Author Topic: Charge Range Probabilities  (Read 10298 times)

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Offline WestRider

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Charge Range Probabilities
« on: July 07, 2012, 05:25:03 PM »
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.
« Last Edit: July 26, 2012, 12:34:45 AM by Kirby »
Anything taken to its logical extreme is depressing, if not carcinogenic.
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Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #1 on: July 08, 2012, 10:18:17 AM »
You just had to issue a math challenge...there goes my day...

FOR FLEET

Optimumly

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%
« Last Edit: July 21, 2012, 07:55:17 AM by Tarrasq »

Offline Chair126

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Re: Charge Range Probabilities
« Reply #2 on: July 09, 2012, 02:44:17 PM »
very helpful thx guys

now do it with terrain!

Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #3 on: July 10, 2012, 09:47:03 AM »
3d6 is a b****!  I won't be able to do that with my phone's calculator this time. Good thing I have the distribution written down somewhere (Thanks MSS!).  I should have that up by Wednesday night.

Offline WestRider

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Re: Charge Range Probabilities
« Reply #4 on: July 10, 2012, 02:17:48 PM »
Someone on another Forum got that one up, including Re-Rolls, and a couple of people are working on the Fleet tables. I'll copy them over and edit them in when I get a chance.

Hope this catches you in time!
Anything taken to its logical extreme is depressing, if not carcinogenic.
- Ursula K. LeGuin

Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #5 on: July 10, 2012, 07:35:28 PM »
I dont care about the answer so much as the puzzle, it's simply a way to kill an hour.  Plus I ALWAYS check someone elses math anyway.

For Charging Through Terrain:

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%

Seems like 4" is the longest reliable charge range through DT.

Still have to do fleet rerolls for DT.  Jump units if they use their jump packs to charge no longer suffer I 1 because of Dangerous terrain and arent affected by difficult terrain.  I dub 6th edition Jumphammer.

Also interesting, you take saves against dangerous terrain now.
« Last Edit: July 11, 2012, 01:39:24 PM by Tarrasq »

Offline Chair126

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Re: Charge Range Probabilities
« Reply #6 on: July 11, 2012, 03:00:07 PM »
man thats restrictive considering. similar to 5th but since shootin is still top doggie...


Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #7 on: July 11, 2012, 06:27:42 PM »
Charging through DT with fleet

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%

This assume you reroll the optimal number of dice after the original 3d6.

So basically fleet is better through terrain than normal infantry on open ground.

Offline Chair126

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Re: Charge Range Probabilities
« Reply #8 on: July 13, 2012, 11:12:27 PM »
does this make shrike super awesome?

Offline WestRider

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Re: Charge Range Probabilities
« Reply #9 on: July 14, 2012, 06:14:04 AM »
does this make shrike super awesome?

Yes. Fleet is great, and Fleet Jump Infantry are totally badass. 12" in the Movement Phase, plus Fleet re-rolls on the Charge, makes for one of the longest Assault Threat Ranges in the Game. It's also amazing for Assault Terminators, giving them a pretty reliable 20" threat radius from a Land Raider.
Anything taken to its logical extreme is depressing, if not carcinogenic.
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Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #10 on: July 14, 2012, 07:26:04 AM »
Beasts are the best charging unit in the game 12" move anxd fleet charge and they ignore difficult terrain.

Jump infantry if they move 12" are slowed by terrain on the charge.  Also if you disembark from a vehicle you can only move to within 6" of the acces point in the movement phase. So assuming you roll a twelve you've only got 17.99999".

Offline WestRider

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Re: Charge Range Probabilities
« Reply #11 on: July 14, 2012, 09:26:41 AM »
- That's why I said "one of" the longest threat ranges. ;)

In some circumstances (Impassable Terrain/Bubble Wrap in the way, basically), Fleet Jump Infantry can do better than Beasts, even tho their raw numbers aren't as good.

- But you can Move the Vehicle 6", then Disembark 6", then get a pretty reliable 7-8" Charge. 19-20" from the closest starting point on the Land Raider. If you're measuring it as an area on the Table, add an extra inch or two to account for the size of the Land Raider.
Anything taken to its logical extreme is depressing, if not carcinogenic.
- Ursula K. LeGuin

Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #12 on: July 14, 2012, 01:27:06 PM »
Gotcha 8)

Offline Kirby

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Re: Charge Range Probabilities
« Reply #13 on: July 15, 2012, 01:20:35 PM »
Beasts/Cavalry are interesting.

Before, you had a 19" charge in the open. 100% of the time. But if you didn't get to charge your opponent, you only moved 7" 100%. 24" charges happened 1/6 of the time.

Now, even with Fleet, 24" charges are far less likely (1/18 I think?) and even with Fleet, rolling a 7" fails 15% of the time (this nets you 19", the bare minimum you had before). But! you have the consistent 12" move every turn which can make up for the poor Fleet rolls you had previously.

Fleet is without the doubt, the best skill a combat unit can have because it gives you some reliability but in terms of consistenty and getting longer charge lengths, they've been knocked back by about an inch on average I think.
- Kirby.

Offline WestRider

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Re: Charge Range Probabilities
« Reply #14 on: July 15, 2012, 02:31:42 PM »
Fleet is awesome, my Game this afternoon showed that without a doubt. Being able to keep the 5 and re-roll a 1 on a 7" Charge totally saved my Hormies. Got me a successful Charge with a Warp Speed-ed Tärvigon, too.

AP and I poked at the numbers for Raveners a bit in the version of this Thread over on Ordo, and they've got an extra d6" on their two-Turn Threat Radius, but lose about an inch of reliable one-Turn Threat Radius. Probably a worthwhile trade-off, but it's still going to hurt the first time I fail a Charge against something that started the Turn 16" away.
Anything taken to its logical extreme is depressing, if not carcinogenic.
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Offline Kirby

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Re: Charge Range Probabilities
« Reply #15 on: July 15, 2012, 02:33:53 PM »
Sounds about right.

WestRider - can you summarise all the charge range probabilities in the first post? Might sticky this.
- Kirby.

Offline WestRider

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Re: Charge Range Probabilities
« Reply #16 on: July 15, 2012, 02:51:38 PM »
I've been planning on doing that, and adding in some numbers people have run for me on other sites (I spammed this post across 4 Forums), but haven't gotten around to it yet.

Unless work really kicks my ass tomorrow, I should be able to get it all consolidated tomorrow evening.
Anything taken to its logical extreme is depressing, if not carcinogenic.
- Ursula K. LeGuin

Offline Tarrasq

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Re: Charge Range Probabilities
« Reply #17 on: July 21, 2012, 08:08:43 AM »
With fleet the 24" charge range probability is closer to 1/10.7.

1/18 would be normal rerolls.
« Last Edit: July 21, 2012, 09:14:43 AM by Tarrasq »

Offline Kirby

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Re: Charge Range Probabilities
« Reply #18 on: July 23, 2012, 02:29:32 PM »
Fair enough. Still about double what it used to be.
- Kirby.

Offline Kirby

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Re: Charge Range Probabilities
« Reply #19 on: July 25, 2012, 05:57:53 PM »
*waits for everything to be summarised in first post*

DOn't make me do it myself West :P.
- Kirby.