'Cos i suck at them more than a sucky thing sucking on a suck-stone.

Can anyone work out probabilities for the following? I'd appreciate it muchly.

OK. d6 rolling. You get to roll a bunch of them depending on the stat that covers a certain skill. Say, Climbing and Strength. For example, Joe's Strength is 4, so for climbing skill checks he gets to roll 4d6. Now instead of having a success number or a roll under/over system, i wondered whether successes could be based on rolling doubles/triples/quadruples etc.

So on 4d6, any doubles would be 1 success (1,2,3,4,5,or 6s) with the possibility of two doubles on 4d6 giving 2 successes, triples give two successes, quadruples 3, quintuples 4 etc, ect. Some of thsoe won't be possible unless you are able to roll that many dice, so your probability of getting better successes go up with any increases in your stat as you get to roll more dice. I also considered whether 'straights' could count as a success, with all dice running through the numbers (ie on 4d6 the results being frex 3,4,5,6).

I also figured a very simple combat/damage mechanic for this. The number of successes against you in combat are the number of dice you lose on all subsequent rolls, making you less effective after every wound.

I'm planning stats to have a range of perhaps 1-8 or 1-10, to keep the dice rolling manageable.

So, as you get to roll more dice, are the probabilties linear on achieving doubles/triples/quadruples and thus can you expect more successes than someone without as many dice as you? Is it worth throwing more dice statistically?

Thanks!

Edit: I should also point out that i'm playing with the idea of a mechanic whereby the player can manipulate the numbers rolled to simulate special skill or magic. As is, the success mechanic is totally random and so perhaps a special skill Climb 1 means that Joe above could change any one number rolled by 1 degree, changing a 2 to a 3 so he gets a double. If he had Climb 2, then he could change 2 numbers rolled by 1 degree or one number rolled by two degrees, etc, etc.)

Edit 2: Me thick. Sorted it out.

By the last line, do you no longer need help with the analysis?

-O

I think I have an answer.

The first step is to think in terms of rolling each die in sequence, then adding one to your total if the die matches any other die. And the probability (out of six) of getting a match on your nth die is equal to the number of dice that haven't incremented your score.

So if you're on your 5th die and your score is 2, that means there are three chances in six that your next die will increment your score. If it does, then there are still three chances in six that the following die will increment your score. If it doesn't then there are four chances in six for the following die.

Following this approach you can develop a recursive method of generating a table of probabilities. That is, the probability distribution for 6 dice could be rapidly computed once you have it for 5 dice, and so on.

Now that I look at it, it's not too hard to do by hand, or even better by spreadsheet.

Let P(s,n) be the probability of scoring s successes with n dice. Then

P(s+1,n+1) = P(s,n)*(n-s)/6 + P(s+1,n)*(7-n+s)/6

The first term is the chance of getting s successes on n dice, times the chance that the next die will be a match for one of those already thrown. The second term is the chance of getting s+1 successes on n dice, times the chance that the next die won't be a match.

We also need to calculate

P(0,n+1) = P(0,n)*(6-n)/6

Then we plug it all into Excel...very carefully, and out comes this:

(EDIT: the txt is just the data output; the zip contains the excel spreadsheet with the formulas.)

Also, I didn't calculate the mean or std dev, let alone analyze the impact of the manipulation mechanic.

I also didn't look at straights.

Just by looking at the table, most rolls are going to produce a pretty narrow range of 3, maybe 4 numbers. It also looks like doubling your dice is going to more than double your average. E.g. 3 dice is going to average around .5, while 6 dice will average around 2. 4 dice will average around 1, 8 dice around 3.5. 5 dice will average around 1.5, 10 around 5.

Wow, thanks Elliot. I'll have a proper look and play tomorrow!

Cool. It's almost exactly how i invisaged it, with 4 dice giving an average of one success. Default stats in the game are all 3 with ten points to distribute between the ten stats, so average is deemed to be 4, which gives you on average one success when rolling! Groovy. I also decided on a mechanism to cut down on dice rolling for anyone/thing with a stat over 10. Just assume that 10 dice gives 5 successes and then roll the amount of dice over ten to get the final result. So a stat of 14 will give you 5 automatic successes and then you roll 4 dice and add any successes from that to the result.

