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I recently made a post in another thread about the value of Ld. 10 over Ld. 9 and thought this table would be useful to the Dakka Community.
There are 36 possible outcomes of two dice. The following tables show the true odds for the specified outcome of the dice. Since our game relies so much on single two dice rolls, for the most part Collumn B is our go-to.

Note: I was slightly off in my previous posting in giving 10 an 8-1 odd - that is the gambling odd but as you can see below it's 11-1.

(A) This column gives the number of possible ways of making the dice total.

(B) This column gives the odds against making the dice total in a single roll.

(C) This column gives the odds against rolling the dice total before a 7.

(D) These columns give the odds against making the higher dice total before the lower dice total. e.g. 12 before 6 = 5 - 1. For making the lower number before the higher, reverse the odds. e.g. 6 before 12 = 1 - 5.

Dice A B C D> >
12 1 35 - 1 6-1 12
11 2 17 - 1 3-1 2-1 11
10 3 11 - 1 2-1 3-1 3-2 10
9 4 8 - 1 3-2 4-1 2-1 4-3 9
8 5 6 - 1 6-5 5-1 5-2 5-3 5-4 8
7 6 5 - 1 - 6-1 3-1 2-1 3-2 6-5 7
6 5 6 - 1 6-5 5-1 5-2 5-3 5-4 1-1 5-6 6
5 4 8 - 1 3-2 4-1 2-1 4-3 1-1 4-5 2-3 4-5 5
4 3 11 -1 2 -1 3-1 3-2 1-1 3-4 3-5 1-2 3-5 3-4 4
3 2 17 - 1 3-1 2-1 1-1 2-3 1-2 2-5 1-3 2-5 1-2 2-3 3
2 1 35 - 1 6-1 1-1 1-2 1-3 1-4 1-5 1-6 1-5 1-4 1-3 1-2 2

http://homepage.ntlworld.com/dice-play/CrapsOdds.htm


Automatically Appended Next Post:
I just realized Collumn D is pertinent as well - but that chart would be best seen at the original page since the numbers got squished in the cut and paste. It essentially tells you the odds of making over a number - so if, say, you had to close a gap of 10 inches on a charge and needed a 6 or better on the dice - that chart willl tell you the odds

Think the Crazy Old Man above your avatar suits this post quite well mate

Notice the little pattern in the second column, where the odds of rolling a 12 is 1/36, 11 is 2 in 36 and so on counting up one each time until you reach the odds of rolling a 7 (6 in 36), then counting down until snake eyes (1 in 36). That little pattern is great to remember, and can help you figure out any calculation in your head during a game.

I understand using the math but there are outliers like round edged die dont roll as true as perfectly square edged. Plus on a flat table at home its more likley then at a store with speacial boards.

Without question there are always outliers - just as at the casino there are outliers (chips on the table bumping a die, different arms tossing those dice at different velocity and magnitude) but the odds are made to show the averages with a slight variance and are as close to true to form as you will get.

Sebster - I haden't noticed that pattern! Thank you I will certainly be doing it in my head from now on rather than having a cheat sheet.

I know people hate admitting to the fact that warhammer is a math game - but whether or not we know it we're doing these calculations in our head. When you measure charge distance and see a 13 on the tape and subtract movement you weigh in your head the chances of getting a 9 or better. Since we all know the best odds are a 7 then we dont take the chance to roll a 9.

Incidentally, I will be looking for 3 dice charts at some point to account for swiftstride and magic rolls on 3 dice. Just from general nerdyness we all know the average of 3 dice is 10 or 11 (from good ol D&D stat rolling) but I'm curious what the hard amd fast numbers are.

Draigo wrote:I understand using the math but there are outliers like round edged die dont roll as true as perfectly square edged. Plus on a flat table at home its more likley then at a store with speacial boards.

Unless you have specific knowledge of the dice in question rolling higher or lower (in which case you should stop using those dice!) then the odds are as given.

Yah, as a semi-regular gambler. Random is random. Yes, hitting chips and hitting the spiked foam edges flip the dice in specific way. But you would have to not only be the greatest athlete in the universe but the fastest calculator in the universe to make use of that data. I.e., casinos, that make money off that, don't give a rat's ass.

I do recall seeing back in the D&D days a 100 sided die. It was basically the size of a golf ball and had beads inside it. I did not consider it altogether trustworthy.

OH, and I knew guys who would soak their dice in oil. Like vegeteble oil on the 1 side, to make it SLIGHTLY more likely to get a 6. Of course the chits itself modify that. But realy ti's so slight as to not be worth calculating.

2000 Volts wrote:
Incidentally, I will be looking for 3 dice charts at some point to account for swiftstride and magic rolls on 3 dice. Just from general nerdyness we all know the average of 3 dice is 10 or 11 (from good ol D&D stat rolling) but I'm curious what the hard amd fast numbers are.

I don't know, I could swear that the average roll on 3D6 while rolling D&D stats is 16.

-Matt

HawaiiMatt wrote:

2000 Volts wrote:
Incidentally, I will be looking for 3 dice charts at some point to account for swiftstride and magic rolls on 3 dice. Just from general nerdyness we all know the average of 3 dice is 10 or 11 (from good ol D&D stat rolling) but I'm curious what the hard amd fast numbers are.

