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Salamanca
Salamanca's picture
Dice Results

I started rolling dice this week to see where the results would fall.  My original thought was to see what the results were for the new mechanic of grouping to ten vs. the old Target Number set up.

I opted to use 6 dice as most of my players seem to start at around 6k3 for their main attack and I thought that would be an accurate spot to gauge the new results.

I rolled 500 sets of results and grouped based on the following priority: most successes possible, leave the fewest dice unused. 

 

on 6 dice I saw the following results:

71% of the results were 3 successes

14% of the results were 4 successes

12.5% of the results were 2 successes

1% of the results were 5 successes

1% of the results were 1 success

.5% of the results were 0 successes

The reroll of one die improved a roll about 9% of the time.

 

I tried some smaller sample groups with 5, 7 and 8 dice and it looks like you can rely on seeing 1 success for every 2 dice. 

 

Now for the tricky part: if the players are or relatively equal strength and rolling the same pool, that is going to lead to a HUGE amount of ties in the initiative pool.  Which may be something we need to find a work around for. 

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Morgan Wolfe
Morgan Wolfe's picture

I applaud you for your work. I considered doing something like that, but realized it was going to take more time than I wanted to put into it. And I say that as a number wonk :-).

There was a program that was great for computing the odds on XkY, but I don't think I have it anymore. He still has a die-roll-probability program at http://www.diku.dk/~torbenm/Troll/ that I haven't played with yet.

Morgan Wolfe
aka Capt. Doña Sir Kestrel of Avalon http://silver-gateway.com/7sea/

Morgan Wolfe
Morgan Wolfe's picture

There's a user-generated rule on the web version for an L5R 3k2 roll, but when I change it to 7k4 it hangs up. I'm still playing with parameters, but this could be a good tool for people who want to compare probability curves for different types of rolls. Ther are also Savage Worlds and Fudge rules to start with.

Edit: Dropping the "Iteration bound" way down to 1 or 2 for high values of rolled dice seems to help, but it also cuts the curve off before it really tapers off. Still, for a free tool it's pretty powerful.

Morgan Wolfe
aka Capt. Doña Sir Kestrel of Avalon http://silver-gateway.com/7sea/

Salamanca
Salamanca's picture

I just had a very slow day at work and some dice in my pocket. 

 

But I always figured actually rolling beats an algorithm any day.  Plus, rolling dice... catharsis.

Doctor
Doctor's picture

There are plenty of dice rollers out there (I have a preference for anydice.com), the problem is that this dice system really highlights why humans are awesome and computers are not yet our overlords. The efficient grouping of dice is something we can do with just a little thought but it gets very complicated very fast for a computer to model. Anyway, I did some rudimentary number crunching for this post but the rank bonuses and the like make the numbers very hard to nail down. This is one of the reasons I am pretty sure JWP did not crunch the hell out of the numbers either. Basically the dice are VERY predictable, so much so that the elemet of rolling dice itself is almost pointless. There would be only slightly less variance if the outcome was determined by a coinflip between X/2 and (X/2)-1 for X numer of dice. 

[Edit note: Looking at it, a coinflip might actually have more variance.]

 

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Morgan Wolfe
Morgan Wolfe's picture

Thanks for the reminder about Anydice. I love being able to see the curve like that. Then again, I'm a number geek married to a system geek, so there's that :-).

Morgan Wolfe
aka Capt. Doña Sir Kestrel of Avalon http://silver-gateway.com/7sea/

Cthulhu Netobvious
Cthulhu Netobvious's picture
Speaking of predictable Dice, the FUDGE dice used by Fate Core almost always cancel out because they use 4 sets of 6-sided dice, with each of the dice having 2 (+) sides, 2 (-) side sand 2( ) sides. The "plus" and "minus" cancel out and the "blank" side offers nothing. If the designers just added one additional speciality die to the set of 4 original dice, this extra speciality die having its 6-sides with 3 (+) sides and 3 (-) sides, then the outcomes would have trended more often towards either (+) or (-), instead of the usual bland outcomes we get with Fate Core now.

TAJ-07: Technopriest And Justicar Of 7thSea2e

Doctor
Doctor's picture

Does anyone have an updated ruleset for the "Cards instead of Dice" option?

