Every day in the frozen north brings a chance for snow. By leaving the relative safety of Rovaniemi and the surrounding villages behind, Külk and Joonas are taking a chance on the weather and the terrain. The wilds are not to be travelled without careful thought...
I had been fast and loose with the environment and weather up until now. I had always assumed that the PCs had some kind of provisions, and that they were wrapping up warm. I kept dropping hints that the weather was going to get worse though, and that heading north would lead to severe snowfall. Precautions must be taken etc.
However, I didn't want to railroad any blizzards or consequences. I wanted the weather to be unpredictable. So before the session on Tuesday I thrashed out a kind of probability-based "Fibonacci-like weather generator". A Fibonacci sequence is dependent on the numbers that came before. So the third number is dependent on the second and first numbers, the fourth number is dependent on the third and second and so on. I decided that a simple way to include this was to say that "today's weather is dependent on the previous two days, with some randomness."
Showing posts with label probability. Show all posts
Showing posts with label probability. Show all posts
Wednesday, 23 January 2013
Friday, 30 November 2012
Fighting Fantasy Maths
In a recent post I started to muse about the likelihood of surviving a Fighting Fantasy gamebook. Of course it is easy to say "the higher the SKILL and STAMINA, the more likely you are to survive." But therein lies a question for maths geeks like me. How much more likely?
Monday, 19 November 2012
Aside: The Maths of Fighting Fantasy
This blog, at least in name, talks about the maths of RPGs. Most of the time I actually just want to talk about RPGs, ideas and what happened the other night at the table, but I thought the following video was worth sharing, as it follows on a little from my post about Murderous Ghosts from last week, and also from the post that noisms made about us playing it at the weekend.
I'd recently been thinking about doing something similar to what this video does with Island of the Lizard King, which I found in a charity shop, but there is no way I could do it as much justice as this video does.
One follow-up question does occur: I wonder how much difference there is in the graph structure of the various Fighting Fantasy books?
And another interesting problem that might be do-able: what is the probability that a person actually makes it to section 400, given the skill/stamina that they start with?
There's some work in figuring that out, but it's essentially coming up with a general formula for calculating the odds of surviving an encounter, and figuring out the various general paths through the book (taking into account when you come across things like traps that you have to roll under skill or suffer penalties). To solve it you would build up a couple of general results, then plug in numbers. Not simple per se, but not hard... The actuarial tables of the Island of the Lizard King...
I'd recently been thinking about doing something similar to what this video does with Island of the Lizard King, which I found in a charity shop, but there is no way I could do it as much justice as this video does.
One follow-up question does occur: I wonder how much difference there is in the graph structure of the various Fighting Fantasy books?
And another interesting problem that might be do-able: what is the probability that a person actually makes it to section 400, given the skill/stamina that they start with?
There's some work in figuring that out, but it's essentially coming up with a general formula for calculating the odds of surviving an encounter, and figuring out the various general paths through the book (taking into account when you come across things like traps that you have to roll under skill or suffer penalties). To solve it you would build up a couple of general results, then plug in numbers. Not simple per se, but not hard... The actuarial tables of the Island of the Lizard King...
Wednesday, 22 August 2012
Games Night: A New Man in Yoon-Suin
Last night was another journey in Yoon-Suin, and my new character didn't disappoint. noisms has given a good account of the session, but states early on that I rolled "a ridiculously lucky set of stats" which, I guess, is probably accurate.
noisms method for rolling stats was to roll in order for STR, DEX, INT, WIS, CON and CHA, and he would allow one switch after they were all rolled (i.e., no re-rolling, but if I wanted to WIS and CON scores I could). Thankfully, the dice were extremely well-behaved last night!
STR 16
DEX 13
INT 11
WIS 13
CON 13
CHA 6
Well, OK, except for Charisma... I decided that these were pretty good stats for a Fighter, and early on decided that the only way to play someone with a Charisma of 6 is to act as someone who thinks they are very charming, and can't understand why others seem to screw their face up at him or roll their eyes. Poor Manjeet.