I don't know, I could swear that the average roll on 3D6 while rolling D&D stats is 16.

-Matt

Lol seems like it! That's why I just let my players pick their stats and let the evil of the world balance around their awesomeness.

HawaiiMatt wrote:

2000 Volts wrote:
Incidentally, I will be looking for 3 dice charts at some point to account for swiftstride and magic rolls on 3 dice. Just from general nerdyness we all know the average of 3 dice is 10 or 11 (from good ol D&D stat rolling) but I'm curious what the hard amd fast numbers are.

I don't know, I could swear that the average roll on 3D6 while rolling D&D stats is 16.

-Matt

3*3.5=11.5. To get a 16 on 3 dice the lowest ANY of them could be would be a 4. You're seriously saying it's "average" for you not roll a single 1,2 or 3 on three dice?

Chance of rolling exactly x on 3 dice, rolling over x on 3 dice and rolling at most x on 3 dice:

Roll Exact At most Over 3 0.46% 0.46% 99.54% 4 1.39% 1.85% 98.15% 5 2.78% 4.63% 95.37% 6 4.63% 9.26% 90.74% 7 6.94% 16.20% 83.80% 8 9.72% 25.93% 74.07% 9 11.57% 37.50% 62.50% 10 12.50% 50.00% 50.00% 11 12.50% 62.50% 37.50% 12 11.57% 74.07% 25.93% 13 9.72% 83.80% 16.20% 14 6.94% 90.74% 9.26% 15 4.63% 95.37% 4.63% 16 2.78% 98.15% 1.85% 17 1.39% 99.54% 0.46% 18 0.46% 100.00% 0.00%

Joey wrote:

HawaiiMatt wrote:

2000 Volts wrote:
Incidentally, I will be looking for 3 dice charts at some point to account for swiftstride and magic rolls on 3 dice. Just from general nerdyness we all know the average of 3 dice is 10 or 11 (from good ol D&D stat rolling) but I'm curious what the hard amd fast numbers are.

I don't know, I could swear that the average roll on 3D6 while rolling D&D stats is 16.

-Matt

3*3.5=11.5. To get a 16 on 3 dice the lowest ANY of them could be would be a 4. You're seriously saying it's "average" for you not roll a single 1,2 or 3 on three dice?

It's a joke - one clearly made by a game master. In the game Dungeons and Dragons "stats" are rolled on 3D6 (sometimes 4d6 and drop the lowest) and in every gaming group there always seems to be TFG who has 16, 17 and 18 in all his stats - in other words impossibly high stats.

2000 Volts wrote:Incidentally, I will be looking for 3 dice charts at some point to account for swiftstride and magic rolls on 3 dice. Just from general nerdyness we all know the average of 3 dice is 10 or 11 (from good ol D&D stat rolling) but I'm curious what the hard amd fast numbers are.

Swiftstride is rolling three dice and dropping the lowest, so just totaling up the three dice can be misleading (for instance, rolling 1, 6 and 6 gives a very different result to rolling 3, 3 and 4).
So here’s the odds of each result, rolling three dice and dropping the lowest;
2 1 0.5%
3 3 1.4%
4 7 3.2%
5 12 5.6%
6 19 8.8%
7 27 12.5%
8 34 15.7%
9 36 16.7%
10 34 15.7%
11 27 12.5%
12 16 7.4%


It’s a weird spread, really. You're more than 80% likely to roll 7 or higher, but from there you're more or less equally likely to roll anything from 7 to 11. I hadn't expected that at all.

The other issue then is how likely it is that a swiftstride unit will be caught by a regular pursuing unit, or how likely it is that a swiftstride unit will catch its pursuer (a tie on a pursuit roll means the unit is caught, doesn't it... I always get that confused).

Anyhow, the table shows the score rolled by the swiftstride unit on the left, with the first table giving the odds of escaping a normal pursuer given you rolled that number, and the second table gives the odds of successfully pursing a normal target given you rolled that number. At the end is an overall figure, that weights the odds of rolling each swiftstride score against the odds of success, to give an overall figure for success or failure.

Successful Escape Successful Pursuit
2 0% 2 3%
3 3% 3 8%
4 8% 4 17%
5 17% 5 28%
6 28% 6 42%
7 42% 7 58%
8 58% 8 72%
9 72% 9 83%
10 83% 10 92%
11 92% 11 97%
12 97% 12 100%
Overall 62% Overall 72%

I was a little surprised that numbers only give a small advantage to the swiftstride unit, particularly when fleeing. I'd have given my pistoliers much better odds of escaping, though I guess in hindsight it works out about right.

A note from my past no one asked about:

I grew up around Washington D.C. and I used to play board games and roleplaying games with people a lot older than me at the local university. A bunch of guys were dorks who worked for the NSA. As well as NASA and FBI. Their jobs were number-crunching on vast, scientific scales.

I did not do well against them.

Especially considering I was like 17-19 at the time. But #'s knowledge gives you a very large advantage if you play them right. And yeah, in D&D there was always the guy who rolled his stats "at home" and comes in with a dude who looks like Thor and is smarter than Einstein while my dude I basically had to make a magic user because then at least he could cast spells cuz he wasn't going to win any sword fights.