Calling people who are better at maths than me!

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Joose
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Calling people who are better at maths than me!

Post by Joose »

I've had an idea for a simple and sillyfun rpg game, which if I can crack the basics should go from not written at all to playable in a week or two, due to it being in a pretty much real world setting and "simple rules" being one of my design aims. Yay!

However, I'm stuck on a largely mathmagical problem involving probabilities and dice, two things I'm fine with individually, but which start to break me when put together. Halp.

The concept of the game will need dice rolls to be both easy and massively scaleable. The trouble is, there are basically two kinds of dice systems in RPGs; rolling higher/lower than a target number (like SLA/DnD) and hit dice (like SR).

The target number system is nice and simple, but has hard limits to how much it scales. If you are using big dice, like d100, that hard limit is pretty high, but the higher you make the upper limit, the harder it is for people on the low end of the skill spectrum.

The hit dice system is massively more scaleable. In fact, it's essentially unlimited, as long as you have an infinite number of dice. However, it's a lot less simple than the target number system, especially when you are using a lot of dice. SR players will attest to how much of a pain in the ass counting hits on a dozen dice can be; imagine if you were rolling 50, or a hundred?

The possible solution I've thought of is a kind of tiered hit dice system. Effectively, a system where you can swap x of your dice for one die that is worth x hits. So if, say, x was 10, then in the above example you could roll 5 dice and multiply the results up.

This should keep the system a lot simpler (in case you are worried, I'm planning on there being a lot less modifiers and such than SR. If you normally roll 20 dice for something, you will almost always roll 20 dice for that thing. Realism is not the focus of this game). I'm a bit worried about what this will do to the probabilities though. I know that rolling 10d6 is not exactly equivalent to rolling 1d6 and time sing the hits by ten, but what I'm not sure about is *how* different that is? Are you at an advantage, or disadvantage, or is it a wash in the long run? What about if there is a mix, like if your dice pool was 13. Is 13d6 going to give you more hits than 1d6x10 + 3d6?

My guess is that the results you can get, you are about as likely to get, it's just more polarised.

In case it's still not clear what I mean, here is a more solid example:

You have 12 dice. 5 & 6 count as hits, and you need 4 hits.

I know from shadowrun (and basic maths) that a third of dice will be hits, so with 12 dice you will avage 4 hits, so you will, on average, pass this test if you roll normally. Does that mean that you have a roughly 50/50 chance? Not sure. Mathfail.

However, with this system, you could choose to roll 3 dice, with one of em counting for ten.

I know this changes the range of possibilities, because rolling normally you could get anything from 0 to 12 hits, whereas this way you can get 0 to 2, or 12, but nothing in between. But does that make it more likely to pass, or less?

Evey time I come up against something like this, I get a little more forgiving of gaming loopholes being missed in released rpg's. :lol:
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Post by fabyak »

Joose wrote:You have 12 dice. 5 & 6 count as hits, and you need 4 hits.

I know from shadowrun (and basic maths) that a third of dice will be hits, so with 12 dice you will avage 4 hits, so you will, on average, pass this test if you roll normally. Does that mean that you have a roughly 50/50 chance? Not sure. Mathfail.

However, with this system, you could choose to roll 3 dice, with one of em counting for ten.

I know this changes the range of possibilities, because rolling normally you could get anything from 0 to 12 hits, whereas this way you can get 0 to 2, or 12, but nothing in between. But does that make it more likely to pass, or less?
Assuming you need 4 hits to pass, the odds would still be 1/3 I think (You can ignore the other 2 dice I think as their result would have no consequence overall on the required number of hits)
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Re: Calling people who are better at maths than me!

Post by Dr. kitteny berk »

Joose wrote:However, with this system, you could choose to roll 3 dice, with one of em counting for ten.

I know this changes the range of possibilities, because rolling normally you could get anything from 0 to 12 hits, whereas this way you can get 0 to 2, or 12, but nothing in between. But does that make it more likely to pass, or less?
Barely knowing how to count, my impressions are:

Surely 3 dice, each counting for 4 would be less mental?

