"Converting odds to dice" Topic

so i was looking at my copy of SSI's old computer wargame 'Battlecruiser' and what is cool about this old game is that in the rules they actually provide the formulae for calculating hits and all the modifiers that apply, which means one could convert it to the tabletop possibly

that being said, the determination of whether a shell hits the target is based on odds – and the modifiers can reduce the odds to the limit if 1/230 at worst. – my question is can odds be converted somehow to dice rolls?

say if for example, the calculated odds to hit came up as 1/93 or 1/131 or something like that – how could one translate that to dice? is this even possible, or would there be a better system that could model odds?

You could just do the calculation, round to the nearest 1% and use percentage dice… 1/131 would round up to a 1% chance the same as 1/93. Odds worse than 1/200 would round to zero but do you relly want such extreme results in a game?
If you really want to keep such small gradations then go to three dice, the extra die being for the tenths of a percent if the other two roll zeroes.

Thanks, I was having trouble trying understand what something like 1/93 would translate to

I guess no i wouldnt want to be dealing with such results and perhaps its only going to be inthe case long range small turning targets that might in poor visibility that might yield such results, but nevertheless there ought to be an easier way to work it out

- i am not sure what a percentage dice is – is it a d100?

i think if it could just be instead something done with d6s or d10s that would be better – perhaps a conversion that groups the percentages into categories of die roll results, – i might yield more hits than the SSI title would do but thats okay

i am not sure what a percentage dice is – is it a d100?

Yes, it is the same thing, and probably the most practical solution (do you really need more granularity than that ib a typical game?).

i think if it could just be instead something done with d6s or d10s that would be better – perhaps a conversion that groups the percentages into categories of die roll results

You can use two d10 dice to form d100 (first dice for the tens, second dice for the units).

Alternatively, you could use three d6 to form so called d666, which despite the name gives you 6x6x6=216 combinations, i.e. the lowest odd you can get there is 1/216, which would be pretty close to the 1/230 that you gave in the original example. However, if you are not used to number-crunching and base-6 number systems this might get a bit impractical.

Without seeing the actual formulae and probability distributions that they produce, it is a bit difficult to suggest a specific solution. However, as a practical issue, it might be worth checking what is the highest chance of hitting that is likely to be encountered in a game.

thanks i will type up what the formulae are when i can a bit later when i am free

i think i am just having a bit of difficulty still comprehending what one would need to roll
- if i were to use the d666 option (most likely i wont) and needed to get 1/216 – would this mean i have to roll 6,6,6?

and if the odds were 1/2 i would need to roll 9 or more?

There are Tables of Probabilities for various D6 combinations and playing cards at back of the Wargame Developments Handbook which can be downloaded free from here wargamedevelopments.org/about

– if i were to use the d666 option (most likely i wont) and needed to get 1/216 – would this mean i have to roll 6,6,6?

The chance of rolling 6-6-6 is 1/216 (as is the likelyhood of any specific combination of the three dice).

and if the odds were 1/2 i would need to roll 9 or more?

Not sure what you are thinking here, but with D666 the dice are not added together (as in 3D6), but treated in the same way as when using three D10 together as D1000 – the first dice is treated like "hundreds" (actually multiples of 36), the second like "tens" (actually multiples of 6) and the last as units. In practice this requires a differently coloured dice for each of the three, so they can be told apart.

It is probably easiest to visualise by starting to draw a chart where you map the number combinations and cumulative probabilities of rolling that number or less. It should look something like this (skipping a lot of combinations here):

- Chance of rolling 1-1-1 is 1/216
- Chance of rolling 1-1-2 or less is 2/216
- Chance of rolling 1-1-3 or less is 3/216
- Chance of rolling 1-1-6 or less is 6/216
- Chance of rolling 1-2-3 or less is 9/216
- Chance of rolling 1-2-6 or less is 12/216
- Chance of rolling 1-6-6 or less is 36/216
- Chance of rolling 2-6-6 or less is 72/216
- Chance of rolling 3-6-6 or less is 108/216

Essentially, every time you increase the last digit by one "pip", the cumulative probability goes up by 1/216.

GeorgBuchner – what I meant by percentage dice were two different coloured d20s, each marked 0-9 (each digit appearing twice to cover the 20 sides).
Personally, I use a black d20 for the 'tens' and red d20 for the 'units', so a black '3' and red '2' would be read as 32%. Any score at or below the percentage required for the test in question would be a success.
If you wanted to use smaller chances than 1% then you can introduce a third different coloured d20 (say green) for the 'tenths of 1%'; thus a black '7', a red '9' and green '4' would be read as 79.4%.

Two easy options:

#1 1/230 = 0.0043 – roll four percentile dice, you can get to 1/10,000 that way. You can recreate any odds perfectly.

Some people would use four colors of dice or the four digits, but if you put them in a compartmented box you can just read them across.

You could also round to 0.004 and roll just three dice, which brings me to…

#2 recollect how the odds were determined. Someone did a bunch of research, a little math, had to fit into a table or into some code, so they just fudged it. Very , very few games have accurate odds, and they have to do some weird gyrations with the dice and tables to get there. In a game with enjoyable mechanics you do your research and then you are painting with numbers, trying to evoke the truth, make a good game, and represent rather than simulate.

