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Calling all you dakkite mathematicians out there.

When you are called to reroll dice, such as when firing a twin-linked weapon, are the odds better if you roll two dice together (a common practice in many areas), or rolling a single die, and rolling it again if you missed? Many units use rerolls such as fateweavers saves or coteaz seize initiative to name a few.

Some seem to think so there is a difference.

Ive done some numbers myself but there are some real math-hammer gurus on this site. So I thought id pose the question to the public.

It makes no difference! How could it possibly make any difference?

if it makes a difference, then my brains had it

I can't seem to think how the way you roll would make a difference, at least statistically. The way to determine which way is best, is to just use the method that works for you. Kind of like how basketball players have a routine when they go to the free throw line(I still remember mine)

Rolling two dice at the same time is safer and likely to be more random as its harder to "game" the dice when you are rolling two at the same time. Rolling one dice oftentimes leads to "dropping" rather than shaking and rolling.

They are equivalent to one another. Even just dropping one dice if you pickup a 'random' dice and hold it in an unbeknownst to you position in your hand is random (or as random as you can get).

The only time it matters is when you have multiple Twin Linked weapons (or twin linked weapons with multiple shots). When that happens, you need to differentiate between pairs of dice for each shot.

For example, take a Twin-Linked Autocanon: Rolling 4 dice and taking up to two hits is different than rolling 2 pairs of dice and taking up to one hit from each pair.

It does make a difference. It s explained to me once.

If you roll a single die your chances of missing at BS4 is 1/3. If you miss you then get a second roll with those same odds. But they are two separate rolls. Rolling two dice at once your chance of missing is 1/9.

Budzerker wrote:It does make a difference. It s explained to me once.

If you roll a single die your chances of missing at BS4 is 1/3. If you miss you then get a second roll with those same odds. But they are two separate rolls. Rolling two dice at once your chance of missing is 1/9.

Totally not true. The probability is the same. The ONLY time rolling one after the other vs. rolling at the same time makes a difference is when you fire multiple TL-shots simultaneously (see my earlier post).

Budzerker wrote:It does make a difference. It s explained to me once.

If you roll a single die your chances of missing at BS4 is 1/3. If you miss you then get a second roll with those same odds. But they are two separate rolls. Rolling two dice at once your chance of missing is 1/9.

So the chance of missing the first roll is 1/3. . . and the chance of missing the second roll is 1/3. . . so the chance of missing both rolls is 1/3 x 1/3. . . which is 1/9. . .

themocaw wrote:

Budzerker wrote:If you roll a single die your chances of missing at BS4 is 1/3. If you miss you then get a second roll with those same odds. But they are two separate rolls. Rolling two dice at once your chance of missing is 1/9.

So the chance of missing the first roll is 1/3. . . and the chance of missing the second roll is 1/3. . . so the chance of missing both rolls is 1/3 x 1/3. . . which is 1/9. . .

Ooh, someone who knows probability math.

For Bud - the probability to miss is the same in both cases. It doesn't matter if you roll twice or at once, each dice has a 1/3 miss chance. Count it up for two dice and the miss chance is 1/9 for both scenarios.

If you look at each individual dice roll compared to two at once there is no difference, the odds are the same.

If you look at a TL BS 3 weapon you roll one dice and there's a 50 percent chance of hitting. then if you miss,roll again there is another 50 percent chance of hitting. if looked at this there is a 50 % chance to hit the frist roll and a 50% chance with a second roll. But with the probability it is 75 % chance to hit. 1/2 + ((1-1/2)*1/2)=75%

Now if you roll two at once there is a 50% chance that both dice will roll a hit and a 75 % that one will hit and a 25% both will miss.

EDIT: added math then edited again for spelling and another to add "EDIT"

I have never seen anyone roll two or more dice for twinlinked weapons , is it allowed ?

If your opponent knows why you're doing it, yes.

Dice are the very basic (one step up from coins) exampls of discrete events. The result of one dice roll has NO bearing on the result of another dice roll, whether simultaneous or not.