That way you'd get 4/8/12

and I suspect the probability doesn't change, but it will matter if the hits are anything more than a yes/no thing.
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Post by Joose »

fabyak wrote:Assuming you need 4 hits to pass, the odds would still be 1/3 I think (You can ignore the other 2 dice I think as their result would have no consequence overall on the required number of hits)
This is true. In fact, this is true for all cases where your dicepool is between 10 and 10 + target number.

Trouble is, although the odds of rolling a hit with a single die is 1/3, im not sure how that scales.
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Re: Calling people who are better at maths than me!

Post by Joose »

Dr. kitteny berk wrote:Barely knowing how to count, my impressions are:

Surely 3 dice, each counting for 4 would be less mental?

That way you'd get 4/8/12

and I suspect the probability doesn't change, but it will matter if the hits are anything more than a yes/no thing.
True, but it needs to be something easy to do in game. You dont want people needing to do division in their heads in order to not have to count more, it kind of defeats the object.

Unless you mean always use 4 instead of 10. Which is fine, but what if the numbers get crazy-huge, with hundreds of dice needed?

Hmm....Unless there are multiple levels, and you can only use the bigger jumps at the higher dice pools? Like so:

up to 10 dice: no substitution allowed
10-50: sub 5 for 1
50-100: sub 10 for 1
100-200: sub 20 for 1

something like that?

I think theres two questions here really:

1) does substituting dice like this fuck up probability in exploitable ways?
2) Presuming the above answers no, whats the best way of subbing dice?
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Post by Roman Totale »

I seem to remember Bali being good at this sort of thing. I didn't read the post in full as 1) I'm rubbish at maths, and 2) I'm on the bog at work
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Re: Calling people who are better at maths than me!

Post by FatherJack »

Joose wrote: I know that rolling 10d6 is not exactly equivalent to rolling 1d6 and time sing the hits by ten, but what I'm not sure about is *how* different that is?
To make it simple, imagine d2's, or coins, with a Head being a Hit.

Tossing two coins separately will produce one of these results:
HH, TT, HT, TH

So, the odds are:
1 hit only: 1/2
At least 1 hit: 3/4
2 hits: 1/4
No hits: 1/4

Tossing a single coin and doubling the result, clearly isn't the same, as all that can happen will be:
HH or TT

The odds being:
1 hit only: impossible
At least 1 hit: 1/2
2 hits: 1/2
No hits: 1/2


Obviously it smooths out to be roughly even as the numbers in the pools get bigger, but by substituting dice for "representative" ones that have a 5x value you are changing the probability.

You're changing it such that you're not saying "these ten dice represent roughly what a hundred dice rolls would produce" you're saying that they are identical, to such a degree that you might as well just have a requirement to roll ten dice from the outset.

The only reason to have 100-dice rolls is because you want the granularity of a result of 37 or 83. Why roll a d10, d20 or even a d100 when you have a 50% chance of success?
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Post by Joose »

Having found Anydice.com and buggered about with it for a few mins, I have come up with this:

http://anydice.com/program/6eb

Which seems to imply that this idea is completely fucked, as substituting dice is a massive advantage. Unless im reading those numbers wrong/programmed it wrong (which is entirely possible).

Ok, so, scrap that idea. Anyone got a better solution?
Actually, I should probably clarify the problem:

The idea is for a simple but flexiable superhero RPG. It occured to me that most RPG's could be converted into a superhero version of themselves by just taking the breaks off. Instead of having upper limits to things like strength and intelligence...just dont. Bam, superhero. With that as a basis, it should be pretty easy to make a simple, not-hugely-realistic but fast to play RPG system.

The trouble is the range. Say normal human strength attributes go from 1 (feeble) to 10 (olympic athelete). You could, if you wanted to, make the worlds strongest moron, and pump all your points into strength, ending up with a strength rating of 500 or something. On the one hand, we need a system that allows for normal humans to be able to do normal human things, but it need to be able to scale up to the point where someone can use an aircraft carrier as a hand to hand weapon. Obviously, there is going to have to be a fair amount of "rounding up/down" in the numbers, but thats fine. Its superheros, its a bit silly, not having super accurate combat systems are forgiveable.

Cant use target number systems like SLA, because after a fairly short point the dice roll becomes irrelevant. 2d10+500, with a target number of 400? autowin.