I'm dropping the straights mechanism, but the skill rating still allows you to modify dice rolls.

I'm looking at skill ratings of:

1= Experienced
2= Advanced
3= Master

then for mythic beasts/races and immortals:

4= Mythic
5= Divine

This mechanism allows anyone with a statistical rating to attempt any skill with a chance of success (skills are split by stat and are affected by the statistical rating), but allows those with special training a big advantage when attempting skills in which they are trained (adjusting a roll within a bandwidth of 33% with each skill point used).

I like this and think it might work rather well.

So an example:

Stat: Physique Rating: 4
Athletics
Delving
Wrestling 1
Applied Strength

On all skill tests that result from running, sprinting, jumping (athletics), rowing, caving, climbing (delving) and lifting capacity, pushing (applied strength), the player rolls 4d6 for the attempt, noting successes by throwing doubles, triples or if he is lucky, a quadruple. However, when he is wrestling (skill rating 1), he can adjust the result of one of his four dice up or down by one. So, if he rolls 3, 5, 6 and 2 for delving, he fails the test, as he got no doubles. If he rolls that for wrestling, he could change the 2 to a 3 or the 6 to a 5 in order to achieve a single success. This simulates his experience in the skill. If he had wrestling 2, he could change both of those in order to get 2 successes (change the 2 to a 3 and the 6 to a 5).

Opposed Tests

When an activity is tried that is opposed by another person, then the relevant stats of the engaged parties are compared and the protagonist rolls an amount of dice modified by this comparison.

Example 1: Joe tries to sneak past a guard. His Agility is 5 but he has no relevant skill in Moving Silently (the relevant skill under Agility). The guard has an Alertness stat of 4 (no relevant skill in Perception, the relevant skill under Alertness). Comparing the stats, Joe, as the protagonist, has a 1 die advantage over the guard. Therefore in the opposed test, he rolls 6 dice for his Move Silently test to determine successes (Agility of 5 +1 for advantage over the guard). The guard does not need to role. If the stats were reversed, then Joe would only roll 3 dice to determine successes.

With your method of resolving cases of >10 dice the extra dice are "shortchanged". For example, if you actually rolled 14 dice, you'd average around 8.5 successes. Taking five for the first 10 and then rolling four will give you an average total of only 6 successes.

This creates breakpoints that you may or may not want to have.

A related issue to bear in mind is that, since average successes scale nonlinearly, there's an incentive to specialize. That is, stripping dice from a stat hurts less than adding additional dice to a stat helps. So, that could be good or bad depending on what you want.

Finally, the effect of skill is tricky to calculate. You might have to resort to doing simulations instead.

Quote from: Elliot WilenWith your method of resolving cases of >10 dice the extra dice are "shortchanged". For example, if you actually rolled 14 dice, you'd average around 8.5 successes. Taking five for the first 10 and then rolling four will give you an average total of only 6 successes.

This creates breakpoints that you may or may not want to have.

I'll have think about that then.

QuoteA related issue to bear in mind is that, since average successes scale nonlinearly, there's an incentive to specialize. That is, stripping dice from a stat hurts less than adding additional dice to a stat helps. So, that could be good or bad depending on what you want.

Good. I'm pretty happy with that. Thanks for your thoughts.

Quote from: One Horse TownI'm planning stats to have a range of perhaps 1-8 or 1-10, to keep the dice rolling manageable.

If I'm reading this correctly, what you're proposing bears a fair similarity to the One Roll Engine -- roll a handful of ten-sided dice, look for matches (doubles, triples, quadruples, etc.).  If this is so, there are two things to bear in mind.

First, if you roll more dice than the number of sides of the dice, you're guaranteeing success.  With a d6, if you roll 6d6, there's at least a chance that you'll roll 1, 2, 3, 4, 5, and 6.  If you roll 7d6, at least two of the dice will match.

Second, there's a huge statistical drop-off from doubles to triples, so much so that you can usually only count on a double.

Other than that, it's a neat way of rolling dice to determine success.

!i!