In light of that, just fudge the numbers you read into numbers you can use. In the end the dice will be capricious anyway, so if it feels right that is more than good enough. Otherwise you risk spending a lot of time on something that won't make the game much better, instead of spending that time on something that will make the game much better – been there, done that.

That's way to much in the weeds for me.

I use one twenty sided die with the numbers in 5% increments:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 00. I use 00 as 100.

None of this looking at two or three dice and adding up numbers. If you are rolling to determine if something has a one out of 230 chance then you are wasting a lot of time on things that will never happen.

I got these as custom dice from Chessex in 2008.

link

Mike Bunkermeister Creek
Bunker Talk blog

thanks all – some great responses, though i don tknow why but i just keep getting muddled up by visualising things as dice rolls – i think the key is to remember that it would be attempting to roll the number or less than

the four percentile dice is the easiest for me to understand, though not everyone has a d100, – in which case the 3d6 would be better

but Bunkermeisters solution might be best overall of course not a 1:1 solution but a more playable one – i guess for everything under 5% its just a roll a 1

here is the page with the details in teh battlecruiser manual – some other things one owul dhave to workout would be how hit location is determined, and whether the hit is vertical or horizontal – the vertical hit chance increases with range – i guess roll first to check hit location/or near miss, and then for the turret/deck/structure if they are the hit locations check to see if its vertical hit , and then proceed to calculate if its a penetration and what damage may ensue

Those calculations are clearly just wargaming WAGs (Wild A*se Guesses) plucked out of nowhere – just the linear nature of some effects and simple halving makes that obvious. With that in mind Bunkermeister's d20 suggestion, marked in 5% increments is eminently sensible. However, in long range naval gunnery even a 5% chance can be quite high so I would roll again, perhaps just using a d6, for probabilities below 5% (assuming you scored a'5' on the d20 first).

If I interpret the given chart correctly, the highest chances of hitting are:

1/30 for DD, DE, TB targets
1/10 for CA, CL, CLAA, AC, AK targets
1/5 for other kinds of targets

Even for targets sitting totally still.

These are quite low chances for a miniatures game where the dice are rolled and checked manually.

i just keep getting muddled up by visualising things as dice rolls – i think the key is to remember that it would be attempting to roll the number or less than

It is also pretty straightforward to calculate the probability for rolling a given number or above, though if you already have trouble with managing numbers this might just cause additional confusion at this stage.

If you are used to doing math in decimal system, then using a bunch of D10 (which are not really all that obscure to obtain) to act as D100, D1000 or D10000 should be the most straightforward approach.

As for game design, do you really want to play a game where the players engage in trading individual long range shots back and forth with a very low probability of hitting? It might be realistic, but it could also get rather tedious after a while if neither side scores any hits within reasonable time.

Gradations of less than 1% aren't worth bothering about; nobody knows hit probabilities to that precision anyway.
So just use percentages and roll 2d10, one for 10s, one for 100s.
If you roll less than or equal to the percentage chance, you hit.

As several of the posters have suggested, you might not want to include very low probability events in a miniatures game.

If your rules allow very low probability events like very long-range hits and you don't either incorporate a limiting factor like limits on ammunition (which requires tracking ammunition use or some other limiting mechanism) or a bonus factor for holding fire until relatively close range (like the "first fire" bonus in some land warfare rules) then some gamers (particularly those of a certain type) will insist on taking every available low probability chance in hopes of hitting the jackpot.

Such behavior can greatly affect the tactics employed by the game players, but more important it wastes valuable gaming time. Every time a player swings for the fences in one of the low probability events he will spend time (in a naval game) measuring range, rolling dice and then checking the hit table to see if the shot hit-and if it did, then, perhaps, checking a damage table to see what damage was done. And all of this activity would be occurring long before the ships even get into what sailors of the time would consider to be effective range.

The foregoing might not be much of a problem in a computer game where the computer could track range and "dice rolls," calculate damage and even keep track of ammo usage on the fly, but in a miniatures game, IMHO, it can make the game very dull.

And all this would be in addition to the time you would apparently have to spend to convert the computer game's formulas into a dice-based odds system. In miniature games I'm generally in favor of eliminating very low probability events as I think they disport player behavior and waste time, and those that would have less than a 5% chance of occurring seems, IMHO, don't seem to be worth including in a game to be played by ordinary gamers.

okay yes, i agree now – getting those very low probabilities on the tabletop would just waste too much time to make it worth any ones while – not that i imagine i would ever actually use these rules in a game with anyone, rather just for my simulation experiments and plus because i really love the old SSI games -

when playing Battlecruiser, or the followup Warship on the computer, i dont recall the misses being so frequent -but then i guess the ranges on not too extreme, such as with savo island, where torpedoe from the IJN start coming in to not too many turns in

anydice.com
you can input dice type, number and get all the percentages.

For an interesting read on gun performance and the 3 gunnery exercises of the 1920-40 scroll down to Examples of actual gunnery exercies. Below that concerning the secondary batteries is also an interesting read on percentages of hits at ranges.
link

As for the provided formula, if somebody wants to play around with them I would recommend building a spreadsheet (Excel etc.) with formulas where you can adjust the different parameters.

It takes a bit of time to construct the formula in the first place, but once you have done that you can repeat it over 20 or so columns and then fill those with various values and see how they affect the "a" value and how this matches expectations.