If you are firing an assault 1, Twinlinked weapon it makes no difference if you roll together or separately. If you fire an assault 2 TL weapon (not gets hot, etc) you MUST know which pair of dice is which.

Hytanthas wrote:

Now if you roll two at once there is a 50% chance that both dice will roll a hit and a 75 % that one will hit and a 25% both will miss.

Close, but not quite. Probability always adds up to 100%

The math is as follows:

1 Die - 50% chance to hit on first roll. If first roll fails, 50% chance to hit on second roll. 50% * 50% (i.e. - chance you will need to roll again * chance you will hit on second roll) is 25%. Therefore, 50% chance to hit on first roll, plus 25% chance that you will need to roll a second die that will result in a hit gives you a 75% chance of hitting.

2 Die - (given maximum result of 1 hit) each die has a 50% chance of hitting. That means a 25% chance of both hitting (not 50%), a 50% chance of 1 hitting (not 75%) and a 25% chance of both missing. 25% chance of both hitting plus 50% chance of 1 hitting gives you a 75% chance of at least one hitting. Given you can only have a maximum result of 1 hit, this equates to a 75% chance of hitting.

Both ways of rolling give you the same chance to hit, but using 2 dice is quicker and less likely to be able to 'rig', though 1 die at a time may be less confusing for your opponent if they're not sure what you're doing...

The outcome of 1 die does not affect the outcome of the other, only whether you look at the second.

Rolling 1 die and missing, then rolling the second and hitting has the same probability as rolling 2 dice, 1 hitting and 1 missing.

There is some math involved there that shows that point, but I can't remember it exactly.

-cgmckenzie

The only time it ever makes a difference would be when shooting "Get's Hot!" weapons, as the order of the dice is important in this case.

For the BS4 example above:
1)
Rolling one dice is a 4/6=24/36 chance to hit, 2/6 will miss.
Out of that 2/6 you will roll a second dice with a 4/6 chance to hit.
So the chance of the first dice missing and the second one hitting is (2/6)*(4/6)= 8/36.
The chance of the first die hitting or the second die hitting is 24/36+8/36=32/36.
2)
Rolling two dice at once, the chance of hitting is equal to the chance of both dice showing any other number than 1 or 2.
There are 6*6=36 possible results for two dice, each has a chance of 1/36
These rolls will result in a miss: (1,1) (1,2) (2,1) (2,2), a total of four results, meaning 32 results will result in a hit.
32 results each have a chance of 1/36, so the chance of rolling one of them is 32*(1/36)=32/36. Same number as above.

Bottom line:

There is no function difference for single shot non-Gets Hot or other special rule weapons (example: Ranger Long Rifle). But, if this isn't immediately obvious to both you and your opponent, the debate and probability courses will take a much longer time than the 0.5 seconds it takes to do a re-roll.

Get's hot only matters if both die miss and one is a 1. And Range Long Rifles (if able to get twin-linked) can not be rolled at the same time.

The these matter is with the Get's hot roll if the "first" dice is a 1' you reroll and if it is not a 1 then nothing happens, but if the first one misses, and the second one is a 1 then you have a get's hot result, so you can not roll two die at the same time as you cannot tell which one was first.

The Ranger Long Rifle, is the same if both hit. Since they get bonuses for hitting on a higher number, if both die rolled is a hit, and only one was a qualifing hit, then you don't know if it was the second or first roll.

never mind

Not to hijack the thread but when you mentioned gets hot it brought up a question. My CCS has 4 PG and the Capt had a PP. Do i roll all the dice at the same time? or do they each have to be rolled separately, or with different colors?

Also if the odds are the same then i see no problem with rolling 2 dice for a 1 shot TL weapon. I do it all the time.

Gets Hot! means you need to know which model gets hot!

Assuming youre within 12" you need to roll:

2 dice for each gunner, either one after the other or differently coloured pairs

1 dice for the PP Captain.

EVen if you roll a double 1 on one gunner, only THAT gunner suffers the wound, noone else.

