"Need math help for old time game" Topic

I have been reading a Featherstone style game that does shooting by rolling a d6 for every 8 line troops, and a d6 for every 6 elite type.

Too often there are fractions of 8 or 6. How can I get the same results by rolling something for each figure? Thus roll as many dice as figures shooting, what constitutes a hit. I would like a d6 option, but percentage would be ok, like with a d10

Thanks to those with better math skills than I have :)

How many casualties are caused by the d6 result?

I used to play a set of rules like that back in the day.

Your problem here is that rolling a d6 over 8 or 6 will always give you one casualty per 8 or 6 figs, at the minimum. So rolling a d12 per 12 will only give you a minimum of one per 12, but 2d6 per 12 will give you two.

See?

JohnG

If I remember rightly, the score on the die is the number of hits?

In which case that gives a mean hits per figure of

Line: 0.4375
Elite: 0.5833

D12 would give 8+ (0.4167) 6+ (0.5833)
D20 would give 12+ (0.4500) 9+ (0.6000)

No enough info given to give an answer as you only describe part of the method.

1) How exactly are the number of hits determined

2) How are any modifiers applied (e.g. change figures per dice, extra 'saving' throws or something different)

It will not be possible to get any system that would give the SAME result with a single die per figure. You could get the mean casualties to be close but not the possible range of casualties.

In the distant past I used a similar system and used a die for the odd figures that was halved – you could use various dividers, not just 2.

So, you want to roll more dice butget the same results?

Why?

Based on the odds above, use a D10 for each figure, line hit on 1-4, elite on 1-6.

Close enough, and a dramatic indication of why almost all of us who played those rules very rapidly found a way of reducing the casualty rate.

50% losses per volley leads to quite a short game….

How are you winding up with fractions in the first place? In classic Featherstone, you roll a D6 for a firing group, then deduct for range to get a number hit. So you roll 1D6 for five line infantry, Deduct 3 from the score at long range, 2 at medium range and 1 at close range. Then there is a saving throw depending on cover. There is absolutely no division, and so no fractions are possible.

To give you a good mechanism for "Featherstone STYLE" you're going to have to explain the firing mechanics in greater detail, because whatever you're doing is not Featherstone.

Another problem is that the results of throwing one die for 6 or 8 figures are highly variable, while anything involving rolling one die per figure firing is going to have a very different distribution curve. Fine if you're OK with that, but always remember the more dice you throw the less randomness in the result.

Maybe he's doing Brigadier Young or Grant. Just slightly later than the aforementioned, Steve Hezzlewood got over the problem by rolling a D10 per figure firing for casualties in his 18thC rules "Pax Britannica".

THis will be close but not exact. But easy.

Roll a D8 for each regular troop.
Roll a D6 for each elite troop.

1 or 2s are hits.

EDIT – could even make it 1,2,3 to get it closer to the distribution.

Easier is for the fraction roll the die for hits like normal but if you get more hits than figures it is a miss.

That gives a slight advantage to the regulars so it could be
1 or 2 figs is 1 extra hit possible.
3 figs is 2 extra possible
4 figs is 3 possible
5 figs is 4 possible
6 or 7 is 5 possible.

Robert – if you take losses from a firing group then you would have less figures so presumably that is where the odd figures come up.

'the more dice you throw the less randomness in the result' – sorry but that is wrong. Firstly because the word 'randomness' can be interpreted in a number of ways and secondly because it depends on how the results of the dice thrown are used.

Until the OP states what the system actually is fully then all the above methods are just guesses. I can see at least 3 different interpretations of the system in the replies.

Gildas, wrong on both points.
First Featherstone has a provision for undersize firing groups. As I recall, three or more count as five, and two or less don't count. Anyway, still no division in classic Featherstone.
And since in this case, we know the OP wants to replace firing groups with a die roll for each casting firing, we know how the results are used--and the results of a firefight will become more predictable with any such system. That's "less random" in English.

But I agree that whatever he's using isn't Featherstone, and we can't give him a one die per figure answer until he describes his system in adequate detail.

Oh. And the only fractions in Young are halves, so it can't be that. And Grant's musketry, again, has subtraction but no division. I'm going to be very interested in what this turns out to be.

Back to you, Bobgnar.