It's a got a slight similarity but not as complex as ORE. Really, in this system, there's nothing special about triples--it's just like getting two doubles. That's what made it easy enough to do the calculations.

Also, ORE uses both the number of matches (the "width") and the actual number being matched (the "height").

No way I would have attempted ORE by any means other than simulations. The number of possible outcomes for even a few dice is too big, and the calculations are pretty messy.

Yeah, i only found out about the ORE mechanism yesterday when i checked out some other forums. I think this mechanism is sufficiently different from it.

The game is meant to be a faux Ancient Greek/Persian Empire game where legends walk, as do mythic beasts and the immortals. The Gods are still active in the world expanding creation and the idea is that the PCs get involved in grand quests that could be for example finding the Fountain of Life, slaying the Beast of Blarg or opposing the wicked mortal offspring of the God of Strife, who is raising an army. Typical fantasy stuff, but with a mythic quality. Characters seek Fame so that their names are entered onto the Roll of Heroes and have Sagamakers write plays about them. They have Devotions to the Gods (several if they fancy) and this Devotion allows them to ask for Boons. These could be as simple as effecting skill rolls or as catastrophic as raising a tidal wave or cursing the King. Devotion fluctuates as the PC makes pilgrimages, raises temples, leads services or dedicate victories. When he asks for a Boon, the cost of the Boon is removed permanantly from his Devotion to that God; he's used up his favours. Then he can start building it again.

The Pantheon of Gods is a fairly simple Life vs Death deal, with all of them taking one part of creation/destruction as their purview. So one God may hold the Secret Flame (magic), another the Pillars of Creation (creation) and another the Hammer of Destruction. The Gods live in mythic places on the earth such as the Gates of Destiny or the Golden Halls and mythic heroes can track these places down.

Enough exposition!

On the successes front and 7dice guarenteeing success. I'm splitting the game into four seperate levels. Mortals (max stat 5), Heroes (max stat 7), Mythic (max stat 9) and Immortal (no max). The idea being that you can run the game from a common man involved in the typical sort of fantasy game campaign and all that involves, through the Hero level which would be on a par with high level d&d and then onto Mythic which will be akin to the stories of the Greek heroes like Jason, Perseus and the like. Then immortals are the offspring of Gods like Hercules or members of the first races.

The split is there to allow people to choose the tone of the game, but i'll also use things like Fame and Resolve to allow movement through those levels.

Callings

Characters choose a race and a calling when devising a character. Race templates might look like this and are added to the PC profile after all of the stats have been agreed apon:

Joe Bloggsian: +1 Interaction, Charm 1, Barter 1
John Doeian: Survival 1, Hardy 1, Foraging 1, Sign reading 1  
Verytallian: +1 Physique, +1 Prowess, Applied Strength 1

Once a race has been chosen, a calling is chosen, like the example below:

Mythmaker

Mythmakers are those who push their bodies past the barriers that others impose on themselves. They strive to go faster, further and higher than those who preceeded them so that their names can be added to the Roll of Heroes. They are athletes, wrestlers and game players. A big ego can sometimes acompany these pushers of boundaries which sometimes turns to arrogance and indifference to those 'below' them. These larger than life personalities sometimes participate in impromptu challenges of skill or strength with worthy adversaries on the road or if within a city can sometimes be followed by cheering crowds. Example Greek comparison: Olympian Athlete.

Physique +1, Endrance +1, Wrestling +1, Athletics +1, Applied Strength +1

The character is named Theoric the Untiring. Theoric venerates Auros the Ox, Consumer of the Void and will dedicate his athletic victories to his patron to build up his Devotion, maybe getting access, after time, to Boons that could make him even stronger. Theoric is a Verytallian. It is a 'mortal' game and so the stat maximum is 5.

Theoric the Untiring
Manual Dexterity 4
Endurance 5
Pragmatism 4
Agility 4
Physique 5 Wrestling 1, Athletics 1, Applied Strength 2
Alertness 4
Leadership 4
Mental Discipline 3
Interaction 5
Prowess 5

Edit: This is turning into a bit of a design blog, so 'll ease up now and see about interest when i'm much further advanced!

