"roll modifiers v. more dice" Topic

it's been at least a week since i've asked TMP to do my thinking/work for me, so i don't feel too guilty about this… ; )

given a bell-curve (say, 2d6) mechanic with various target numbers for success (based on the difficulty of the task). in the past the subject of the improved odds if a +1 were given as an advantage on the roll was covered. i'm wondering about the effect of --instead of a direct bonus/penalty of + or – this or that number-- the use of additional dice from which the highest rolls are used to determine the result. ie: instead of +1 to the roll, the player is allowed to throw three dice and pick the best two. are the odds for success improved the same? less? more? does adding two dice (doubling the number rolled) improve the chances for success the same as adding 2 to the roll of two dice?

i'm interested from the standpoint of knowing/regulating how big an advantage is given to units for greater skill levels --i feel that using a finer gradation (without getting too bogged down in bookkeeping) is better insofar as it allows for the awarding of skill levels without handing players +bazillion swords of infinite accomplishment.

This site--that deals with Crossfire--may give you some idea as to the probability differences when adding dice:

link

Percentage chance of each outcome on 3d6, keep best 2 :
Number Percentage
2 0.46%
3 1.39%
4 3.24%
5 5.56%
6 8.80%
7 12.50%
8 15.74%
9 16.67%
10 15.74%
11 12.50%
12 7.41%

Average number = 8.46
So rolling one extra dice is better than 2d6+1 but not as good as 2d6+2

thanks!

is there a link/formula for calculating those multiple-dice odds so that i could continue the progression (to three or more dice) myself?

So rolling one extra dice is better than 2d6+1 but not as good as 2d6+2

I think that depends. If a 2 meant instant self-destruction, I'd prefer 2d6+1 to 3d6 keep 2.

Well, you probably know how I feel about this.

More charts and more modifiers just burn precious time and impart a (unjustified) advantage to those that know the rules best.

I'd rather use variable numbers of dice to determine outcomes than go through a bunch of charts and calculations.

mjc

Mike,
i guess for myself remembering that you need to roll a six with 2d6 or need to roll 6's on multiple dice is a case of "six of one and a half-dozen of another".

the issue i'm curious about is the size of the advantage given to a player/unit to reflect a greater skill: is giving more dice to roll a greater bonus than giving a +1 to a target-number roll? if so, how much?

in our aircombat games, allowing a better pilot to roll five rather than three dice and/or giving him a +1 to a 2d6 roll provides for a certain advantage --the question is, how much is that advantage? and does either method (more dice or modifiers) provide a better set of "steps" on which to base the awarding of that advantage?

ps- i'm asking/dealing with this in conjunction with a new game, and just wondered about the best/easiest way to reflect advantages and -more importantly- player choices regarding resource allocation.

I'd rather use variable numbers of dice to determine outcomes than go through a bunch of charts and calculations.

Out of curiosity, how does the former differ from the latter? You still have to look up how many dice you need, do you not?
--
Tim

3 choose 2 changes the distribution of the results.
The effect can also depend on whether you allow results greater than 12 on 2D6+1.

Since the distribution shape changes, which is "better" can depend on the target number for success. 3C2 tends to be more advantages with low target numbers.

Example Target No. 6+
3C2 fail 10.6%
2D6+1 fail 27.8%

Target No. 11+
3C2 fail 80.1%
2D6+1 fail 82.3%

This skewing of the curve may have unintended consequences.

If you really want gradations this fine use percentile dice…

"…percentile dice…"

i used to use 'em (and still design with percentages), but have become a d6-junkie lately…i could cite a few practical reasons but in truth it comes down, i suppose, to "just 'cuz"… ; )

the "curve skewing" mentioned is one of the advantages i see in using a 2d6 bell curve: an advantage (whether it be given as an extra die or a +1 modifier) gives its greatest benefit with the more difficult tasks (higher target numbers) which i think is a good reflection of greater skill.

since i'm using a straight 2d6 as my "normal" (benchmark) roll/ability, it is the size of the advantage for additions (or penalty for subtractions) that i'm exploring the effect of.