I don't have a clear picture in my head yet of what Manjeet actually looks like; I'm thinking tall, shaved head but with a few days of stubble coming in around his chin. His family are artisans (again, the luck of a random roll; after my previous success with stats and maximum hit points everyone was rooting for my personal history to reveal I was a eunuch) so I guess he would be fairly well turned out.
When I first met Marich (David) and Anil (Patrick) in the forest they gave great short descriptions of themselves. Patrick said, "You see a short, squat, bald man." David: "You see Prince Harry in a wizard's robe."
A high point of the session for me was being the one to deliver the killing blow to Manesh, the Bandit Chief who we battled against last time. I think we were really well coordinated, and Patrick's idea to hire retainers and to kit them out properly worked well. Not only did they hold their own quite well in delaying large numbers of attackers, but because we bothered to armour them up they didn't just die as soon as an opponent looked at them.
noisms claims I was ridiculously lucky; a quick bit of calculation and it turns out he is probably right: there's approximately a 1 in 6.8 million chance of me being that "lucky". And that's before you factor in the max HP roll as well. I just see it as the dice rewarding me for the spectacular fails in the last session. I wonder if I will be so lucky next Tuesday. When you have a Charisma of 6 you really have to make your own luck I guess...
noisms method for rolling stats was to roll in order for STR, DEX, INT, WIS, CON and CHA, and he would allow one switch after they were all rolled (i.e., no re-rolling, but if I wanted to WIS and CON scores I could). Thankfully, the dice were extremely well-behaved last night!
STR 16
DEX 13
INT 11
WIS 13
CON 13
CHA 6
Well, OK, except for Charisma... I decided that these were pretty good stats for a Fighter, and early on decided that the only way to play someone with a Charisma of 6 is to act as someone who thinks they are very charming, and can't understand why others seem to screw their face up at him or roll their eyes. Poor Manjeet.
I don't have a clear picture in my head yet of what Manjeet actually looks like; I'm thinking tall, shaved head but with a few days of stubble coming in around his chin. His family are artisans (again, the luck of a random roll; after my previous success with stats and maximum hit points everyone was rooting for my personal history to reveal I was a eunuch) so I guess he would be fairly well turned out.
When I first met Marich (David) and Anil (Patrick) in the forest they gave great short descriptions of themselves. Patrick said, "You see a short, squat, bald man." David: "You see Prince Harry in a wizard's robe."
A high point of the session for me was being the one to deliver the killing blow to Manesh, the Bandit Chief who we battled against last time. I think we were really well coordinated, and Patrick's idea to hire retainers and to kit them out properly worked well. Not only did they hold their own quite well in delaying large numbers of attackers, but because we bothered to armour them up they didn't just die as soon as an opponent looked at them.
noisms claims I was ridiculously lucky; a quick bit of calculation and it turns out he is probably right: there's approximately a 1 in 6.8 million chance of me being that "lucky". And that's before you factor in the max HP roll as well. I just see it as the dice rewarding me for the spectacular fails in the last session. I wonder if I will be so lucky next Tuesday. When you have a Charisma of 6 you really have to make your own luck I guess...
Friday, 17 August 2012
Getting My Maths On
Watch this space; I've been struck by inspiration somehow today, and so am finally getting maths thoughts out of my head where they have been stewing for ages. I've been writing for a work-type project (I do skills training with PhD students and research staff) and need a different kind of outlet. I thought that was going to be figuring out whether or not to use Apocalypse World, GHOST/ECHO or Cyberpunk as the basis for a small campaign that I want to GM, but it turns out that I've had this growing thought about finally figuring out the In A Wicked Age dice-rolling probabilities that has been bugging me. I don't know the answer now, but I SEE the connections.
In maths, when you have enough pieces, sometimes you can just run them together and get an answer spit back out. Building proofs from the conceptual machinery of algebra is dizzying. You can go so far so quickly.
Of course, there are probably resources out there that have looked at this. On an internet with this many connected souls, the chances are quite high that that's true. However, there is something great about sitting down, spending the time and doing some maths for the sake of it. So that's what I'm doing.
