[dice pools] - swapping 10 dice for Y # of successes

[ShaneNINE]

Say you have a game that uses d10 dice pools and a fixed target number of 7 ::cough::exalted::cough::  Now suppose you had a rule for large die pools that basically said that for every 10 dice in your pool you could take X number of successes. So if your pool was 25 you could take 2*X successes and only roll 5 dice.

Two questions:

1. Is that the dumbest idea ever? Would it totally break the game?

2. What would X be?

Thanks (for not making fun of me).

[Valamir]

rolling a 7 (or higher I presume) on a d10 is a 40% chance.  So the expected number of successes on 10 d10 would be 4 (10x.4)

So for a pool of 25 you could take 8 successes and roll only 5 dice.

However, theres a down side.  

While it is possible to roll below average on the 5 dice, it would not be possible to roll below average on the 20 dice you didn't roll.  So you'd essentially have a floor of 8 successes.  There's no way you could roll worse than 8 successes.

While unlikely you could certainly roll worse than 8 successes on 25 dice if you actually rolled them; so essentially you've skewed your number of successes higher.

Better would be to simply cut most of the dice in half and simply count 2 successes for every success.  You'd want to make sure to have 1 die of a different color (if the total dice was odd) to represent the left over success counting it only as a single, or if the number of dice came out even, you'd want to have 3 dice of a different color...to ensure that an odd number of successes was still possible.

Thus for 25 dice you could roll 12d10 @ 2 and 1d10@1.  Not quite as much of a cut as the first method but it doesn't screw with the odds.


If you wanted you could divide by 4 to get even fewer dice but the larger your divisor the less smooth your curve.

[ShaneNINE]

I was thinking about this all day and I only came up with a few minor problems. Then, in the 20 minutes after I made this post I suddenly thought of a bunch of major problems And now I feel stupid for even bringing this up.

So, um... nevermind. ::goes back to corner with pointy hat::

[HMT]

... While unlikely you could certainly roll worse than 8 successes on 25 dice if you actually rolled them; so essentially you've skewed your number of successes higher ...

I disagree. Five dice plus eight successes has the same average. In fact, you picked the number eight so as to get the same average. The top of the range is being truncated as well as the bottom. Twenty-five dice can yield more than thirteen successes.

[M. J. Young]

I disagree. Five dice plus eight successes has the same average. In fact, you picked the number eight so as to get the same average. The top of the range is being truncated as well as the bottom. Twenty-five dice can yield more than thirteen successes.

The problem Ralph is targeting is not that the mean has altered but that the extremes have altered.

Rolling 25d10 you do have a chance of getting zero successes =>7. It's an incredibly slim chance, but it's there. You also have a chance of getting twenty-five successes--even slimmer. However, if you convert twenty dice to eight successes, you can't get more than fewer than eight nor more than thirteen successes.

There are a lot of situations in which that would be significant. Obviously, if I need eight successes, I can declare success automatically by opting for this--but then, if I need fourteen, can the referee declare that I automatically failed? Also, if these are opposed rolls, the question of whether you're going to beat the odds on those twenty dice becomes more significant.

Now, I don't play the game in question, so I don't know how important it is. I know that someone who writes extensively for it uses a random number generator (a programmable calculator, I think) for his rolls when he runs it and gets over a certain number of dice on his side. He tells the players they're free to roll real dice if they like, but he finds it too inconvenient to have all those dice on the table and is comfortable with the mechanical results.

--M. J. Young

[Christopher Weeks]

The effect of having the extremes limited is certainly present, but I'm not so sure it's a problem.  For one thing, I'm imagining a character with 25 dice as having a fairly high degree of competence.  Why not let them take some kind of safe route for their roll in which they're guaranteed only a moderate success?

Maybe for Dramatic rolls, that's not appropriate, but for lots of rolls it seems to me like it would be.  And you could assign only two or three successes to ten dice instead of four to make it less valuable.  It sounds like a lot would depend on the system.

Chris

[Valamir]

... While unlikely you could certainly roll worse than 8 successes on 25 dice if you actually rolled them; so essentially you've skewed your number of successes higher ...

I disagree. Five dice plus eight successes has the same average. In fact, you picked the number eight so as to get the same average. The top of the range is being truncated as well as the bottom. Twenty-five dice can yield more than thirteen successes.