ps- since my current project deals with resource allocation by the players (to accomplish various tasks in a turn), using variable numbers of dice that could each, individually score a success (by rolling, say, a 6) is definately an option --i'd still meed to know the scale of the advantage for using multiple dice, ie: how much better are the odds if you roll two instead of three dice? what are the odds of getting two (or 3 or ?) 6s if you roll four, five, or six dice?

sorry for dumping this in the TMP lap --my brain has never been good at wrapping around probabilities (too artsy-fartsy)-- and many thanks for the help offered.

this is more of a game design aspect, but didn't want to start another thread…

related to the "process v outcome" and the "saving throw" ideas already covered in other threads:

when, as a player, do you tire of having input? is one roll to determine both success and degree good enough, or would you rather roll for success and then roll again how well you did? …or is rolling for the rare critical hit (or its converse: the fumble) enough? …or too much?

on the defensive: is letting your opponent's rolls determine what happens to your unit(s) satisfactory, or does it somehow feel better to have a roll/say in the outcome (even though the game effect is the same)?

basically: when does participation (allowing for the fact that everyone around the table gets to do so, not just you) interfere with speedy play --which is, for me, one of the big sacred cows of game design-- and/or when do you say "fine, roll the die and if i'm dead i'm dead" ?

ps- should this be moved to the general "game design" forum?

"is there a link/formula for calculating those multiple-dice odds so that i could continue the progression (to three or more dice) myself?"

No, sorry. It's on a spreadsheet. It's quite easy to do 3d6 keep 2, and I've got a spreadsheet for 4d6, keep 3, as there is a formula in excel to find the minimum of a list of numbers. But I can't do 4d6 keep 2 as I would have to find the two lowest from each set of numbers which isn't so easy to do.

Don,

I tried and tried to get statisticians, mathematicians and economists to do the odds for me. They all throw up their hands after a while. Suffice to say it is difficult to figure out all of the permutations.

That said. Odds of rolling at least one '6' on a six sided die is:

One Die ---- 1/6 or about 17%
Two Dice --- 11/36 or 31%
Three Dice --- 91/216 or 42%
Four Dice --- 671/1296 or 52%
Five Dice --- 4651/7776 or 60%
Six Dice ---
Seven Dice ----
Eight Dice ---

Sorry but my calculator is starting to hurt.

Don't ask me about the odds of at least two dice showing '6' as you roll successively larger numbers of dice. This is where the pro's have their eyes glaze over and they start running for the door.

By adding one more die, you incrementally increase the chance of success profoundly between one and two dice and by about 10% when rolling 3 to 8 dice. After that you get diminishing returns.

Rolling a lot of dice will increase the odds of rolling multiple '6's';

But after about 12 dice, rolling lots of dice does not do much for your odds of rolling at least one six.

What I like about doing this is that you never achieve 100%. There is no certainty of success. In war, my bias here, nothing is a sure thing. There is always something that can go wrong.

mjc

MJC,
Perhaps the statisticians, mathematicians, and economists threw up their hands because you asked for 'odds' computations but insisted on computing 'probabilities.' Odds are computed as the probability of success to the probability of failure.

Out of curiosity, how does the former differ from the latter? You still have to look up how many dice you need, do you not?"

Plus use a dice cup and count the dice.

Regardless of the math I don't see any benefit to buckets of dice. A chart placed in convenient area to look at doesn't take that much time off any game to warrant a total overhaul of rules. Many other things take far more time off play then reference charts. Having to figure all this math out is far more complex then any game with a reference. I see so many trying to avoid math in games but then have this. I find a very complex path to try to "simplify" or speed up a game.

"is there a link/formula for calculating those multiple-dice odds so that i could continue the progression (to three or more dice) myself?"

I wrote a program in the statistical package I use, SAS, because it has some functions that most software doesn't have. It let be generate tables of things like 5d8 choose 3.

Actually it didn't complain about D13 and such either as it's using a uniform distribution model to do parts. I'll have to see if I can find the program and see if it might translate to anything else easily.

Quidveritas,
I do have all of your missing odd. Call me if interested.