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).

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.

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::

Valamir wrote: ... 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 ...

HMT wrote: 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 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

HMT wrote:

Valamir wrote: ... 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.

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).

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)

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.

Lxndr wrote: 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).

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.

Valamir wrote: 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.

Valamir wrote: 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.

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.

JamesSterrett wrote: 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.

I think the concept clicked now - thanks!

Seems to me this would work best in Gamist games that have more explicity currency (I'm not seeing how to apply it to The Pool, which is probably a matter of my simply not see how yet.)

So you might, following your example, trade a guaranteed stat of X in exchange for a Y% reduction in the rate at which experience points were gained? (I've seen mechanics like this in RPGs before - the CRPG Fallout comes to mind - "buy this advantageous trait at the cost of earning N% fewer EXP".)

Or you trade some of your dice to another player in exchange for N% of that player's experience points.

Play with protagonization by tying your character's advancement explicitly to some other character's (you level up/gain dice/whatever when and as they do)?

In Donjon, you'd trade some of your available successes to another player in exchange for N of their level-up dice at the end of the session? (This would require some careful narration to make sure the supporting character was appropriately involved and at risk?)

Looking over The Pool, does the "gamble your dice pool" mechanic introduce an element of a futures market? You're making an explicit statement about the importance of getting a 1 by the number of dice you throw in; and the "At Death's Door" mechanic allows other players to give dice to save another character, valuing that character's survival against their own future/potential difficulties.

JamesSterrett wrote: Seems to me this would work best in Gamist games that have more explicity currency.

Thierry Michel wrote: you could also make the player "pay" by simply lowering the stat unconditionally (ending with, say a roll 3d6 -2, with a minimum of 8, the 2 points would be the premium of the option).

Christopher Weeks wrote: If I'm getting it then 'certain equivalency' would be the point at which players were equally likely to take or not take the modified option.

How is that transferring 'risk' among the players (or characters, or whatever)? And what exactly is 'risk?'

There are a lot of potential approaches...mostly interesting as an intellectual exercise and not necessarily as a killer mechanic.

But take as one approach, Put and Call options:

To put them in simple non jargony terms: When you buy a Put, you're paying for the privilege of foisting your bad luck off on someone else (Putting it onto them) When you buy a Call, you're paying for a chance to take someone else's good luck (Calling it to you).

When you sell a Put you're accepting the risk of having someone foist their bad luck on you in exchange for a fee (which you get to keep, even if that bad luck never happens). When you sell a Call you're accepting the risk of having your own good luck cut short and taken by someone else in exchange for a fee (which you get to keep, even if you don't experience the good luck, so no one takes it from you).

The "Fee" (or premium in jargon terms) depends on alot of factors so complicated people have won nobel prizes trying to figure out a way to calculate what's "fair" by a formula.

Conceptually though, the fee is pretty simple. The more bad luck you're trying to foist with a Put or good luck you're trying to take with a call, the more expensive it is. The longer the term that the arrangement is good for, the more expensive it is. The greater the chance that something bad will happen (to foist) or good will happen (to take), the more expensive it is.


So, from here one can get an inkling of the type of mechanic you could develop that would mimic an options market. Define "good luck" "bad luck" as being "good roll", "bad roll". Charge the "fee" in some game resource (XPs, damage, whatever). And then allow the players to buy and sell Puts and Calls amongst themselves, foisting off bad rolls on to others and taking others good rolls for themselves. The fee that players would negotiate for this would be a good measure of the value they are assigning to risk.

Of course, what makes a real options market (or any security market for that matter) work is liquidity...which basically means having enough people willing to sell a Put for all the people that want to buy them, and vice versa. A handful of gamers around a table, isn't going to be enough to form a "market" to make this work. But, a MMORPG, with several thousand players very well might.

Further, in markets where liquidity is important but there may not always be enough of it, there is the concept of a "specialist" the person whose job it is to provide liquidity (required to handle all trades for which one can't find another party to match) in exchange for certain privileges. In an RPG, this person would obviously be the GM, so the GM would have to be the "counter party" on such deals.


Now of course, its difficult to imagine exactly what the purpose of such a mechanic is, in game terms. I think it would be interesting as a novel idea in the way that playing a hand of poker makes for an interesting novel mechanic...but not one broadly suited to most games.

BUT, I do think, that there is a potential there to use something like this as a magic system. Many cultures idea of magic basically centers on the notion of making deals with spirits. "Oh spirit of rain, I promise to sacrifice two loaves of bread and a young lamb if you bring fertility to my fields"...that sort of thing.

I think one could take the above Put Call mechanic idea and use it in such an enviroment to model the "I'll pay you to take away the bad stuff" / "I'll accept your bad stuff in exchange for a fee" kind of nature of it.

Valamir wrote:
Now of course, its difficult to imagine exactly what the purpose of such a mechanic is, in game terms. I think it would be interesting as a novel idea in the way that playing a hand of poker makes for an interesting novel mechanic...but not one broadly suited to most games.