You're right of course.  It being equally possible to roll higher than 8 successes on 25 dice.  What I should have said is that you're greatly reducing your standard deviation, making average results even more likely.

Of course, with a 25 die pool you've already got a pretty tight standard deviation, so it really only is impacting the extremities in a noticeable manner.

[Lxndr]

If you're doing this for Exalted in particular, a 7 or higher is a success, but a 10 is "2 successes."  Which supposedly evens the # of successes per die at an average of 0.5.

That said, I'd still take Ralph's solution 'cause it assumes no tens are rolled.  Which makes the choice between "take the assumed average" and "roll the dice" a harder one.

HERO does something similar with the advent of 5th edition.  With some powers, you can choose a flat value of "3" instead of rolling 1d6 (and you can even combine this with dice, such that you might have 9 + 2d6, instead of rolling 5d6).

[Thierry Michel]

Economist advice:

when converting dice to numbers, then convert below the expected value,  to take into account risk aversion.

(Tangentially, it would be amusing to see hedging strategies applied to role-playing)

[Valamir]

Interesting you should say that Thierry.  A fellow financier gamer and I once whiled away an evening drinking and speculating about how dice rolls in a game form a spot market where players are essentially pricing risk as it occurs, and whether it would be possible to build a forward / futures market or an option market structure into a viable game mechanic.

The details got a little fuzzy as we worked our way closer to the bottom of the bottle, however.

[John Kim]

That said, I'd still take Ralph's solution 'cause it assumes no tens are rolled.  Which makes the choice between "take the assumed average" and "roll the dice" a harder one.

HERO does something similar with the advent of 5th edition.  With some powers, you can choose a flat value of "3" instead of rolling 1d6 (and you can even combine this with dice, such that you might have 9 + 2d6, instead of rolling 5d6).

As a player, this seems a little screwy, because the high tail is often more valuable than the low tail, particularly for damage.  Simple example:  I am rolling 1d6, the opponent has defense of 2 (PD or DEF in HERO).  If I roll the die, my results are 0/0/1/2/3/4 = average of 2.  If I take 3 instead, I only do 1 point of damage -- half the average if I rolled.  

Second case: 2d6 vs DEF of 5 = average of 2.28 damage goes through, compared to 1 if you used the "fixed-3-per-die" rule.  

Of course, there are some situations where you don't about the total average: i.e. if just 1 point more is enough to knock out your opponent, then it is better to be guaranteed to do that 1 point.  But particularly for damage I would almost always want to roll.  I guess that's intended to some degree.  If you have a working system, it is always better to add new options which are usually suboptimal, because if the new option is often better, then you break a lot of things and cause inflation, whereas a less-useful new option can easily be ignored.

[Jaik]

I'm going to follow Christopher and Thierry and suggest a sub-average number of automatic successes, either 2 or 3 successes per 10 dice depending on how much you want to punish risk-aversion.  That way, the "roll" ends up being a sure thing, but not a great thing.

Two little extra thoughts:  
1)  Doesn't Exalted already have a rule for changing huge pools into automatic successes?  
2)  And if changing a roll like this makes sense to the game, frex low-pressure "neat" rolls, why roll at all?  If the character has 25 dice to throw at a small problem, let 'em shine, tell them how great it went, or even better, let them tell you.

[Thierry Michel]

A fellow financier gamer and I once whiled away an evening drinking and speculating about how dice rolls in a game form a spot market where players are essentially pricing risk as it occurs, and whether it would be possible to build a forward / futures market or an option market structure into a viable game mechanic.

The problem is to find a counterpart on the risk market, unlees the GM automatically matches offers.

But yes, it's fun to consider.

[Thierry Michel]

A fellow financier gamer and I once whiled away an evening drinking and speculating about how dice rolls in a game form a spot market where players are essentially pricing risk as it occurs, and whether it would be possible to build a forward / futures market or an option market structure into a viable game mechanic.

The problem is to find a counterpart on the market, unless the GM automatically matches offers.

But yes, it's fun to consider.

[JamesSterrett]

Could you guys - in another thread if inappropriate to this one - go into more detail on applying risk and market modelling to game mechanics?

I'm intrigued, but don't know enough to follow through to the implications.