Charge Distances and Probabilities (Updated)

[WestRider]

Almost all of the discussion of Charge Distances that I've seen has been talking about Average Charge Distances under various circumstances. While it has it's uses, I don't think the Average is the best tool for actually thinking about how this affects the decisions we make on the Tabletop.

After all, we can pre-measure now, so mightn't it be more useful to think in terms of the odds of a given Assault succeeding or failing?

First, the chances of succeeding at a given Charge Range with no other factors, the usual bell curve:
2" - 100%
3" - 97%
4" - 91%
5" - 83%
6" - 72%
7" - 58%
8" - 41%
9" - 27%
10" - 16%
11" - 8.3%
12" - 2.7%

I've rounded down in every case to encourage conservative estimation, rather than going for long shots.

Tending fairly strongly toward conservativism in this sort of thing, I wouldn't consider anything longer than a 5" Charge to really be reliable if you have no Re-Rolls on open ground. Anything over 7" is gambling, pure & simple.

Now, with a re-roll on both dice, the other simple form:
2" - Still 100%
3" - 99.9%
4" - 99.3%
5" - 97%
6" - 92%
7" - 82%
8" - 65%
9" - 47%
10" - 30%
11" - 15%
12" - 5.4%

Again, rounding everything down. Obviously, plenty of improvement all around, but not that much increase in what's really reliable. 7" is about the limit on the truly reliable Charges, and it goes downhill very fast indeed after that.

Partial Re-Rolls for Fleet and the effects of Difficult Terrain are too much work for me to do by hand. If someone can work them out in Excel or something, that would be awesome. I'm fairly certain that the option for partial Re-Rolls gives a bit more of a boost over a straight Re-Roll, but I doubt it adds more than an extra inch reliably. I'm not familiar enough with the "3d6, drop the highest" distribution to make any more than the most general prediction: It makes it worse.

Note also that you're usually going to want to factor an extra inch or two into your estimate of the total distance to take casualties from Overwatch into account. More if you're charging into something like a Guard Blob.

Finally, a note for those who claim that the possibility of 12" Assaults makes up for the possibility of failing 3" Assaults in clear ground: Because anything over 5-9" (depending on the circumstances) is a total gamble, and you have to take Overwatch Fire just for declaring the Assault, it's going to be much rarer that people even attempt Assaults outside of our previous Range. So the average range of successful Assaults is going to come down substantially.

For some Units, it got very noticeably worse: across clear ground, Raveners had a guaranteed 19" Threat Range before, while now they've got almost a 1/5 chance of failing what used to be a sure thing. They had a 1/6 chance of a 24" total distance, while now it's barely more than 1/20. And, again, that's not taking into account the odds of losing at least one Model off the front from Overwatch.

UPDATED:
Difficult Terrain:
Had a couple slightly different sets of numbers here. From Carnogaunt on The Tyranid Hive:
2" : 216/216 = 100%
3" : 200/216 = 92%
4" : 173/216 = 80%
5" : 138/216 = 63%
6" : 103/216 = 47%
7" : 69/216 = 31%
8" : 42/216 = 19%
9" : 22/216 = 10%
10" : 10/216 = 4.6%
11" : 4/216 = 1.8%
12" : 1/216 = 0.46%

And from Tarrasq on the 3++ Forum:
2 = 100%
3 = 93.5%
4 = 80.0%
5 = 64.3%
6 = 47.6%
7 = 31.9%
8 = 19.4%
9 = 10.6%
10 = 5.0%
11 = 1.8%
12 = 0.46%

The differences on a couple look greater than rounding error, but not enough to change the overall conclusion: Going for more than a 4" Charge through Cover is just Gambling.

Carnogaunt also supplied numbers for Difficult Terrain and straight re-rolls, for Jump Infantry and such:
2" : 100%
3" : 99%
4" : 96%
5" : 86%
6" : 72%
7" : 53%
8" : 35%
9" : 19%
10" : 9.0%
11" : 3.6%
12" : 0.92%

Better than a plain charge in open ground up until 6", then it crosses over and gets worse. 5" is still the longest truly reliable Charge here.

Fleet: Things start varying a bit more as people use different algorithms to decide what to re-roll when.
Tarrasq:
3 = reroll both 99.9%
4 = reroll both 99.3%
5 = reroll both 97.0%
6 = reroll both unless you get a four 92.9%
7 = reroll both unless you get a four or five 84.9%
8 = reroll both unless you get a four or better 71.0%
9 = reroll both unless you get a four or better 56.9%
10 = reroll both unless you get a four or better 39.8%
11 = reroll both unless you get a five or better 23.6%
12 = reroll both unless you get a six 9.3%

Maeloke on TTH used some approximations and came up with some slightly more conservative numbers, but still in the same ballpark:
2": 100%
3": 99.3%
4": 97.9%
5": 95.8%
6": 90.2%
7": 81.2%
8": 68.7%
9": 54.1%
10": 37.4%
11": 18.6%
12": 6.1%

Either way, Fleet takes you up to a pretty reliable 7" Charge.

