--but it isn't as intuitive as getting a single die.

I'm still not convinced I need to change it back to the original rule on this, so I'll leave it alone for now.


Title: Dice probabilities in the Pool
Post by: Paganini on July 06, 2002, 07:00:38 AM
Quote from: James V. West

So, it seems that some people like the one-die reward better than the two-die reward. Let me clarify why I changed it in the first place: There were a couple of discussions about "thrashing", as Paul pointed out earlier in the thread. I wanted to help the problem by giving players a slightly higher reward. Because you tend to start with few dice, you tend to lose them fast. Getting two dice in stead of one helps with this problem--but it isn't as intuitive as getting a single die.


And now I *am* going to make a suggestion. :) If it were me, I wouldn't change anything, in terms of what you already have. (At least, not without really finding something that fits the nature of the Pool as it already stands.) I'd just make it more open. Include both rules, explain the reasons that each one might be chosen, and leave it up to the indie-vidual ;) group.

Of course, I did have one crunchy thought... the number of reward dice could vary throughout the game. It could be related to the Pool, something like "if the pool is greater than 9 dice only one reward die is recieved." Or it could be determined by the number of dice you roll. If you succeed with fewer than 6 dice you get 2 reward dice instead of one.

I'd offer all of these as suggestions for game technique, however, rather than set rules. Frex, handle reward dice the way you handle difficulty dice. Right now the rules are pretty much "The GM gives you 1 to 3 difficulty dice." It doesn't really say how many difficulty dice he should choose in a given situation. It makes a brief mention of difficulty, and leaves it up to the GM.

You could do the same thing with reward dice. "If you succeed you may take a MoV - blah blah blah - or you may choose to recieve reward dice from the GM," - leaving the number of reward dice up to the GM. He could do it by feel - if you're thrashing, he can give you 2. If you have a +99 Pool Of Dominion he can give you 1 - or he could go by one of the suggestions above, or whatever.


Title: Dice probabilities in the Pool
Post by: James V. West on July 06, 2002, 07:55:52 AM
Quote from: Paganini

You could do the same thing with reward dice. "If you succeed you may take a MoV - blah blah blah - or you may choose to recieve reward dice from the GM," - leaving the number of reward dice up to the GM. He could do it by feel - if you're thrashing, he can give you 2. If you have a +99 Pool Of Dominion he can give you 1 - or he could go by one of the suggestions above, or whatever.


This isn't a bad idea, really. No goofy rule add-ons, just an extension of the current rule for gift dice.

I wasn't going to include any "optional" rules with the game, but what do you folks think? Perhaps a bit of guidance in terms of tweaks such as this one wouldn't hurt as an aside?

[edited for stupid typos]


Title: Dice probabilities in the Pool
Post by: Buddha Nature on July 06, 2002, 12:19:52 PM
I would say put your vision of the game first, then as an Appendix (of sorts) put an optional rules saection w/ all the different ideas and the reasons for and against them.  Let the GM/Players choose how they want to alter the game, but it is your game first and foremost.

Paganini: I second your motion for the variable (keep it 1-3) dice reward system - leave it up to GM discretion - they are going to be "on scene" and will be able to tell what is neccessary for their game and for the player's pool.

-Shane


Title: Dice probabilities in the Pool
Post by: Jeffrey Straszheim on July 06, 2002, 04:42:09 PM
Quote from: James V. West

This isn't a bad idea, really. No goofy rule add-ons, just an extension of the current rule for gift dice.


I agree.  It is a great solution.

Quote

I wasn't going to include any "optional" rules with the game, but what do you folks think? Perhaps a bit of guidance in terms of tweaks such as this one wouldn't hurt as an aside?


The thing is, folks are going to tweak the system anyway to match whatever setting/mood/theme/etc they have in mind.  So, I think it would be a good idea to at least catalog what sorts of tweaks are common, and what sort of effects they have on play.

For example, by this logic the QB system can be seen a simply one of the many possible flavors of The Pool.  Myself, I plan to use QB's notion of the Accord in any The Pool games I play, regardless of if I'm playing with Fuzzy Knights or not.