Topic: How much Math is "Too Much Math"

[Marc R]

I did open this with the proviso that addition, subtraction, and multiplication by whole numbers appear to be fine. . .division by whole numbers appears to be tolerable. . .So rolling dice and adding them to a bonus seems to fall into the green zone.

[pastaav]

I think that it easy to forget that rounding is actually something that in essence is hard. Like for instance 2.5...should that be rounded to 2 or 3? Many people would say that you of course should round to 3, but that gives a bias. More correct would be to round up and down half the time.

[Andraax]

I think that it easy to forget that rounding is actually something that in essence is hard. Like for instance 2.5...should that be rounded to 2 or 3? Many people would say that you of course should round to 3, but that gives a bias. More correct would be to round up and down half the time.

I was always taught that when rounding .5, look at the digit before it, and round to an even digit. So, 2.5 rounds to 2, and 3.5 rounds to 4. Of course, this presumes no other rules are in play. Bankers typically round down when it's not in their interest and round up if it is in their interest. Many game rules specify that you "always round up" or "always round down".

[markc]

I think that it easy to forget that rounding is actually something that in essence is hard. Like for instance 2.5...should that be rounded to 2 or 3? Many people would say that you of course should round to 3, but that gives a bias. More correct would be to round up and down half the time.

I was always taught that when rounding .5, look at the digit before it, and round to an even digit. So, 2.5 rounds to 2, and 3.5 rounds to 4. Of course, this presumes no other rules are in play. Bankers typically round down when it's not in their interest and round up if it is in their interest. Many game rules specify that you "always round up" or "always round down".

 Was that in math class or from a RPG?
MDC

[Andraax]

Was that in math class or from a RPG?

The rounding to an even number? Math class.

[markc]

 I was taught to round up if the number was .5 or higher and round down if it was .4999 (repeating) or lower. Can you give me some more info on the math class? The reason I ask is that it is a very strange way to round numbers.


MDC

[Marc R]

when rounding, I always go 0,1,2,3,4 down, and 5,6,7,8,9 up. . .unless there's a "round down" in place so even .9 is down, or a round up for even .1 is up. . .

[Kristen Mork]

Rounding x.5 to the nearest even is designed to eliminate statistical anomalies.  If you consistently round x.5 up, you end up over-estimating the average.  For example, the average of 1.5, 2.5, 3.5, and 4.5 should be 3.  But, if you round each value up you get 2, 3, 4, 5, which average to 3.5, which rounds to 4!  But, if you round to the nearest even, you get 2, 2, 4, 4, which average to 3, the correct answer.  Hence, the even rule.  See http://en.wikipedia.org/wiki/Rounding#Round_half_to_even for more details.

[rdanhenry]

The only time not to round .5 up is in cases where aggregate rounding error matters and you have numbers where .5 (or .25., .5, .75) is the only decimal part you have. If you always round up in that case, you get cumulative error that consistently leads to numbers that are too high. In those cases only, it is better to alternate rounding up and rounding down. I doubt there is any case in a game where this would be advisable. If you have 3.5 either round up to 4 or terminate to 3, just do it consistently.

[Marc R]

(we close in on reaching the point of "too much math" heh)

[David Johansen]

NONSENSE THERE CAN NEVER BE TOO MUCH MATH!!!

[markc]

Rounding x.5 to the nearest even is designed to eliminate statistical anomalies.  If you consistently round x.5 up, you end up over-estimating the average.  For example, the average of 1.5, 2.5, 3.5, and 4.5 should be 3.  But, if you round each value up you get 2, 3, 4, 5, which average to 3.5, which rounds to 4!  But, if you round to the nearest even, you get 2, 2, 4, 4, which average to 3, the correct answer.  Hence, the even rule.  See http://en.wikipedia.org/wiki/Rounding#Round_half_to_even for more details.

 I was taught never to round until the end or the math is all done. of course if you round in the middle you will have many problems. That is why you work with a raw data set and not something that is already manipulated in some way.


MDC

[Marc R]

If I need a series of rounded numbers, then a total, rounded. . .

Set excel to total to the right, set decimal to 0, add the right column to the bottom, set decimal to 0. . .rounds each line in display, but adds the actual raw unrounded figures, and rounds the result.

[Kristen Mork]

Given the computer's binary representation for numbers, rounding is a necessary evil, and often performed on halves.  So, in the real world, not much of an issue.  But, in the digital world, rounding can be a big problem.

[yammahoper]

Ok, this entire conversation has become an example of to much math.

In fact it's reminding me of Aftermath with its 50 or so hit locations: overkill.

Now, the memory of giving that game away is a pleasent one, though I wanted to keep the box at the time (kids are weird).  I'm sure those physics geeks played the tarnation out of it.

[Marc R]

Playing in an Aftermath game right now. . .the hit locations are one of the good things about it. . .it's just a picture with numbers on it. . .the character development/experience mechanics are kinda "meh" to me.

Back to rounding logic.

How about the tyranny of the d20 in percentile systems?

i.e. the fact that almost everything is done in 5s?

RM does go away from 5s in diminishing returns skill ranks, and RM2 smoothed stats or RMSS stats. . .but a lot of the system works in 5s.

I get the logic of the drunkard's rule, and don't object to rounding the final result to 5s if you really like round results. . .

But everything rounded to the nearest 5, does contribute to some problems like bonus stacking. . .if the smallest bonus is a 5, then if you get three of any bonus, the smallest it can be is +15. . .and if the increments are in 5s, then three level two bonuses are +30. . .it rapidly scales up and out of control. . . . .because you can't have a +3, or a +12.

[yammahoper]

Playing in an Aftermath game right now. . .the hit locations are one of the good things about it. . .it's just a picture with numbers on it. . .the character development/experience mechanics are kinda "meh" to me.

Back to rounding logic.

How about the tyranny of the d20 in percentile systems?

i.e. the fact that almost everything is done in 5s?

RM does go away from 5s in diminishing returns skill ranks, and RM2 smoothed stats or RMSS stats. . .but a lot of the system works in 5s.

I get the logic of the drunkard's rule, and don't object to rounding the final result to 5s if you really like round results. . .

But everything rounded to the nearest 5, does contribute to some problems like bonus stacking. . .if the smallest bonus is a 5, then if you get three of any bonus, the smallest it can be is +15. . .and if the increments are in 5s, then three level two bonuses are +30. . .it rapidly scales up and out of control. . . . .because you can't have a +3, or a +12.

I have +7 swords or +6 DB armor.  I achieved this by making a simple rule that reduced the time needed to manufacture an item by making the bonus less than the maximum allowed by the spell.

So a Weapon I can make a +1, +2, +3, +4 and +5 weapon.  +1 magic weapons are far more common in my world than any other as they take less time, cost less to make and confer the same advantages as a magical +5 weapon other than the bonus (same level to resist destruction, able to strike special creatures, etc).

Of course, I depise big numbers just for the sake of big numbers.  My work as a machinist also taught me their are many paths to finishing a job, and not all produce the same quality.

I miss that job.