Watch this space: soon we'll have the final word on rolling dice for In A Wicked Age!*
*because, you know, that's what everyone has been waiting for in RPGS...
In maths, when you have enough pieces, sometimes you can just run them together and get an answer spit back out. Building proofs from the conceptual machinery of algebra is dizzying. You can go so far so quickly.
Of course, there are probably resources out there that have looked at this. On an internet with this many connected souls, the chances are quite high that that's true. However, there is something great about sitting down, spending the time and doing some maths for the sake of it. So that's what I'm doing.
Watch this space: soon we'll have the final word on rolling dice for In A Wicked Age!*
*because, you know, that's what everyone has been waiting for in RPGS...
Monday, 16 July 2012
A quick note on Ammo Maths
Some time ago I wrote about a curious little thought that I had had when writing out an ammo mechanic for the zombie game that I will get around to one of these days. I duly set about working on some all powerful equation that would calculate everything. This is what (some) mathematicians do, I did it quite often during my PhD: you reach to try and prove everything, building up from small cases until you have it all.
Except that that doesn't happen all too often in my experience. Instead, you find that the particular case you are looking in to has no easy way of stating it, and in particular, no nice way of explaining it to someone. You can talk in generalities, but often you are glossing over details. You don't find the "beauty" that you are looking for.
That's what happened to me while I was looking for my formula for the "Ammo Maths" problem. It dawned on me during one of those times I have been working on the problem that I was going about it all the wrong way. Sure, the formula(s), when complete, would have some novelty value or interest. But they, in themselves, weren't the interesting thing. In the first case, it would be great to know the answers to the two questions I asked originally.
But more importantly, it would be better to have a meaningful answer to the general case. There is no point in presenting a formula really. Who would use it? Instead, I'm working on typesetting the tables that (may) accompany the mechanic. They could be useful to GMs or players so that they have some idea about just how many shots they might get off. Having a narrative mechanic is a way of avoiding counting bullets and shells, but it would still be good for people to have some idea of just how high up the food chain they are.
So that's what I'm checking at the moment, what the numbers say and tell us, and then I will typeset it (which takes a little time as my HTML for tables is hopeless; I'll be copying and pasting over from word processor instead).
Except that that doesn't happen all too often in my experience. Instead, you find that the particular case you are looking in to has no easy way of stating it, and in particular, no nice way of explaining it to someone. You can talk in generalities, but often you are glossing over details. You don't find the "beauty" that you are looking for.
That's what happened to me while I was looking for my formula for the "Ammo Maths" problem. It dawned on me during one of those times I have been working on the problem that I was going about it all the wrong way. Sure, the formula(s), when complete, would have some novelty value or interest. But they, in themselves, weren't the interesting thing. In the first case, it would be great to know the answers to the two questions I asked originally.
But more importantly, it would be better to have a meaningful answer to the general case. There is no point in presenting a formula really. Who would use it? Instead, I'm working on typesetting the tables that (may) accompany the mechanic. They could be useful to GMs or players so that they have some idea about just how many shots they might get off. Having a narrative mechanic is a way of avoiding counting bullets and shells, but it would still be good for people to have some idea of just how high up the food chain they are.
So that's what I'm checking at the moment, what the numbers say and tell us, and then I will typeset it (which takes a little time as my HTML for tables is hopeless; I'll be copying and pasting over from word processor instead).
Thursday, 7 June 2012
Games Night: LotFP/Isle of the Unknown
I've missed talking about our regular Lamentations of the Flame Princess game for a couple of weeks. Last time on the Isle of the Unknown, Patrick was DMing us through a dungeon underneath an old keep. We had killed some Cthulu-worshippers, some giant bats and avoided some traps along the way. All was well with the world, and I was enjoying playing my new cleric, Priam, servant of the powerful god Venn. Charley/Henry Shortbread, the specialist, had disappeared into the undergrowth, and Priam had just happened to walk along and find the party as they were on their way to the keep.