Sorry Robert, random is a word like unique. A system either produces random results or it does not, there is no 'more' or 'less' random. The term is much misused (like so many others) but that is its meaning in a mathematical context.

Saying that it more predictable may be correct but I'd have to consider the outcomes and how they are distributed before I could agree or disagree with that.

You are making an assumption about what system the OP is using so neither you nor I can be right or wrong on the other point.

Need to know:

* What constitutes a hit
* How hits are allocated (esp. how losses are distributed across line and elite).
* What the starting numbers of each are

Gildas, having thought it over, I will accept the correction on "random"--mostly because I've taken your position over "unique" and "proximity."

But I don't see any way to give our OP a system which involves rolling six times as many dice each one of which is supposed to generate the same hit probabilities as the original system, without changing the outcome distribution curve to make it more predictable.

Of course, I don't see any way to give out OP a system at all if he doesn't give us more information.

Sorry I was too vague. Here is the actual rule

(iii) Calculating effect: For all troops in close order: a die thrown for each group of firers, six grenadiers, eight line infantry, or six light infantry. The number on the die gives the standard number of casualties at short range.

In that case, it appears to be Carlos von B for the win. But you know, you never did need fractions. Just decide that for line, four or more leftovers are a firing group and three or fewer are disregarded, and for elites the numbers are three and two.

But even for close range, that's ferocious. I don't like to criticize a mechanism out of context, though. Is there some sort of automatic saving throw?

It sounds like the Peter Young firing system. No, there are not any savings throws. Charles Grant used a similar mechanism, but you subtract either 2,3 or 4 depending on range.

I'm sure there must be some modifiers or saving throws involved somewhere though, Bobgnar?

We're in agreement then Robert.

It can't be done.

If you must have a 'buckets of dice' approach then you usually have to accept a larger range of possible outcomes and a different distribution.

The original system has equal probability of each outcome over the range but a BoD system would be bunched toward a mean value (which is what Robert was meaning about it being more predictable).

The range of outcomes in a BoD system is the same for groups of 6 (though not once any modifiers are applied) but higher under most circumstances.

This is what I find most objectionable about BoD systems, players tend to believe it worthwhile trying their luck because ludicrously high hit rates are possible (unlikely but possible) and historical tactics are just ignored.

Interesting, Gildas. I tend to prefer throwing more dice--not because I dislike using historical tactics, but to avoid situations in which three bad (or good) die rolls decide the game.

Even from the winning side, they're not altogether satisfactory. ("How did you win the game, Robert" "Well, Joe played just as well, but he failed two activation die casts, the on the melee die roll, he had a 1." Is that really something to brag about?)

There are solutions to both problems Robert but many wargamers don't like them.

Tables can translate a dice result into a combat result and allow a certain freedom from the distribution patterns of dice and also allow the designer to limit the range of possible casualties or exclude extreme results except in acceptable circumstances.

Reduce combat to an event based system and scrap any numerical relationship between dice score and casualties can help but is still prone to extremes if not carefully designed.

The problem is that, while dice (or any other randomising agent) are used to any significant extent, you will always have situations where a critical part of a game will be decided on by a dice throw. It isn't necessarily a bad thing, chance plays a part in any human activity, but if it happens as the norm then I feel the rules are just snakes and ladders with soldiers.

Don't ask me what the solutions are, pointing out the problem is as far as I have managed to get. I've done quite a bit of fiddling with systems over the years but never come up with something I think does the job as I want it done.

For me I want some fair semblance of reality to be there for a game to be 'fun'. I can play and enjoy some games that are just that, games with the 'Hollywood' approach, but I prefer games that are better simulations – at least in most respects.

I like a dash period flavour but not so much it overwhelms.
Like making a glass of orange cordial. You want just a bit of juice in there. Too little and you don't taste it. Too much and you can't drink it.

I think individual figure removal is a bit of a nuisance.

I'd suggest changing to opposed rolls and a dice per platoon or something.
Up the dice size for better troops.

(iii) Calculating effect: For all troops in close order: a die thrown for each group of firers, six grenadiers, eight line infantry, or six light infantry. The number on the die gives the standard number of casualties at short range.

