"Rounding" Topic

Okay, the rules call for some calculation of chance to hit or whatnot. The fire you are doing is halved for terrain, yielding a result of 8.5 on a d20.

Do you round up, down, sideways, what?

I use a convention that I ran across in a math class ages ago: Round to the even number.

Usually round down.

Always down.

I try to avoid using rules where you have to do such calculations.

However, mathematically, rounding to the even number is the most sensible method, since you will round up or round down in roughly equal proportion.

Always rounding up, or always rounding down, slightly skews the probability.

Always rounding to a specific rule is definitely best – in other applications outside gaming halves often round up but rounding to even/odd result at least gives a 50-50 split, in theory anyway.

The problem arises when the numbers with fractions are small, say no more than 3 or 4. Then almost any scheme ends up being biased.

The default maths approach that I was taught was to round .5 upwards, and everything below that downwards.

For gaming purposes, I would try to arrange any division in such a way that you would not need to worry about rounding. For example, if the firepower needs to be halved under some conditions, then make the basic (non-halved) firepower ratings even, so halving them will not result in fractions.

Or roll randomly whether to round up or down for a given case.

Some rules (Saga for instance) always round up. Even for 1/3.

What does round to the even number mean? Does it mean 8.5 goes to 8, but 9.5 goes to 10? What about 9.1?

Mathmatically 0.5 would normally round up.

Round down. This is usually in favor of the defender

What does round to the even number mean? Does it mean 8.5 goes to 8, but 9.5 goes to 10?

Yes. (see below)

What about 9.1?

Rounds down.

Mathematically 0.5 would normally round up.

Actually, no. Under the "even rounding" scheme:
0.1 to 0.4 would round down.
0.6 to 0.9 would round up
0.5 would round to the nearest even number.

There are several different ways of rounding:
link

Round down. This is usually in favor of the defender

Assuming you are rounding the target score, then that is true only if you have to roll a target score or less to hit. If you are rolling a target score or greater then it favours the attacker.

Depends on the rules. Sometimes it isn't nessessay.

With your example, say you have to roll the value or greater. Then an 8 is lower and you fail. A 9 is a success.

If you had to roll that score or less, then 8 is a success and a 9 is a fail.

DBMM does similar when calculating allied contingents. If after deviding the number allowed by 1/4 or whatever, you end up with being able to take 2.3 elephants (say). 3 elephants are more than 2.3, so you can only take 2 elephants.

Cheers,
JohnG

The rules should specify whether to round up or down.

I use a convention that I ran across in a math class ages ago: Round to the even number.

I've never heard that before and I'm a maths teacher. In the UK we teach that 0.5 or above rounds up, less than 0.5 rounds down.

In calculations it is common to round 0.5 and above up – that is conventional in most western arithmetic but not always true for other cultures – I have seen both all fractions rounding up AND all being discounted (i.e. rounding down) as the accepted 'rule' taught in other countries. After many years teaching students from across the globe you realise 'standardisation' is pretty non-standard.

Dealing with games is a different matter – ideally you would like any rounding to 'even out' so that it favours neither player. This is never entirely possible as any scheme is flawed for different reasons in different circumstances.

to Margard. In engineering and the under-grad chemistry and physics course leading up to it for my undergrad engineering degree it was always round to the even number. Same at Royal Military College of Science at Cranfield (Schrivenham), though I was only there for a three week electro-optics and image processing course.

The reason for doing this is exactly the same as what Gidas describes for evening things out in games.

However, before university, though throughout school up to the end of high school, we were taught the .5 goes up as Marshal Mark describes. It really seemed weird to adjust to the even number method!

On the other hand, a lot of computer program rounding functions do the .5 up! I suspect this is because of what is taught at school level and language coders are not necessarily engineers or scientists.

I don't know why at school age we are taught the round up method, and in engineering and science work we do it the other way. From what GF and MM say, it's not just a problem in Canada!
--
Tim

Typically down. In the example the chance to hit is by rolling an 8.5 or less. If you roll a 9 or more, that is greater than 8.5 and so would be a fail/miss/whatever.

I would say consult your rules. If it's not in there then I would go with what I learned in school. .5 or more up, anything less down. I would also consider writing the author for their clarification. Failing these, I would find rules that were clearly written. Any rules not clarifing such an obviuos situation make good TP.

In the western world you Round up. .5 and more to the next integer.

Go sideways, just for a bit more variety.