Patrick has a nice house rule when it comes to magic; as with many D&D type games, you have your spell slots, but you can also try to cast any spell appropriate to your level, so long as you roll for success. Success is determined according to the Apocalypse World success rules: 2d6 plus or minus any modifier, a 10+ gives you what you want (the successful spell), a 7-9 gives you success plus a roll on a "something bad happens" table and a 6 or less just gives you the roll on the "something bad happens" table.
The Bless cleric spell/prayer in LotFP, as understood by me, means that you get d6+level points to spend/declare for future rolls. So having points like that means I can spend points to attack, to evade, for WIS checks - or even, to try and get future spells using Patrick's magic house rule. So if I get a good Bless result early on, then I have points in reserve for the night. I just needed to make that first AW-style roll.
It worked last week. It didn't last night.
I roll a 9, so get my blessing, but immediately have to spend the points to get favour from Venn again in order to cast cure light wounds on myself. Why? Displeased with my constant requests, Venn placed a small dog in my abdomenal cavity. Yes, that's right: A SMALL DOG. Not warts or boils on my face, or a limp, or blindness. A SMALL DOG. Luckily I was able to perform a caesarean on myself and have enough HP to then invoke cure light wounds (using many of the bless points that I just got).
Phew. I was up on the deal I guess. The dog was out, I had more HP than I had had before, I had some bless points left, and a dog that (rolls for loyalty)... hates me.
Lesson learned: don't try to game your deity.
Despite having the highest wisdom in the group I failed four rolls in a row - which is improbable enough - but then for the first three rolls I rolled a 16 each time. A one in eight thousand chance.
The small dog, Priestly, was eaten by a giant moth, we had our first big toe-to-toe battle with some giant Amber Scarabs (was touch and go), escaped from a crazy trap, got suspicious about the Bandit/Cleric who put us up to the job in the first place and the younglings were shouting at each other so much at one point that I passed Patrick the encounter die and said "You may as well just roll."
I can't make it for a couple of weeks, so have asked Patrick if my character can try to slip out of the dungeon (so that he isn't killed in the background when the others do something incredibly reckless). We'll see what happens. I'm enjoying playing a cleric much more than playing a specialist, so am hoping that I'll be able to get him back into play at some point soon.
Patrick has a nice house rule when it comes to magic; as with many D&D type games, you have your spell slots, but you can also try to cast any spell appropriate to your level, so long as you roll for success. Success is determined according to the Apocalypse World success rules: 2d6 plus or minus any modifier, a 10+ gives you what you want (the successful spell), a 7-9 gives you success plus a roll on a "something bad happens" table and a 6 or less just gives you the roll on the "something bad happens" table.
The Bless cleric spell/prayer in LotFP, as understood by me, means that you get d6+level points to spend/declare for future rolls. So having points like that means I can spend points to attack, to evade, for WIS checks - or even, to try and get future spells using Patrick's magic house rule. So if I get a good Bless result early on, then I have points in reserve for the night. I just needed to make that first AW-style roll.
It worked last week. It didn't last night.
I roll a 9, so get my blessing, but immediately have to spend the points to get favour from Venn again in order to cast cure light wounds on myself. Why? Displeased with my constant requests, Venn placed a small dog in my abdomenal cavity. Yes, that's right: A SMALL DOG. Not warts or boils on my face, or a limp, or blindness. A SMALL DOG. Luckily I was able to perform a caesarean on myself and have enough HP to then invoke cure light wounds (using many of the bless points that I just got).
Phew. I was up on the deal I guess. The dog was out, I had more HP than I had had before, I had some bless points left, and a dog that (rolls for loyalty)... hates me.
Lesson learned: don't try to game your deity.
Despite having the highest wisdom in the group I failed four rolls in a row - which is improbable enough - but then for the first three rolls I rolled a 16 each time. A one in eight thousand chance.
The small dog, Priestly, was eaten by a giant moth, we had our first big toe-to-toe battle with some giant Amber Scarabs (was touch and go), escaped from a crazy trap, got suspicious about the Bandit/Cleric who put us up to the job in the first place and the younglings were shouting at each other so much at one point that I passed Patrick the encounter die and said "You may as well just roll."