A SR style dice pool system gives better scalability. Doing normal things as a normal person has a good win/lose chance, but doing mental things as a mental person also has a good win/lose chance. Trouble is, would any human want to count 5's and 6's on 500 dice? Does anyone even *own* 500 dice?

Other than "use a dice roller app to count for you", anyone got any ideas?
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Post by ProfHawking »

Preface: I dunno anything about RPGs or anything, so this may be stupid.

You want to be able to generate a random number in a range that could be

0 - 10
0 - 100
0 - 1000
0 - 10000
0 - 100000

etc. Is that right?

Why not roll a ten sided dice, once for each digit of the range.
so if you want a result of up to 10000, you would roll 4 x 0-9 dice, giving you a random value from 0 - 9999
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Post by FatherJack »

How about this: http://anydice.com/program/6ed ? (click graph)

A simulated ~400 dice roll using 3 x 10d6s. Bit of maths, but not much.
Joose
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Post by Joose »

Its just occurred to me that there is a really easy fix for this situation. Instead of spazzing about with complex dice substitutions, just scale everything down. So, for example, if its supposed to be 50d6 against a target of 20 hits, divide everything by 10 and make it 5d6 against a target of 2. Much more manageable, approximately the same odds of success. It would lose some granularity, but I think that would be on an acceptable level.

I feel like a twat now.

There would need to be a few clarifying rules. For example, there would need to be a minimum size dice pool before you can use it. Also, situations where someone with a dicepool in the hundreds trying to do a regular difficulty thing could probably be allowed to just auto-succeed. Superman trying to pick up a fridge is as trivial as a normal person trying to pick up a pencil. You dont need to roll for everything.
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Post by Dog Pants »

Star Wars has good scaleability - in fact it's essential to the game. It works on success IIRC, like Shadowrun, on D6. Your stats and skills take the form XD+(1 to 2). So the scale would follow like this:

1D
1D+1
1D+2
2D
2D+1
2D+2
etc.

It scales by having, erm, well scales:

Character
Speeder
Walker
Starfighter
Capital
Death Star

I'm struggling to find it, but I remember it working by substituting something like three dice for each scale up or down. So a starfighter attacking a character would get +9D damage, but the character would get to dodge with +9D. It all worked pretty well.
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Post by deject »

Oh man, I remember playing some 2nd Edition Star Wars RPG (before they switched to the d20 system). That game was awesome.
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Post by buzzmong »

Just don't go down the Warhammer route of trying to horse everything to work on a single D6.
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Post by Anhamgrimmar »

Dog Pants wrote:Star Wars has good scaleability - in fact it's essential to the game. It works on success IIRC, like Shadowrun, on D6. Your stats and skills take the form XD+(1 to 2). So the scale would follow like this:

1D
1D+1
1D+2
2D
2D+1
2D+2
etc.

It scales by having, erm, well scales:

Character
Speeder
Walker
Starfighter
Capital
Death Star

I'm struggling to find it, but I remember it working by substituting something like three dice for each scale up or down. So a starfighter attacking a character would get +9D damage, but the character would get to dodge with +9D. It all worked pretty well.
Friend Computer informed me that this is the same sort of deal that Paranoia works with (especially the damage scales) But i'm buggered if i can find my red clearance rule book
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Post by Dog Pants »

There was a few by the looks of it: http://en.wikipedia.org/wiki/D6_System
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Post by Baliame »

I was expecting a challenge where I might put my knowledge to good use.

I am disappoint.
Joose
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Post by Joose »

I kind of like that system, but it might still give issues with scale. Either it scales up quickly, which would mean a reasonably strong guy wouldnt be much different to a very strong guy, or it scales slowly, so there is an appreciable difference between reasonably strong and vey strong, but you then get superman strong rolling a bajillion dice again, which is a pain in the ass.

Unless...could you maybe do both? Use the standard d6 system (roll xD6+y as your stat states, against a target number) for most rolls, but dividing hoog stats and target numbers down to more manageable dice numbers?

For example, if you had a stat of 50d6+3, you could instead roll 5d6+3 against target number/10.

That seems like the best of both worlds. As long as the probabilities work ok. In other words, does xD6+y against target number of z have the same chance of success as x/10D6+y against a target number of z/10? I know that some of the "granularity" would be lost, but I think thats ok.

Bali! MATHS US!
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