As this is meant to be a game set in a faux mythic Greece in ancient times, i'm aiming to do away with currency. There is none. There is only barter. This is a concept us modern people find difficult and counter-intuitive, so i wonder whether i could post thoughts here for comment on how intuitive my system will be.

Barter Value (BV)

All goods and equipment (including mass trade goods) will have a BV. The barter value is a very simple mechanism based on how much food & water it takes to keep one person for one day. So a BV of 1 is equal to that amount. Each piece of equipment or item will have their BV listed with that as the base.

For Example:

Sheep BV 10
Trained Guard Dog BV 15
Sword BV 40
Floppy Hat BV 3
Lodging BV = number of nights stayed + 1

So a PC wanting to buy a new sword could trade 2 trained guard dogs and a sheep for it or 13 floppy hats and a days food (BV1). Obviously, this is just using the 5 examples above. There will be the normal amount of equipment listed so that interesting trades can be made.

The only complication to this very basic mechanic will be a 'regional variance' table which will just be a multiplier to the base value such as x0.8 or x1.2 etc. Also a conditional modifier can be applied, such as 'war footing', 'drought' and other likely conditions that can affect the base BV of goods.

Just a few examples of Boons that characters can call upon with their Devotions. I expect i'll have between 8 and 10 for each God.

Characters build up devotions by making pilgrimages, dedicating victories to the God or by certain actions that the patron approves of and quests. PCs can have devotions to many Gods if they wish, although that may cause some petty jelousy and gaining the attention of said divinities. The Devotee calling is dedicated to a single God (basically priests) and receive larger Devotional rewards than other callings. The cost of the Boons below is permenantly removed from the relevant Devotion score once it has been called upon.

Calling the Juggler Radiant
Patron: Hyssh, the Many Handed, Keeper of Eternity
Cost: 3

Description: The supplicant asks to be instilled with the divine manual dexterity of his patron. For one scene he increases his Manual Dexterity by 1 point. This affects all Manual Dexterity skill rolls.

Thunderclap
Patron: Hyssh, the Many Handed, Keeper of Eternity
Cost: 8

Description: The supplicant places his palms together and implores his patron to instil in him the power of the twelve-handed God. The supplicant then claps his hands together and the roar of the twelve-handed God shakes the air. Any Devotees of the Cerenesian Pantheon within earshot must roll an Endurance (Diehard) test. Failure results in loss of consciousness for 10 minutes and deafness for 1 day upon awakening, 1 success results in deafness (no hearing based Alertness tests allowed for 1 hour), 2 successes results in a ringing in the ears (-1 die to all hearing based tests for 10 minutes).    

Cyroxix Chrysalis
Patron: Hyssh, the Many Handed, Keeper of Eternity
Cost: 25

Description: The character is gifted with a shimmering silver chrysalis that pulses softly. The chrysalis must be kept warm and dry for six months. Once six months is up, one of the children of Cyroxix (Hyssh's mount) hatches from the cocoon. This magnificent creature will serve the supplicant until either the death of the beast or the master.

Profile

Manual Dexterity 8, Trickery 3
Endurance 7, Diehard 1, Hardy 3
Pragmatism 4
Agility 8, Avoidance 2
Physique 6, Athletics 2
Alertness 6, Perception 1
Leadership 2
Mental Discipline 4
Interaction 2
Prowess 5, Trample 1
 
Qualities: Sniff the Wind (Alertness), Darksight (Alertness), Twelve Hands of Hyssh (Manual Dexterity), Deathless (Endurance), Telepathy – Empathy (Mental Discipline), Chase the Horizon (Physique)

Slow Erosion
Patron: Hyssh, the Many Handed, Keeper of Eternity
Cost: 50 (supplicant must have at least one statistic of 7)

Description: The supplicant asks his patron to give him a measure of eternity. The supplicant must carry out a quest for his God in order to achieve this. If he is successful, then the number of his days is extended to double his natural lifespan. Although he ages normally during this time and is subject to death by violence, he does not die of natural causes until the allotted time is up. Hyssh does not let slip of eternity lightly and has been known to smite those who call upon this Boon frivolously or on more than one occasion.