I can't make it for a couple of weeks, so have asked Patrick if my character can try to slip out of the dungeon (so that he isn't killed in the background when the others do something incredibly reckless). We'll see what happens. I'm enjoying playing a cleric much more than playing a specialist, so am hoping that I'll be able to get him back into play at some point soon.
Wednesday, 6 June 2012
In Which I Fail To Blog
Time pressure, work, maths not working, not making time, yadda yadda yadda.
noisms does make some good points that there might be a broader question here connected with styles of DMing and what they might be used to as well; I can't really comment on that: I've only played under the GMing of noisms and Patrick and I know them both to be fair but lethal, so I know what to expect.
Anyway, more soon. I promise. (and you know what that leads to, right?)
- The maths has come together for my ammo maths question (or at least partly), so I'll be typesetting that over the next few days and putting it up - along with some thoughts on why this is interesting in general.
- noisms is really knocking it out of the park with his latest blog posts; two in particular have been really good. I really liked his thoughts on Hanafuda cards, and the discussion underneath really seems to have sparked something (in me and in other readers) thinking about using cards in play generally.
- The other post was a bit of AP from the LotFP game that we are both involved with. My nephew and his friend joined us, and last week brought along another two friends. This has really added something to the game, and noisms makes some really interesting observations about differences in play styles.
noisms does make some good points that there might be a broader question here connected with styles of DMing and what they might be used to as well; I can't really comment on that: I've only played under the GMing of noisms and Patrick and I know them both to be fair but lethal, so I know what to expect.
Anyway, more soon. I promise. (and you know what that leads to, right?)
Tuesday, 15 May 2012
Simulating a dX
I've been thinking for a few months about how to best simulate rolling a dX, which is the same as indexing X entries randomly. It takes time to sort ideas and thoughts out; this is a starting point for collecting things together.
There are six standard polyhedral dice: d4, d6, d8, d10, d12 and d20. When using these we assume that the dice are fair - each side is equally likely to come up. If we were to create or simulate a die with X sides it would be best if it were fair. We cannot simulate a d11 using 2d6 directly - we get a range of 11 possible values, but there are different probabilities for each value. The simulated die would not be fair.
We can simulate a few dice with the six standard polyhedral dice through either re-rolling on the high value, or by "halving the die". It is not too difficult to introduce simple notation to account for both of these actions.
d6/2 gives a d3. We let d6r stand for the situation where we reroll the 6. We only want values 1-5 so d6r results in a fair d5. However, d10/2 also gives d5, and without the reroll. From the standard polyhedral dice we can simulate the following dice easily:
We could also simulate a fair d9 by rolling two d3s; these act as indexing nine entries in a table. We could denote this with d3 x d3 or (d3)^2.
These various actions - re-rolling, halving and dividing across tables - allow us to build up a greater number of simulated fair dice. I'll go into more detail in future posts, and see if I can start to make sense about how we might simulate a dX for any positive integer X.
There are six standard polyhedral dice: d4, d6, d8, d10, d12 and d20. When using these we assume that the dice are fair - each side is equally likely to come up. If we were to create or simulate a die with X sides it would be best if it were fair. We cannot simulate a d11 using 2d6 directly - we get a range of 11 possible values, but there are different probabilities for each value. The simulated die would not be fair.
We can simulate a few dice with the six standard polyhedral dice through either re-rolling on the high value, or by "halving the die". It is not too difficult to introduce simple notation to account for both of these actions.
d6/2 gives a d3. We let d6r stand for the situation where we reroll the 6. We only want values 1-5 so d6r results in a fair d5. However, d10/2 also gives d5, and without the reroll. From the standard polyhedral dice we can simulate the following dice easily:
| d2 = d4/2, d6/3, etc. d3 = d6/2, d12/4. d5 = d10/2, d20/4. d7 = d8r. |
d9 = d10r. d11 = d12r. d19 = d20r. |
We could also simulate a fair d9 by rolling two d3s; these act as indexing nine entries in a table. We could denote this with d3 x d3 or (d3)^2.
| d3 x d3 | 1 | 2 | 3 |
| 1 | 1 | 2 | 3 |
| 2 | 4 | 5 | 6 |
| 3 | 7 | 8 | 9 |
These various actions - re-rolling, halving and dividing across tables - allow us to build up a greater number of simulated fair dice. I'll go into more detail in future posts, and see if I can start to make sense about how we might simulate a dX for any positive integer X.
