Availability thoughts (re: Ally, Contact, Patron)

[evileeyore]

Something I've thought about using (but haven't had reason to try out yet) was allowing for a bonus to the roll to see if an Ally, Contact, or Patron were available based on how many sessions they'd been left unasked for*.

I'm torn between a flat +1 per session† and using the SSR table‡.

I already give bonuses for trading favors and bribery...



* Mostly as this would help to drive down the cost by inherently reducing the needed Availability level.
† Which would work great in DF, not so much in other genres.
‡ Which would great in long haul campaigns, not so good in DF style "every session is a new mission".

[whswhs]

Originally Posted by evileeyore

Something I've thought about using (but haven't had reason to try out yet) was allowing for a bonus to the roll to see if an Ally, Contact, or Patron were available based on how many sessions they'd been left unasked for*.

I'm torn between a flat +1 per session† and using the SSR table‡.

That's mathematically equivalent to raising the availability number by some amount. You might as well just do that.

[Refplace]

I just average it over the campaign.
So using B171 as a guide...

• <6 or less is 9.3% or 1 day in 10
• <9 or less is 37.5% or 1 day in 3 (base cost)
• <12 or less is 74.1% Likely the first day of trying (double cost)
• <15 or less is 95.4% (triple cost)

And some things will modify that roll anyhow.
So I just eyeball the odds or time required based on the situation and how often the player asks for help rather than rolling.
Really Contacts would I think be mostly fixed if Frequency of Appearance was not used the way it is, or at all.
Maybe an extra point to the base cost for accessibility.
Lets see +1 Highly Accessible, -1 difficult to access or reach.

[johndallman]

Originally Posted by evileeyore

Something I've thought about using (but haven't had reason to try out yet) was allowing for a bonus to the roll to see if an Ally, Contact, or Patron were available based on how many sessions they'd been left unasked for*.

That make sense for some A/C/P, but not others. For example, the last Contact I had on a character, in a just-ended campaign, was a wise-woman in an immigrant community in London. The availability was simply "was she in when I tried to visit?" If she was unavailable, she was elsewhere. Having her become more available if I didn't use her would not be very plausible.

So I think this needs to be an Enhancement on A/C/P.

[evileeyore]

Originally Posted by whswhs

That's mathematically equivalent to raising the availability number by some amount. You might as well just do that.

Except I don't want them to have a permanently raised Availability.

I just want for their Undead Slayer buddy to generally be available every few sessions when they decide "Okay, we're finally going back down into the Tomb of the Mad Heirophant" (for example). And him randomly not being available sometimes when they check (because 17 and 18 still get rolled) is fine as well.

I like them being Available when called upon after a "down time" period, or having them available as per the normal roll if "called on" all the time.

Originally Posted by Refplace

I just average it over the campaign.

I've done that as well. But I've also had Players that wanted to roll every session to see if their Ally showed up (especially when it was a 6 or less*), or tried to use their Contact or Patron constantly. In these cases "No, you can't see your Ally for another 9 sessions" doesn't cut it the way "Well, the roll failed, better luck next week" does.


* Something I've noticed, Players either want A/C/P Always Available (and will pay the premium) or they take the lowest possibility and contrive ways to check every session to maximize the few points they've spent.

So... this was just an idea I've had to see if I can't bring those two things together and reduce the number of "Let's check on our 6 or less Ally this session" rolls.

[whswhs]

Originally Posted by evileeyore

Except I don't want them to have a permanently raised Availability.

Suppose you look at a thousand rolls against 9 or less. In 375 cases, you'll succeed the first time; in 234, the second time; in 147, the third time, and so on up to 1 roll will not succeed till the 16 time (assuming statistically expected outcomes and rounding to the nearest whole number). This comes out to 2.663 rolls being needed in the average case, which is a 38% chance of success, or success in 81.11 out of 216 rolls, which is almost exactly the odds for 9 or less.

With your procedure, you succeed the first time in 375 cases, the second time in 313, the third time in 195, the fourth time in 87, the fifth time in 25, and the sixth time in 5. Adding up 375x1 + 313x2 + 195x3 + 87x4 + 25x5 + 5x6 gives 2089, or an average of 2.089 rolls being needed, or a 48% chance of success, or 103.40 successes per 216 rolls, which is very nearly the odds for 10 or less. So you've effectively gotten the same improvement as if you just gave +1 to the roll and had done.