My take on that would be to roll a D6, and on a 1 – 3 you round down. On a 4 – 6, you round up.

Trow a die to decide whether to round up or down.

BTW, the common rule of thumb used in arithmetic to round .5 upwards, doesn't have any meaning, except when you know what the underlying application of the numbers are, or when there are legal guidelines (e.g. in bookkeeping).

My take on that would be to roll a D6, and on a 1 – 3 you round down. On a 4 – 6, you round up.

The Random method. See the link in my previous post.

My group just quits playing the game and does something else as there are too many arguments about how to round the numbers.

Decide before the game. Round up, OR round to the even number (it's the first time I hear about this solution too, but after some thoughts it doesn't seem so stupid that it looks).

Don't roll another die to decide what you must do with the first. That's how games become long and boring dice-throwing hours. If you spend more time rolling dice than the time the action would have taken in reality, it's not worth it.

I'm sorry, I'm late to this topic, but here goes.

Rules which require rounding fail to meet one of the basic requirements all wargames should have, simplicity.

With d10s capapble of producting 100 possible outcomes, there is no reason for rounding. The requirement to round confuses the issue, determining an outcome, and unnecessarily slows the play of the game.

Bob Coggins

How many rules have something like "Half the number of figures can participate in the fighing …"? That's a simple rule, but it often requires rounding. If not codified in the rules, players should at least make a decision on the spot.

Sometimes having rounding in your rules keeps things simple.

BTW, a D10 has nothing to do with it. You can produce an insane amount of results with any die.

Phil,

I am afraid I disagree. The question is clarity and speed of resolution. I am unaware of rules which stipulate "Half the number of figures can participate in the fighting…" In whatever set of rules it is located, for the lack of specifying you should round up or down, it is a poorly written rule.

D10s do not produce an insane number of results they simply produce the same result of less efficient dice, such a d6s, without having to roll multiple numbers of them or roll saving throws. They save time and eliminate confusion.

Bob Coggins

Bob,

I a sense I do agree that rounding should/can be avoided. But sometimes, within a presumed framework of the rules, rounding can be ok.
E.g. some rulesets have shooting rules that specify that each figure rolls a die, but under certain conditions (cover, range, …) half or 1/3 of the figures can shoot. That by itself is a simple rule to add modifiers to the expected number of casualties – change the number of dice rather than the target number. But it requires some agreement on rounding issues.
Another example is what you see in many morale rules: 'When a unit has lost 50% of its figures …'.

Now, we can disagree about whether the fact that rounding creeps in makes the rule less elegant. I agree in a sense, but if eliminating rounding would make the rule more complex as a whole, one has gained nothing.

But I'm also in favour of having clear and simple rules which are well thought out instead of hodge-podge rules with lots of exceptions glued on as an afterthought.

Most sets of rules that I have seen, including my own house rules, will require rounding at some point. Classic examples are: half the figures count in melee when the unit is disordered; a unit that moves over a half move fires at half strength; a unit firing in support of a unit charging or being charged fires at half strength; hits are halved when firing at night; a broken unit loses one-third of its figures as it runs away; mounted cavalry/dragoons dismount at 3/4 strength, the rest holding the horses – when they remount, they get all the horse holders back; a unit must check morale after losing 10% of its figures.

There are a lot of conventions in rules that make perfect sense, are quite simple, and play very well, but they will require rounding every now and again.

"Round to the nearest whole number" is never ambiguous….

just visitng wrote:

"Round to the nearest whole number" is never ambiguous….

So, you are claiming that (7.5 – 7.0) <> (8.0 – 7.5)?

I'm afraid I'm going to have to ask to see your working for that.

All the best,

John.

<.5 is the round up point; everything less rounds down. Simple….

1.5 is not closer to 2.0 than it is to 1.0.

There are several conventions one might choose to follow when breaking ties for the nearest integer. Even if you weren't aware of them before, you could have found out about lots of them by reading the other posts in this thread. But you haven't actually bothered to read the thread, have you?

John.

Omemin,

Because most sets require "rounding" doesn't mean its necessary or a good practice.

Conventions in rules can make perfect sense to one person and no sense to another. And there-in lies the problem. Who decides what does and does not make perfect sense?

Indeed one only read the discussion between John D Salt and just visiting to understand the problem with perfect sense. You can drive a truck through their differences and when they occur during a game the game stops to allow a convention to be established, if possible.

Bob Coggins