Dice probabilities in the Pool

[Paganini]

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?

[Paul Czege]

Hey Nathan,

Three threads you should read if you haven't:

1) http://indie-rpgs.com/forum/viewtopic.php?t=689">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 http://indie-rpgs.com/forum/viewtopic.php?t=683">Anti-Pool. Someone should play this thing.

3) And http://indie-rpgs.com/forum/viewtopic.php?t=1138">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

[Paganini]

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.

[Buddha Nature]

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"]

[Valamir]

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.

[Paganini]

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.

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.)

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.

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.

[Paganini]

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.

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.)

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.

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.

[Paganini]

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! :)

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.

[Michael Bowman]

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

[Ron Edwards]

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

[Paganini]

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.

[Mike Holmes]

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

[Valamir]

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...

[James V. West]

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

[Paganini]

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.