Or, if you prefer, you've gone from roughly every third game to roughly every other game.

I don't intrinsically object to having different procedures for this. But I think your proposal may be more complicated than either "every other session" or "10 or less." You have to keep count of how many sessions it's been since each Ally, Contact, Dependent, Enemy, or Patron showed up, possibly for multiple sessions, to figure the bonus. That's a lot of record keeping for a fairly small adjustment. If it were me, I'd find it exasperating to keep track of.

And in any case, you have changed the odds, making success more frequent.

[evileeyore]

Originally Posted by whswhs

With your procedure...

In what manner are deriving these numbers?

Because with my procedure... it may very well be that with that "9 or less" they wait 6 sessions every time before rolling, not just one, or two, or whatever amount you're using (which is rather my question above).

And in any case, you have changed the odds, making success more frequent.

Unless they roll every session, in which case nothing has changed.

What I'm aiming to change is the above line, the "roll every session to see if their 6 or less Ally shows up".

[whswhs]

Originally Posted by evileeyore

In what manner are deriving these numbers?

It's pretty standard probability theory.

If the roll is a 9 or less, they have 81 chances out of 216 of the Ally (or whatever) showing up. That leaves them 135 chances out of 216 of the Ally not showing up. The next time, they have the same odds; so that's 135/216 x 81/216 times the Ally shows up on the second roll, and 135/216 x 135/216 times it doesn't. The third time, it's 135/216 x 135/216 x 81/216 chances of the Ally showing up, and 135/216 x 135/216 x 135/216 not.

For convenience, rather than using exact fractions, I started out with a sample size of 1000, and then repeatedly split it 21/216 and 135/216, or 3/8 and 5/8. That gave me a series of numbers, 375, 234, 147, 92, and so on. So I multiplied the first number by 1, the second by 2, the third by 3, and so on, and summed up the products to get 2663, which I divided by 1000 to get an average of 2.663 rolls till the Ally showed up.

Then for your procedure, I did the same, but the multipliers changed, from 81/216 and 135/216 to 108/216 and 108/216 to 135/216 and 81/216 and so forth. That gave me a sum of 2089, which implied 2.089 rolls till the Ally showed up.

These were approximations with rounding errors, but they come fairly close to exact numerical results.

So what they show is that giving +1 to the chance of an Ally showing up for each previously missed roll does not give you the same odds as if you just keep the same required roll.

[evileeyore]

Originally Posted by whswhs

So what they show is that giving +1 to the chance of an Ally showing up for each previously missed roll does not give you the same odds as if you just keep the same required roll.

I'm not talking about them missing rolls, I'm talking about them skipping rolls.

AS in, instead of rolling every session, they they don't ask to have siad Ally/Contact/Patron for several sessions and then gain a bonus based on the number of sessions skipped.

[whswhs]

Originally Posted by evileeyore

I'm not talking about them missing rolls, I'm talking about them skipping rolls.

AS in, instead of rolling every session, they they don't ask to have siad Ally/Contact/Patron for several sessions and then gain a bonus based on the number of sessions skipped.

Oh, okay. In that case, though—suppose they have 9 or less rolling every session. That's a 5/8 chance of the Ally not showing up. If you want the same odds after two sessions, you want it to be a 25/64 chance, or about 84/216, which is an 11 or less. For two sessions skipped, the odds on the third session would be 125/512, or about 1/4, which is about 12 or less. For three sessions, it's 625/4096, which is about 13 or less. So in that case, your +1 per skipped session isn't far off.

With 12 or less, it's 0.26 for every session, which is 0.07 for every two sessions, or roughly 15 or less; it goes to 16 or less for every three sessions, and 17 or less for four sessions. Having that first step be +3 makes +1/session a poor approximation.

I'd probably just roll the dice two or three or four times, and see if the requisite number ever comes up. It's more exact than using one roll and rounding off to the closest approximation, and it doesn't take much time.