We can parameterize damage per figure based on number of grenadiers (g), line infantry (i), and light infantry (l):

( 21/36 * g/6 + 21/36 * i/8 + 21/36 * l/6 ) / (g + i + l)

But we still need the ratio of different unit types in the formation. If we assume they are equal all the time (at start and as they get removed) we get:

x = g = i = l

( 21/36 * x/6 + 21/36 * x/8 + 21/36 * x/6 ) / (x+ x + x)

( 21/36 * (x/6 + x/8 + x/6 ) )/ 3x

( 21/36 * (8x/48 + 6x/48 + 8x/48) )/ 3x

( 21/36 * (22x/48) ) / 3x

( 462x / 1728 ) / 3 x

154 / 1728

77 / 869

as the average kills/unit. Or

~.0886

~1/11.28

So, each unit would hit on a 1 on a roughly 11.28 sided (fair) die. So rolling a d10 or d12 per unit and scoring ones as hits is pretty close.

( 21/36 * g/6 + 21/36 * i/8 + 21/36 * l/6 ) / (g + i + l)

If I am not mistaken, you are of by a factor of 6 here, and the above line should instead be:

(21/6 * g/6 + 21/6 * i/8 + 21/6 * l/6 ) / (g + i + l)

Which for the assumed case g=i=l would then likely equal as 924/1728.

As I said, I am not so good at math. etotheipi, why do you put each type of figure into the single equation. Each unit is of only one type.

Does you conclusion mean that for every line infantry shooting, a "1" on a d12 is a hit, and for Grenadiers and Lights, a "1" on a d10 is a hit. That means it is possible for all misses. Yet if you throw a d6 for 8 figures, and the number thrown is number of hits, then you always get at least 1 hit.

By the way, no saving throws.

Bobgnar: So WHOSE rules are they? Can you give us the name of the author?

That only comes up with a mean number of hits, not a suitable probability to apply to a BoD approach. I'm afraid the solution won't produce the same results.

As I said before Bobnagar, it can't be done exactly using a simple BoD approach.

Many solutions to most problems, Gildas--and often some I dislike. I was merely comparing single die roll to multiple die roll.

Andy, lots of rules record individual casualties without basing figures individually. There are a dozen ways to indicate which figures on a stand are "dead." For myself, I find I'm going more to the extremes--either a relatively small number of individually-based figures--max possibly 200 a side--in 1/72 or larger, or stand-removal systems at 15mm and smaller. Obviously rosters are possible, but for me they're quite literally too much like work. (I used to be a ground forces order of battle analyst. If I have to keep track of how many tracks the 23rd Guards Tank Division has running, I expect to get paid.)

But if we were all happy with the same rules we wouldn't be miniature wargamers.

Bobgnar, we did tell you--repeatedly--that we can't change from firing with one die for six or 8 men to one die per casting and still get the same distribution curve. The best we can do is get you the same average result, which Carlos von B appears to have done. To put it another way:

"Captain, I canna change the laws o' probability!"

As I said, I am not so good at math. etotheipi, why do you put each type of figure into the single equation. Each unit is of only one type.

OK … that was one of the things I didn't know. I assumed the units had a mix of different troop types. So you want an averaging answer for each unit type. That makes the scope different. Two simpler answers (three unit types, but only two different stats) instead of one more complex one.

… recalculating …

The mean number of hits per figure is 3.5/6 [58%] for elites & 3.5/8 [44%] for line. (3.5 being the mean score of a D6 – no need for long winded calculations).

Nearest with 1D6 would be the same at 50% [4,5 or 6 to hit] but a 1D10 would differentiate at 60% & 40%, but would exaggerate the difference by a fair bit. A D12 would be closer at 42% [8 or more] and 58% [6 or more].

This would still have the problem of a very different distribution of hits compared to the original and a simple add/subtract to the dice would no longer produce the same effect – nowhere near the original I fear.

Roll your D6 for each 6- or 8- troops. Then roll a number of dice equal to the D6 score. Each 4+ hits. For the remainder/fraction of a 6- or 8-, just roll one D6, hit on 4+.
Be warned, though, that firefights might become protracted events… ;-)

4DJones. These are from one the war-game classics. 79PA knows the history of his hobby:)

Charge or How to Play War-games. Peter Young and JP Lawford, 1967. I got my copy in 1969 for 55 Shillings. Now going for $80 USD-100.

All historical wargamers should play this at least once in their careers.

Thanks for all the help. Next game on Friday, hope to have a simplification by then.