5d6 Bell Curve

[Lindeloef]

You want a DC right? so if you set a Number, lets say 14, in this 5d6 bell curve you hit a 14 or higher to 84.80%. Which is the percentile of 14 till 30 added up.

 

[Morrus]

If you want to know what is the smallest slice of numbers that occur the most often up to 50%, then sure, that works. I think everyone else assumed you meant "everything from this and higher is 50%", like a D&D Difficulty Class.

Oh, yeah, that's just 18. I didn't need a graph for that! No, I was trying to construct a mental image in my head of how often folks will roll within a certain range. Or rather, the reverse; what range will they tend to roll within about half the time. I'm trying to simulate in my head (prior to starting playtesting, which will simulate it in actuality) what will tend to happen at the game table.

 

[Nagol]

Oh, yeah, that's just 18. I didn't need a graph for that! No, I was trying to construct a mental image in my head of how often folks will roll within a certain range. Or rather, the reverse; what range will they tend to roll within about half the time. I'm trying to simulate in my head (prior to starting playtesting, which will simulate it in actuality) what will tend to happen at the game table.

Convert the distribution into an ess curve.

Drop the distribution into a spreadsheet. Assuming high values are good, use the row below the result probability to add the columns probability to all higher results. That gives you the probability of success for arbitrary DCs.

If you graph that result, the line will start growing slowly, pick up steam as you approach the mode and then trail off slowly as it is passed.

 

[Jan van Leyden]

OK, so if I add up:

10.03 + 10.03 + 9.45 + 9.45 8.37 + 8.37 I get 55.7%

So can I therefore say that - roughly half the time - a player will roll from 15-20?

(I think I output the graph wrong above - it should be highest at 18, no?)

Essentially, yes. You introduce an error when using the percentage values; the sum of the percentage value is 99.96 not 100. But this shouldn't be a problem in this case.

 

[Umbran]

(I think I output the graph wrong above - it should be highest at 18, no?)

Yes, that graph is inaccurate. 5d6 *cannot* give you a result of 2, 3, or 4, but it shows those with non-zero probability. Something is incorrect.

Your system is "roll 5d6, and beat a target number" right? And you'd like to know the probability that the player will succeed (or probability that they'll fail) yes?

Go to that Any Dice page again, and check out the "at least" and "at most" buttons above the graphs. The chance that they'll roll at least your target number is the chance they'll succeed. So, if the target is 5, they're sure to succeed. If the target is 13, there's a 90% chance they'll roll at least that and succeed. There's a 50% chance they'll roll an 18 or better. There's only a 15% chance they'll roll a 22 or better, and so on.

 

[Morrus]

Yes, that graph is inaccurate. 5d6 *cannot* give you a result of 2, 3, or 4, but it shows those with non-zero probability. Something is incorrect.

Your system is "roll 5d6, and beat a target number" right? And you'd like to know the probability that the player will succeed (or probability that they'll fail) yes?

No, I want to know what range of scores folks will fall within 50% of the time. We've established that's 15-20.

 

[Umbran]

No, I want to know what range of scores folks will fall within 50% of the time. We've established that's 15-20.

Whoops. Sorry, I skipped ahead without reading fully.

 

[Storminator]

Your graph is simply shifted by 4. If you add 4 to all the numbers in the bottom axis it's all fine.

PS

 

[Nagol]

No, I want to know what range of scores folks will fall within 50% of the time. We've established that's 15-20.

The simplest way to find the 50% mark on NdM dice is to take the (minimum + maximum + 1 ) / 2 -- in this case 18. 50% of the time, players will roll less than that. 50% of the time, players will roll that or above.
For odd numbers of (even-sided) dice, it is the exact 50% breakpoint. Centre spreads like 15-20 will give a about 50% result is chosen well but are unlikely to be exact.

 

[LittleMonkeyMojo]

<5? How?

How would it be possible to get anything less than 5 with a 5d6 roll?

Absolutely perfect - thank you! I used that, then put the results in Excel to make my own graph. That's exactly what I needed!

View attachment 59956



Just 5d6.