Quick(?) probability query:

[anonymouse]

Abe rolls a D6.
(He gets a 4.)
Barry has to get a number of successes equal to the result, at a TN of said result.
(So Barry needs to get at least 4 dice to come up as 4.)

Limiters:
Abe only ever rolls 1D6.

Unfortunately, at the moment I don't think there's a limit on Barry's dice pool, but maybe a cap of 18 or 24 for argument's sake.

I really like the idea of this, but I have a feeling that if Abe ever rolls a 5 or 6 it's going to get stupid hard unless Barry spends a lot of dice. And maybe not even then.

[Brian Leybourne]

Uh, you forgot to ask the question :-)

Assuming you meant "what's the chance that Barry succeeds", it's not really that tricky (although you need to set a die pool for Barry to have it be meaningful) but the numbers are a bit silly. I'll assume 24 dice.

There's a 1/6 chance (Abe rolled a 1) that Barry is guaranteed to succeed even with just one die (he needs one 1)

There's a 1/6 chance (Abe rolled a 2) that Barry needs two 2's or higher, the chances of failing this with 24 dice are astronomical (he would need 23 1's and a single 2 or all 1's - The chance of that is, uh, 25 in 6^24, so that's about 1 in 189 quintillion, which is 189 with fifteen zeroes after it). That's the chance he fails.

There's a 1/6 chance that he needs 3 threes, similar (but smaller) numbers result.

Basically, it only gets difficult when you get up to Abe rolling a 5 or a 6. If Abe rolls a 6, then Barry needs 36 dice to have an odds-on chance of getting six sixes, but he's only got 18 or 24, so it's unlikely. The chances of getting five 5's or more are actually pretty good with 24 dice, but only so so with 18.

In essence, to be honest, it's not that workable as a die system :-)

Brian.

[james_west]

I got the impression that he had to spend dice out of his pool, not neccesarily roll them all at once. That would be more workable, and the average number of dice he'd have to roll are indicated by your essay (essentially, a 6 would mean it wasn't happening.)

The problem is that the difficulty does scale -very sharply- with what the target number rolled, which is probably not a wonderful way to set difficulties. It's not really much different, in practice, than flip a coin, heads you win, although it has a much higher handling time.

- James

[anonymouse]

Whoops. Yes, it would be more helpful if I posed an actual question, huh? But you nailed it anyway. ;)

And yeah, the idea being that Barry has a pool of dice he has to spend from which, at any point, will have no more than (for example) 24 dice.. but he might choose to just roll 7 or 8 depending.

But yah.. I figured it would get a little too sharp, but wanted some confirmation. Thanks!

[Brian Leybourne]

And yeah, the idea being that Barry has a pool of dice he has to spend from which, at any point, will have no more than (for example) 24 dice.. but he might choose to just roll 7 or 8 depending.

Ah, cool. Well, that's still easy. Bary should spend the following to have a average or slightly better-than-average chance to succeed:

1) 1 die
2) 3 dice
3) 6 dice
4) 10 dice
5) 15 dice
6) 36+ dice.

Interestingly, it's a linear progression (1,+2,+3,+4,+5) until the last one. That in itself I find interesting enough to suggest that you could try something along these lines as long as 6 was never used as a TN. Ideally, it should be something supported by 21 dice (+6 on the previous total), which would be seven 5's or better or 3.5 6's or better. Doesn't really work, but if you made 6 mean "reroll" so the TN was always 1-5, there's a nifty progression going on.

But yah.. I figured it would get a little too sharp, but wanted some confirmation. Thanks!

No problemmo.

Brian.

[anonymouse]

Or treat 6 as some kind of bonus, maybe; either add the new roll + 1 (although that makes rolling a 5 trouble all over again) or some other bonus to one of the participants (free lollipop! and roll again!).

The linear progression is pretty interesting, though, and hard to resist! I shall have to give it a good thinking.

[M. J. Young]

Perhaps off topic, but what would happen if you inverted it? Like this:

If Abe rolls 1, Barry must roll at least one die not exceeding 1.

If Abe rolls 2, Barry must roll at least two dice not exceeding 2.

If Abe rolls 3, Barry must roll at least three dice not exceeding 3.

On to Abe rolling 6, in which case Barry has to roll at least six dice, but he's guaranteed that they'll all be successes.

Now, there are three ways this can be set, each of which would be different:[list=1][*]Barry may roll dice one at a time until he has the requisite number of successes, unless he exhausts his dice pool or decides to give up.[*]Barry must decide how many dice to roll from his pool once he sees the target number.[*]Barry must decide how many dice to roll before he sees the target number.[/list:o]I think that it's even odds of success in every case if you roll six dice; but that's seat of the pants, and I'm really much more interested in how the curve plays.

Any observations on this one?

--M. J. Young

[james_west]

This is, as far as I can see, a curve that is absolutely flat in average result; it just changes standard deviation (the width of the curve) substantially as you move.

To be explicit; for a 6, you MUST roll 6 dice, but you're automatically successful. For a 1, you could do it with 1 die, but you could also need a dozen, with about the same probability. Intermediate target numbers produce intermediate full-width half-maximum (FWHM) values for the gaussian.

Hard to imagine really needing that, but then y'all have a lot of imagination ...

- James

[Harlequin]

Actually, that last is really interesting if you instead applied it (as some have talked about) to a scaled "how big a role should chance play?" system, presumably for some other game than the one being asked about in the originating post.

For example, you could handle it as an attribute of the character, a sort of inverted "Luck" vs. "Skill" measure.  "Predictability," for example, or something flavourful in an appropriate system ("Order" in a fantasy system, etc).  I'll treat that last, as it feels like it has good potential.  This attribute governs which variant on the mechanic you use, for all your rolls; we would want everything else to be independent of this, it just affects how dependent you are on luck.

To succeed on a standard task, you must set aside Nd6 from your pool, and get (Order) successes, where a success is a roll of (Order) or less on any d6.

With an Order of 6, you always need six dice, and you always get that standard success.  Period.

With an Order of 1, you don't need to set aside more than one pool die, but your odds are lousy.  You hit fifty-fifty at about four dice (~51% of success), but on the other hand at six dice you're still only up to about two in three (~66% of success) and need way more dice to "guarantee" success.

In a system which didn't allow retries, this would be really kind of neat.  Makes the allegiance to Order/Chaos really matter, but not in the normal way.

The trouble with that system would actually be in applying modifiers.  Changing the TN, or the successes required, by anything flat (rather than a multiplier, like "twice as many successes", but that scales poorly), ends up preferring either Order or Chaos types over the other, which obviously wouldn't be desirable for a generic "+X because of Y" modifier.  The only place where the two really touch is at the number of dice applied, so you'd need to have an easier-than-normal one give you +N dice to roll (letting Order-max types spend less than their flat six dice, increasing Chaos-max types' odds even with minimum or zero dice expenditure), and - more usefully - a more difficult roll costs you N dice to even attempt, a la TROS' activation costs; this modifier is essentially comparable for all values of Order/Chaos.

You'd then need some way to get around the six-dice-is-magic granularity level (esp. with Order=6 kicking around), probably by having this pool not function as a frequent-full-refresh type (like TROS' combat pools) but having it instead refilled piecemeal (a la The Pool, or TROS' Sorcery pool) based on in-game actions/results/what have you.

But with a little care and nurturing, this baby has real potential...

- Eric