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Jacob
Jacob's picture

Here are the rules I was working from: https://www.dropbox.com/s/f2gw22r3oqysj7k/sorte%20cards%2020160222a.pdf?dl=0

My suggestion though is to use one card as a replacement for the 'good narration' dice you would normally give. Too may court cards slows down play, and you want them to feel special and linked to the narrative, so restricting them but linking them works nicely.

 

Doctor
Doctor's picture

Thanks, where did that come from? 

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Jacob
Jacob's picture
Doctor
Doctor's picture

Thanks, totally missed that. I'm going to numbers-crunch but I think the deck might give more interesting results, especially if you meddle with the reshuffle rules.

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Bradley
Bradley's picture

This thread is probably the one of the best examples of why RPGs are better nowadays than when Gary Gaigax first made DnD. The community is helping crunch the numbers and show the curvatures on the rules whereas the lack of internet made early modeling dificult and made balance far trickier since it would requie a lot more work to see how things ended up really scaling.

Also, instant feedback is a double edged sword that allows for quick community level numberrr crunch and attampts at breaking the system, but also results in a desire to try and please everyone and ending up with no one pleased.

Never change internet. You are beautiful.

Salamanca
Salamanca's picture
I don't see how my rolling dice improves stuff but, OK. Arneson and Gygax pretty much modeled everything in terms of combat mechanics off the wargames they had been playing. Most of that was straight Bell curve work. The difference was they had no idea if anybody would buy the concept of an RPG. JWP knows people will buy an RPG, they just need to do it in a way that is mechanically original, fits their thematic style and is fun to use. Hard work, mentally rewarding but still not easier with an audience.
Doctor
Doctor's picture

The Problem with the Card Option

 

I had some suspicions about the card option but I didn't want to post until the numbers were crunched. Now that I have crunched them, it turns out my concerns were warranted. The problem is the Minor Arcana (Face Cards). For a hand of a given size, here are the odds of drawing all numbers, which would give a result equivalent to dice.

 

#Cards             Odds of All Numbers(%)

1                      71.42857142857143

2                      50.64935064935065

3                      35.64213564213565

4                      17.226170056358736

6                      11.821881411226585

 

The math gets very, very wonky after that. I am still trying to figure it out exactly: any number nerds, feel free to ping me. The bottom line is that the larger your pool, the more likely you are to essentially take a penalty and it looks like that for a six card hand you're likely to have at least 2 face cards, meaning the penalty in terms of raw numbers is substantial (about 1 Raise vs Dice).

 

The Face Cards are problematic because they both provide no numerical benefit within the hand and require the expenditure of a Hero Point in order to retain the card. While there is absolutely no way to calculate accurate odds of whether a given face card will be useful for the Risk in which it is drawn, it is not unlikely that a player using the cards will pay a Hero Point and suffer a penalty (some benefit) or pay no Hero Points and suffer a penalty (no benefit). I am working out the odds of getting X number of Face Cards in a hand of Y cards. More to come.

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Salamanca
Salamanca's picture
And that doesn't even touch the sociological/psychological issues of convincing the player to give up their beloved d10's. As an admitted dice junkie, I know that switching to cards would involve the words "from" "cold" "dead" and "hands" in some combination. But stats unseen, I just know that drawing from a deck of cards is going to skew things. Worse if it's a tarot style deck with an extended range of Arcana cards. Either each player will need a deck ranging 1-10 for each pip (and then we hit the hassle of rebuilding for each test as we switch skill and trait) OR we play from a standard deck and never have the chance at all the possible results (because you can't draw five cards out of a standard deck and get five 10s).
Doctor
Doctor's picture

Major Arcana should be set to the side and used for other things. Anyway, I think you could solve it with a simple tweek like "a face card, if not used for it's intended special effect, can be paired with any numerical card to make a Raise." which might make the deck mathematically more appealing as there is a slightly higher chance of getting Raises and with the option for special effects. 