Tuesday, 24 April 2012
Ammo Maths
Almost as soon as I posted Tracking Ammo it dawned on me that an obvious series of questions arises:
- If I find a handgun with a 5 rating, what's the likelihood that I will get at least ten shots from it?
- If I have a shotgun with a rating of 3, how many shots am I likely to get from it?
- If I have a gun with a rating of X, what is the probability, p, that I get N shots from it?
- If I have a gun with a rating of Y, how many shots, Z, am I likely to get from it?
Thursday, 5 April 2012
Tuesday Night's Stats Lesson
GHOST/ECHO was pretty amazing on Tuesday night, another great example of a wonderfully complex story being built up from simple pieces collaboratively. That was one of two amazing things that happened on Tuesday.
The second was when someone (I feel like I should protect his identity) rolled three d6s and said, "Wow, look at that!" He had rolled three 6s. Which is quite amazing - but more amazing was the comment that followed next from him: "There's only a 1 in 18 chance of that."
My head snapped around like Linda Blair. "Whaaaaaat?!" I cried. "1 in 18? 1 in 18?!!!"
"What? What's wrong?"
Sigh. What do they teach people these days?
If two (or more) events are independent - meaning that one has no bearing at all on the other (and vice versa) - then we can take the probabilities of these two events and simply multiply them together. So if we had a coin and a d6, and wanted to know the probability that upon flipping and rolling them we got a Head and a 5, we would take the two probabilities (1/2 and 1/6 respectively) and multiply them together to give us 1/12. Job done.
The same holds true in this case for our three 6s. For all intents and purposes we can assume that they do not affect each other. So rolling three 6s is (1/6) times (1/6) times (1/6) or 1/216 in total. If you're a percentage kind of person that means there's slightly less than a 0.05% chance of rolling three 6s. 1 in 18 is around 5.5%.
The second was when someone (I feel like I should protect his identity) rolled three d6s and said, "Wow, look at that!" He had rolled three 6s. Which is quite amazing - but more amazing was the comment that followed next from him: "There's only a 1 in 18 chance of that."
My head snapped around like Linda Blair. "Whaaaaaat?!" I cried. "1 in 18? 1 in 18?!!!"
"What? What's wrong?"
Sigh. What do they teach people these days?
If two (or more) events are independent - meaning that one has no bearing at all on the other (and vice versa) - then we can take the probabilities of these two events and simply multiply them together. So if we had a coin and a d6, and wanted to know the probability that upon flipping and rolling them we got a Head and a 5, we would take the two probabilities (1/2 and 1/6 respectively) and multiply them together to give us 1/12. Job done.
The same holds true in this case for our three 6s. For all intents and purposes we can assume that they do not affect each other. So rolling three 6s is (1/6) times (1/6) times (1/6) or 1/216 in total. If you're a percentage kind of person that means there's slightly less than a 0.05% chance of rolling three 6s. 1 in 18 is around 5.5%.
Tuesday, 27 March 2012
Random and Biased
Following on from my post "Different Dice" a few days ago, I think there is another important distinction to be made between the ideas of random and biased.
For example, if we roll a fair d6 - i.e., one which is not weighted in favour of any particular result - then whatever it lands on we know that it the result is both random and unbiased, because the die is fair. If we roll 2d6, paying attention to the sum as the result of this event, then while the result itself is still random it is biased. Because of the different ways that you can make a total of 7 from rolling two d6 dice, a 7 is six times more likely than getting a result of 2 or of 12 (both of which have only one way of being achieved).
