Probability of the 3D6 Charge

[Diagramdude]

I had a situation in a game where I popped Descent of Angels for Capt. Smash after Wings of Firing him. I needed a 9 on 3D6. The entire game hinged on making this charge.

 

I rolled a 5, 1, 1. I then had to decide whether to CP Reroll one of the 1s, which I would then need a 3+, or reroll the entire 3D6 because of the Angel's Wing. I ended up using a CP reroll, stuck the 3+ and made the charge, but I wish I had known the following:

 

On 3D6, you have a 74.07% chance to roll 9 or more. So, if you fail your 3D6 9" charge, if a single CP reroll would mean you only need to stick a 2+, then your best odds are to reroll that one die and hope for the 83.33% chance of making that. (And it will cost you a valuable CP). 

However if the single reroll will need a 3+ (66.66%) chance or worse, then you are much better off picking up all 3D6 and rolling again (provided you have access to reroll failed charges, such as from the Angel's Wing or Lemartes). 

 

Below is the probability table for 3D6

 

Dice Score Result or more

3                 100

4                 99.53

5                 98.14

6                 95.37

7                 90.74

8                 83.79

9                 74.07

10                62.5

11                50

12                37.5

13                25.92

14                16.2

15                9.25

16                4.62

17                1.85

18                0.46

[Jolemai]

Whilst this fails to take into account Sod's Law, it's very useful information all the same. Thanks for posting :tu:

[Leonaides]

Just a slight query - but i thought you actually couldnt declare a charge at something further than 12" away. Admittedly the extra movement from a 3D6 charge could be used to pass over the target to assault from the far side (slingshotting a consolidate move afterwards maybe?).

[Panzer]

Just a slight query - but i thought you actually couldnt declare a charge at something further than 12" away. Admittedly the extra movement from a 3D6 charge could be used to pass over the target to assault from the far side (slingshotting a consolidate move afterwards maybe?).

 

You can't but you may have to charge over terrain and there are rules that reduce your charge range.

For example charging a T'au Commander with the Grav-inhibitor Field Signature System (Relic), sitting in a ruin and having a Grav-inhibitor Drone from a Pathfinder unit nearby reduces your charge range by 6".

[Indefragable]

Well done, Brother.

 

...now about with re-rolls?

[Brother Crimson]

You can find the odds of a single reroll by finding the number you need.

 

Rerolling all 3 will give you another 74%

 

This is better than trying to reroll a single die for a 3+.

[Diagramdude]

If you want to know total probability with rerolls, then you could take the 74.07% initial chance of success and then, with the 25.93% fail chance, another 74.07% chance to succeed. The total chance to make the 3D6 charge with rerolls then is 93.28%

To illustrate with 10,000 rolls:
7407 succeed first try
2593 fail the first try and reroll

1921 succeed on the reroll
672 fail again on the reroll

So out of 10,000 attempts, 9328 succeed and 672 fail. 93.28% total chance of success.

However my main point is when you have to decide to pick up all the dice and reroll all, versus just picking up one and using a CP reroll. If a single die would just need a 2+, then CP reroll is your best shot. If the single die needs a 3+, definitely reroll all of them.

I think this is invaluable knowledge for Blood Angel players because making that 9" charge can often be the difference between victory and defeat!

[The4thHorseman]

I thought the CP Re Roll had to be the whole Roll, when the roll consists of more than one Dice. I beleive that was in an FAQ. Not sure though.

[Panzer]

I thought the CP Re Roll had to be the whole Roll, when the roll consists of more than one Dice. I beleive that was in an FAQ. Not sure though.

 

The CP re-roll specifically says you re-roll one dice. There was a FAQ entry and it confirmed that you re-roll only one dice and not the whole roll. ;)

[Arkhanist]

40k rules FAQ.

 

"Some rules allow you to re-roll a dice roll, which means you get to roll some or all of the dice again. If a rule allows you to re-roll a result that was made by adding several dice together (e.g. 2D6, 3D6, etc.) then, unless otherwise stated, you must roll all of those dice again. You can never re-roll a dice more than once, and re-rolls happen before modifiers (if any) are applied."

 

"Command re-roll stratagem:

you can re-roll any single dice."

 

I.e. a CP re-roll is 'otherwise stated' to only apply to a single dice.

[The4thHorseman]

Well, probably will be making more charges now.

[The Unseen]

The FAQ was covering stuff like "re-roll a psychic test", and people were only rerolling 1 die of it when it was advantageous.

Like say you needed 8, and you rolled a 6 and a 1, and your an eldar farseer, so you can reroll psychic tests.

Their ability says "reroll the test", so you have to pick up both dice.

 

But the command reroll is always 1 die.