"Quick and Dirty 3-die bell curves?" Topic

Does anybody know a website or applet, or a quick & easy way for the mathematically-impaired to play around with three-die bell curves?

Like: roll 3d12s… what does the curve look like? Three d10s? Three d8s? and so on.

I'm trying to figure out, in each case, things like: what are the odds of rolling higher than X, using 3 dice of whatever size.

Use the random number generator in Excel and then plot the results:

link

Then generate die rolls and plot the results. If you made 100 rolls for each die, you;d get a bell curve close enough to what you want.

This might help:

link

Thanks – I also found the ÜberDice Java applet that is pretty simple.

Probability curves are odd beasts.

There is no function based on number of dice and sides that can generate a curve.

But there is a function that considers the number of sides and dice to generate a function that can generate the curve. :)

what are the odds of rolling higher than X, using 3 dice of whatever size.

Geez. It would be much simpler to go percentile or to another flat curve system like D20, D10. Makes your values and modifiers easy to figure. Your players will appreciate that.

But … as Crusoe says, make a chart for a particular value on each 3Dx where x is the number of faces, then use it to make the chart you need.

So, to get a particular number on 3D4:
3,12 = 1/64 ~ 1.56%
4,11 = 3/64 ~ 4.69%
5,10 = 6/64 ~ 9.38%
6, 9 = 10/64 ~ 15.63%
7, 8 = 12/64 ~ 18.75%

Then add them up to get the chart you need:

On 3D4:
12 ~ 1.56%
11+ ~ 6.25%
10+ ~ 15.63%
9+ ~ 31.25%
8+ ~ 50%
7+ ~ 65.63%
etc.

As a player though, let me say I always wonder when I see a game design where it's possible to have an event that happens if say, I roll 24 on 3D8. Does the game developer seriously think I'm going to consider an action with a 0.2% chance of success -- 1 in 500 tries?

Actually, donrice, the purpose is to have modifiers have different effects with different base likelihoods of success. for example, if you have a very low chance of success and you're rolling 3d8, a +1 modifier might double your chance of succeeding. If you're already around a 50% chance, a +1 might multiply your base chance by 105% (from 50% to 52.5%, say). If you already had a 98% chance of success, it might only multiply your base chance by 101% (to almost 99%).

Compare this to a straight +5 on a d100 roll. With a base 50% chance, that's still a 105% multiplier. With a base 2% chance, it's a 250% multiplier, and with a base 98% chance you can't figure the effect, because it's off the chart!

Bell curves are quite handy to the game designer.

[Bell curves are quite handy to the game designer.]

Indeed. I've got a very specific need for that particular shape of probability curve. (Not to mention a reason why I want to use three dice.)

Anyway, thanks.

emckinney:Actually, donrice, the purpose is to have modifiers have different effects with different base likelihoods of success.

I understand a designer might say this is what he is after. But does he consider what it looks like from the other side of the board? A game system which uses dice bell curves is going to make probabilities difficult for the player to calculate, since +1 means different probabilities at different times. Is that intended?

And let's consider your two examples:

if you have a very low chance of success and you're rolling 3d8, a +1 modifier might double your chance of succeeding.

Excellent example. 3D8, I need a 24, that's an 0.2% chance of success. +1 so I need a 23+ … that's an 0.8% chance of success -- not doubled but quadrupled. (Did you know your example was so good?)

So what? Both chances are so low, no player would ever make a tactical decision based on getting that outcome. So in real play, having these tiny probabilities in the game system adds complexity, but no real gameplay value for it.

If you're already around a 50% chance, a +1 might multiply your base chance by 105% (from 50% to 52.5%, say).

Another excellent example. To put it another way, on average, if a player has two games in both of which he has to make 50 3D8 rolls to determine events, then with this bonus in a game he will be successful at one more event than in the other. Now, presumably setting up those 50 event tests are part of the game's tactics, and presumably he can still win without that bonus … so, again, what did winning that one extra event that one time bring to the table?

I'm really not trying to rain on anyone's parade, and for all I know, considered all together, a very nice game system might use 3-dice bell curves. But it might not be one which encourages players to learn what their units can be relied upon to do. Maybe that's a design goal, in which case … more power to you.

So what? Both chances are so low, no player would ever make a tactical decision based on getting that outcome.

Depends how many chances they get at the low % event.

In WHFB, for example, fighting a tough hero you might have to throw a low chance of a hit, a low chance of a wound, put up with a high saving throw and then another magic saving throw. Yet since you might get a couple of dozen shots at it, you are grateful for every +1 in there.

(Not that I'm advocating their system, but a large part of the game is aggregating a large amount of individually unlikely events.)

In my case, I'm doing a model for naval gunnery. There are three range-bands. Each is represented by one of the dice. Each salvo is thus three dice of a certain type.

If your gun uses d10s, for instance, then your Short Range is 0-10, Medium is 11-20, and Long is 21-30. If you use d8s, your gun's range bands are smaller – increments of 8.

I like the bell curve because I want it to be unlikely to score hits at extreme range, but there is still the incentive to try, as you try to acquire the target, and thus get positive modifiers.

So I want a bell curve, and I want three dice.

Sam,
I have a program that will generate curves for all types of dice and generate odds to boot. Send me an email and I'll shoot it to you. If you have any problems I think I can get you down the road fairly fast.