I'm interested in this kind of bias a lot at the moment; I was tinkering/hacking together a zombie game* based a little on Risus and a little on Apocalypse World. Apocalypse World works well with its main dice mechanic because it is so straight forward: for around 60% of the time on a general (unmodified) roll your action carries - or at least you get some success. For less than 20% of the time the dice give you exactly what you want. This seems like a neat way to do it: the outcome is random, and there is a slight overall bias towards success.
But in the messed up post-apocalypse, maybe those are the kind of odds you need.
*more on that setting/game another time!
For example, if we roll a fair d6 - i.e., one which is not weighted in favour of any particular result - then whatever it lands on we know that it the result is both random and unbiased, because the die is fair. If we roll 2d6, paying attention to the sum as the result of this event, then while the result itself is still random it is biased. Because of the different ways that you can make a total of 7 from rolling two d6 dice, a 7 is six times more likely than getting a result of 2 or of 12 (both of which have only one way of being achieved).
I'm interested in this kind of bias a lot at the moment; I was tinkering/hacking together a zombie game* based a little on Risus and a little on Apocalypse World. Apocalypse World works well with its main dice mechanic because it is so straight forward: for around 60% of the time on a general (unmodified) roll your action carries - or at least you get some success. For less than 20% of the time the dice give you exactly what you want. This seems like a neat way to do it: the outcome is random, and there is a slight overall bias towards success.
But in the messed up post-apocalypse, maybe those are the kind of odds you need.
*more on that setting/game another time!
Sunday, 25 March 2012
Different Dice
I've been thinking about notation. A quick Google shows me that there are lots of people out there who are interested in probability questions with dice - and by extension with RPGs. Or perhaps that flows the other way, they are interested in games, and then start to get interested in how probabilities come from dice mechanics.
In either case, there are people out there who are interested in these areas. It's not my interest largely (when it comes to maths and RPGs) but it is definitely a good place to start, and one that throws up interesting points. Dice have different contexts. Rolling 2d6 in Apocalypse World, when you want to know the sum, gives you a value from 2 to 12, and those 11 values are distributed unevenly. In this case, you don't really care what either of the dice actually gives. You care about the total.
Rolling two d6s when you care about the values of each dice gives you a different proposition. Picture having a red d6 and a blue d6. Rolling 2 on red and 5 on blue results in something different from 5 on red and 2 on blue. Rather than have 11 values given by the sum of the faces, we have 36 possibilities, each with the same probability of occuring.
For future posts then we can consider 2d6 in the normal way and, to be clear, two d6 for the situation when we care about each individual result on the two d6s. Or three d8s. 3d10 is different from three d10s. A numeral in front of a die size will indicate that we want to sum them, a number in words will indicate that we want to use each result from the dice.
All sound fine? It might be a basic sort of thing to write about, but this is the foundations: important in games (of all kinds) and maths. On foundations we can extend outwards, upwards and in as many ways as can be supported.
In either case, there are people out there who are interested in these areas. It's not my interest largely (when it comes to maths and RPGs) but it is definitely a good place to start, and one that throws up interesting points. Dice have different contexts. Rolling 2d6 in Apocalypse World, when you want to know the sum, gives you a value from 2 to 12, and those 11 values are distributed unevenly. In this case, you don't really care what either of the dice actually gives. You care about the total.
Rolling two d6s when you care about the values of each dice gives you a different proposition. Picture having a red d6 and a blue d6. Rolling 2 on red and 5 on blue results in something different from 5 on red and 2 on blue. Rather than have 11 values given by the sum of the faces, we have 36 possibilities, each with the same probability of occuring.
For future posts then we can consider 2d6 in the normal way and, to be clear, two d6 for the situation when we care about each individual result on the two d6s. Or three d8s. 3d10 is different from three d10s. A numeral in front of a die size will indicate that we want to sum them, a number in words will indicate that we want to use each result from the dice.
All sound fine? It might be a basic sort of thing to write about, but this is the foundations: important in games (of all kinds) and maths. On foundations we can extend outwards, upwards and in as many ways as can be supported.
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