Jidmah wrote:The only time it ever makes a difference would be when shooting "Get's Hot!" weapons, as the order of the dice is important in this case.

For the BS4 example above:
1)
Rolling one dice is a 4/6=24/36 chance to hit, 2/6 will miss.
Out of that 2/6 you will roll a second dice with a 4/6 chance to hit.
So the chance of the first dice missing and the second one hitting is (2/6)*(4/6)= 8/36.
The chance of the first die hitting or the second die hitting is 24/36+8/36=32/36.
2)
Rolling two dice at once, the chance of hitting is equal to the chance of both dice showing any other number than 1 or 2.
There are 6*6=36 possible results for two dice, each has a chance of 1/36
These rolls will result in a miss: (1,1) (1,2) (2,1) (2,2), a total of four results, meaning 32 results will result in a hit.
32 results each have a chance of 1/36, so the chance of rolling one of them is 32*(1/36)=32/36. Same number as above.

Thank you for actually writing that out so that I didn't have to. I don't understand how this isn't common knowledge by now. It's a relatively simple probability calculation however you slice it.

More simply one could say there is a 66.67% chance to hit with the first die, and a 66.67% chance to hit with the second die if the first misses, giving you 0.6667+(0.3333*0.6667) = 0.8889 or an 88.89% chance (after accounting for rounding errors). If rolling both dice together, it's a 4/36 to miss as you stated above, so 32/36 to hit which translates to 88.89%, or exactly the same number. Multiplication and division can be done in any order, and addition and subtraction can be done in any order. In fact multiplication and division are exactly the same thing (division can be expressed as multiplication and vice versa), as are addition and subtraction, so it stands to reason that the dice can be rolled in any order, because probability math is only glorified multiplication and/or addition. You could roll the re-roll die first, followed by the primary die, and it would make no difference on the statistical outcome.

*Resets clock*

Probabilities are easy

100 dice 4+ to hit

50 hit 50 miss

twinlinked? From the 50 miss

25 hit

25 miss

total of 75 hit.

Just work it this way for all probabilities.

But this is never accurate.

Budzerker wrote:It does make a difference. It s explained to me once.

If you roll a single die your chances of missing at BS4 is 1/3. If you miss you then get a second roll with those same odds. But they are two separate rolls. Rolling two dice at once your chance of missing is 1/9.

This is what you stated mathematically:

(0.333 * 0.333) vs. (0.333) * (0.333) which are mathematically equal.

I think the reason why people roll two dice together is because the dice will move much more while rolling together than rolling each one by themselves, which gives a better distribution, thus more consistent rolls.

Generally it's safer to roll 1 die and then reroll if you miss.

If you're firing a single weapon, your opponent might wonder why you're rolling 2 dice. Leads to explanation.

If you're firing salvo, you have to explain what each color die represents. Leads to explanation.

Just roll 1 die and then reroll it if it misses. Less room for confusion, even if statistically irrelevant.

Budzerker wrote:It does make a difference. It s explained to me once.

If you roll a single die your chances of missing at BS4 is 1/3. If you miss you then get a second roll with those same odds. But they are two separate rolls. Rolling two dice at once your chance of missing is 1/9.

^ This is completely wrong...

The correct odds with BS4 are:

(4/6 + (2/6 * 4/6))

Or

89%

Given that you have already missed the first shot... the second shot retains its 1/3 chance to miss, but that's assuming the first one missed. The chance of either the first or the second one scoring a hit is the above formula.

CageUF - so you showed a 8/9 chance of hitting, and the poster you quoted stated the chance of missing was 1/9

Both of you are correct.

biccat wrote:Generally it's safer to roll 1 die and then reroll if you miss.

If you're firing a single weapon, your opponent might wonder why you're rolling 2 dice. Leads to explanation.

If you're firing salvo, you have to explain what each color die represents. Leads to explanation.

Just roll 1 die and then reroll it if it misses. Less room for confusion, even if statistically irrelevant.

As soon a you're shooting more than one twin-linked weapon, simply rolling one dice for all of them and then picking up misses is always going to be faster anyway.