Only Tarrasq rose to take on the Big Bad:
Fleet through Difficult Terrain:
2 = 100%
3 = 99.7%
4 = 98.2%
5 = 93.4%
6 = 77.6%
7 = 64.6%
8 = 49.7%
9 = 35.4%
10 = 20.7%
11 = 8.9%
12 = 2.6%

Very impressive numbers, really. Almost entirely better than a regular Charge across open ground. Not quite good enough for a reliable 6" Charge, but a rock solid 5" threat range.

Entirely separately, Purple Reign cranked a bunch of these numbers and made some Graphs and Charts that I found rather helpful getting it into my head:
- Basic Charges & Fleet
- More Fleet and Difficult Terrain Comparisons

Thanks to everyone who's pitched in on the discussion on 3++, Ordo Fanaticus, The Tyranid Hive, and The Imperial Guard Message Board. And sorry it took me so long to get it all collected together, I haven't been particularly with it the past few weeks.

[liquid405]

I started working on it, but it literally became a 4th dimensional problem. I dont think in 4d. Its a pain in the butt.

[sturm]

Nice work. Like I said to my local opponents, the average doesnt matter. It all comes down to that one roll. Just today, i failed a 5" charge because i rolled a 1 and a 2. The average tells i should be fine, but the roll says otherwise.

Side note: i sacrificed 3-4 gargoyles to the overwatch so my large brood of termagants could charge in right after. Gargoyles were wipped, and then termagants failed the charge. So much for he strategy.

[coredump]

The numbers I posted match Westriders, as does our take on the good/bad of the balance of long shots.

What we will be able to do, is take an occasional chance roll if somewhere safe. I move my raveners into a ruin, and there is a bad guy 10" away. What the heck, I will give it a shot.

OTOH, that 'good' is never going to balance out all the time we blow that 5" charge that leaves us in the open.


Oh, I keep thinking about trying to figure out the 'only reroll 1 die' numbers.... and it keeps seeming like a lot of work. It will have to wait until I am *really* trying to procasinate....

[WestRider]

Jul 8, 2012 4:53:30 GMT coredump said:

Oh, I keep thinking about trying to figure out the 'only reroll 1 die' numbers.... and it keeps seeming like a lot of work. It will have to wait until I am *really* trying to procasinate....

I see at least one way to do it, but it involves a lot of time and graph paper. Especially when combined with Difficult Terrain

I missed that you'd posted these already, too. Was it in the Rumour Thread? I didn't pay much attention to those.

[Jabberwocky]

What I think is useful is thinking not about single turn threat ranges but 2 turn threat ranges.

Since we can't assault from reserve, can't assault from 1st turn (in most cases with new deployments/infiltrate) and since our enemies often try to get away from us.

This is where the beast and fleet changes start to help. A reroll on your run the turn before not only closes the gap quicker but makes it safer to reach terrain. Same goes for 12" move rather than assault.

[N.I.B.]

The charge lenght through difficult terrain would be really interesting to see, since it's one of the major nerfs for Nids in 6th ed.

[WestRider]

Jul 8, 2012 6:19:51 GMT Jabberwocky said:

What I think is useful is thinking not about single turn threat ranges but 2 turn threat ranges.

Both are worth thinking about, but they're used at different points in your planning. Two-Turn Threat Ranges are what you want to be planning out in advance, but the pure Charge Range, with nothing else taken into account, is what you need to be looking at at the start of each Assault Phase, when trying to decide whether or not to risk Overwatch and such.

[liquid405]

Charge through terrain is not nearly as bad. It is a 3d problem, which is doable. Its just a matter of thinking of all of the possible charge distances, and realizing that the 3rd roll MUST be equal or greater than the highest roll needed of the two dice equivalent.

This means it needs to be broken down into all combinations, but again, not as abad as the fleet one.

[coredump]

Yeah, but what he wants is probability to Fleet through Diff terrain. :-)

[liquid405]

Jul 8, 2012 19:39:45 GMT coredump said:

Yeah, but what he wants is probability to Fleet through Diff terrain. :-)

Oh god, why?

I could do this, but it damn well better get pinned.

[Bot]

Ah... Thanks a lot WestRider.

I've been to lazy working this out in my head, so I'm glad someone else took the time to do it.

*Bookmarked*

[WestRider]

Yeah, that's kind of the holy grail here, since it's one of the most common situations for us. I'll probably get around to it eventually, but if someone knows some kind of tricks that can do it faster than Brute Force, or can get a Computer to do it, it would be much appreciated.

[liquid405]

Jul 9, 2012 1:25:33 GMT WestRider said:

or can get a Computer to do it, it would be much appreciated.

Good idea! I can write a c# program that can do just this. 50 million test runs enough?

[coredump]

Dude, I am not even sure I can think of where to start for this...

Of course, I am limited to Excel, and can't do any programming.