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Doctor
Doctor's picture

Also, the "can't draw 5 tens" issue is not very big for me, as the odds of rolling 5 tens are less than 0.001 percent. On the other hand, in a 5 card draw, the odds of drawing 5 face cards is 0.1143510577472842%

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Evan Sageser
Evan Sageser's picture

I tried the card drawing option during the quickstart, but I thought the face cards would make things a little too complicated so I just left them out. I thought they worked out fine, but I admit I never modeled them to check their odds versus dice. 

Somebody mentioned leaving face cards in as a seperate deck for flair draws, which I thought might be a good way to keep them feeling special without having to worry about them ruining your roll.

And then of course you leave the major arcana for the larger effects they described in the rules.

Doctor
Doctor's picture
      Min Max   Mean Wt. Mean Dice Mean vs Dice
Odds for a Two Card Hand             7.85714 11 -3.1429
0 Minor Arcana 50.64935064935060%   2 20   11 5.5714286    
1 Minor Arcana 41.55844155844150%   1 10   5.5 2.2857143    
2 Minor Arcana 7.79220779220779%   0 0   0 0    
                   
Odds for a Three Card Hand             11.7857 16.5 -4.7143
0 Minor Arcana 35.64213564213560%   3 30   16.5 5.8809524    
1 Minor Arcana 45.02164502164500%   2 20   11 4.952381    
2 Minor Arcana 17.31601731601730%   1 10   5.5 0.952381    
3 Minor Arcana 2.02020202020202%   0 0   0 0    
                   
Odds for a Four Card Hand             15.7143 22 -6.2857
0 Minor Arcana 24.88224563696260%   4 40   22 5.474094    
1 Minor Arcana 43.03956002069210%   3 30   16.5 7.1015274    
2 Minor Arcana 25.48395001225190%   2 20   11 2.8032345    
3 Minor Arcana 6.09872307985516%   1 10   5.5 0.3354298    
4 Minor Arcana 0.49552125023823%   0 0   0 0    
                   
Odds for a Five Card Hand             19.6429 27.5 -7.8571
0 Minor Arcana 17.22617005635870%   6 49   27.5 4.7371968    
1 Minor Arcana 38.28037790301940%   4 40   22 8.4216831    
2 Minor Arcana 31.03814424569140%   3 30   16.5 5.1212938    
3 Minor Arcana 11.43510577472840%   2 20   11 1.2578616    
4 Minor Arcana 1.90585096245474%   1 10   5.5 0.1048218    
5 Minor Arcana 0.11435105774728%   0 0   0 0    
                   
Odds for a Six Card Hand             23.5714 33 -9.4286
0 Minor Arcana 11.82188141122650%   8 58   33 3.9012209    
1 Minor Arcana 32.42573187079290%   6 49   27.5 8.9170763    
2 Minor Arcana 33.77680403207590%   4 40   22 7.4308969    
3 Minor Arcana 17.04054978194820%   3 30   16.5 2.8116907    
4 Minor Arcana 4.37224632563145%   2 20   11 0.4809471    
5 Minor Arcana 0.53812262469310%   1 10   5.5 0.0295967    
6 Minor Arcana 0.02466395363177%   0 0   0 0    
                   
Odds for a Seven Card Hand             27.5 38.5 -11
0 Minor Arcana 8.03887935963407%   10 67   38.5 3.0949686    
1 Minor Arcana 26.48101436114750%   8 58   33 8.7387347    
2 Minor Arcana 34.04701846433250%   6 49   27.5 9.3629301    
3 Minor Arcana 22.06751196762290%   4 40   22 4.8548526    
4 Minor Arcana 7.75345015078644%   3 30   16.5 1.2793193    
5 Minor Arcana 1.46907476541217%   2 20   11 0.1615982    
6 Minor Arcana 0.13811814033790%   1 10   5.5 0.0075965    
7 Minor Arcana 0.00493279072635%   0 0   0 0    

“Every normal man must be tempted at times to spit on his hands, hoist the black flag, and begin to slit throats.”
- H.L. Mencken

Cthulhu Netobvious
Cthulhu Netobvious's picture
Wow! Doctor, excellent work. I can hardly wait to upgrade this site and introduce the "tagging" system for high quality content. :-D

TAJ-07: Technopriest And Justicar Of 7thSea2e

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