Tag Archives: reroll

16 December 2012

Terrain Wreck

By WarHamSandwich

So I left you last week with a cliffhanger, namely how much does terrain impact your odds of reaching assault?  More specifically:

Is Barra the Berzerker better off charging guardsmen in the open 8” away, or going for a squad in terrain 6” away? What about with rerolls, or with Fleet?

When terrain comes into play, the assault range mechanic gets a little more complicated.  Instead of a straight 2d6 roll, it becomes 3d6 drop the highest.  To show the difference this makes, here’s a straight up comparison:

OpenVsTerrain

So the red line shows the probability of achieving an assault distance in the open, and the green shows the same for terrain.  Unsurprisingly, terrain always makes it harder to reach your opponent, but what’s more important is by how much.  I’ve highlighted two points here as they give us the answer to part of the question I posed.  At 8” the berserker has a 42% chance of reaching the guardsmen in the open, but at 6” he has a 48% chance of reaching the guard in terrain.  The guardsmen in terrain are the right choice of target.

But what about rerolls for the Icon of Wrath?  How does Fleet affect it?

AssaultAll

The chart may seem daunting at first, but hopefully a quick bit of explanation will make it more accessible.  The three red lines are the odds of assaulting a certain distance in the open with no reroll, with a reroll, and with Fleet.  The three green lines are the same but for assaults through terrain.  To address our specific question about 8” in the open vs 6” in cover I’ve again added the relevant dots with percentages.  These clearly show that in a ‘like for like’ comparison (i.e. with a reroll, with fleet) it’s always better to assault 6” in terrain than 8” in the open.  So to answer the original question, Barra the Berzerker should go for the guardsmen in cover in all of our scenarios.

That said, I didn’t build the chart just for this one scenario, you can use it to compare all kinds of situations – and can draw some interesting insights from examining it.

For example, comparing the darkest red line with the darkest green line, we can see that a unit with Fleet charging through terrain has equal or better odds of making assault than a normal unit charging the same distance in the open.

Similarly, checking out the mid-tone green line versus the dark red shows us that when assaulting though terrain units that can reroll charge distance (not Fleet) are also better than normal units charging in the open but only for distances up to 6”.  After this point we see a crossover in the lines and a normal charging in the open is better from 7” onward.

Even simply taking a look at the normal line, vs the reroll line, vs the Fleet line can really highlight how big a difference these abilities can make.

I do have to apply the caveat that my analysis assumes that the player using Fleet always makes the optimal choice for which dice to reroll.  But you’ll have to wait for those rules until next week…

1 Comment   |  tags: , , , , | posted in Probability

12 December 2012

A Pinch of Assault

By WarHamSandwich

Assault ranges were one of the biggest changes in the move to 6th edition.  In total opposition to 5th ed, we gained the right to premeasure the charge range, but lost the ability to know exactly how far we could charge.  I’m sure Heisenberg would be proud… So here’s a question for you:

Barra the Berzerker Champion is leading his unit to collect more skulls for the brass throne of mighty Khorne.  8” to his left in open terrain is a squad guardsmen, 6” to his right is another guard squad in cover – which is he more likely to reach?  If he had a banner of wrath how would that affect his chances, and what if it had been a unit of Possessed rather than of Berzerkers?

For most units in 6th ed, the charge range is determined by the sum of 2d6, or if in terrain, 3d6 dropping the highest.  The mechanics get more complicated as some units can get a reroll, and others can reroll specific dice (i.e. Fleet).  As most of you know, 7 is the average result on 2d6, but this can lead to the unfortunate assumption that you should expect at least a 7.  I’m sure as more people get some games in and launch assaults in 6th, they realise that this is not the case…

Let’s look at the no terrain mechanic first.  I’ve charted the odds of making the charge for a straight 2d6, 2d6 with a reroll, and Fleet (i.e. reroll either or both dice). AssaultOddsOpen

Unsurprisingly, having a reroll improves your chances, and being able to pick and choose which die to reroll increases your odds even further.  That assumes you know when is the best time to reroll just one dice (i.e. my results assume you make the optimal choice in all instances).

We can see from the chart that at 8″ our Berzerker friend has only a 42% chance of reaching the guardsmen in open terrain.  If his squad has the Icon of Wrath, then he can reroll charge distances, which would bump his odds of reaching them to 66%.  A Possessed Chaos Marine has Fleet, which enables him to pick and choose which dice to reroll – raising the odds of reaching those guardsmen to 72%.

To make life easier for you dear reader, for units with fleet, I’ve got some rules to make sure you make the best reroll you can:

Range: 3” or 4” reroll both

Range: 5” reroll anything ❤

Range: 6” to 10” reroll anything <4

Range: 11” reroll anything <5

Range: 12” reroll anything <6

Note1: when I say reroll anything <x I mean if both dice are <x reroll both, and if one die is <x reroll just that one.

Note2: If the above rules don’t work for a specific result then reroll the lowest die only e.g. range 10” and you roll a 4 and a 5 (say), just reroll the 4.  In the case of doubles, just arbitrarily pick one for the reroll and keep the other.

So what about the terrain?  In the question above the Guardsmen in terrain are closer, but does the terrain make it less likely to reach?  You’ll have to tune in next week for that one my friends!

3 Comments   |  tags: , , , | posted in Probability

12 August 2011

Stacking the Odds Part II

By WarHamSandwich

The previous post on the probabilities for making lots of saves generated a bit of interest, and (as usual) some clever readers pointed out scenarios that should bear further analysis.  Altmann from the Penny Arcade forums asked:

“Can you work in the probability of making 4+ feel no pains as well? I know we’re getting into NASA shit but I’m curious”

Followed by Joe “Maynard” Cullen (of WarHeads fame) who pointed out that some wargear items also add complexities:

“The Wolf Tail Talisman gives a 5+ invulnerable save that happens before the armour save”

So in a similar fashion to my ultimate Ballistic Skill chart, I took it upon myself to rank the performance of a variety of armour types with rerolls, with Feel No Pain (FNP), and just plain regular saves.  This will give some insight into the relative merit of the saving throws we normally encounter in 40k.

As with Stacking the Odds Part I, the chart shows how likely each type of save is to take no casualties from an increasing number of saves.

So chart number one:

This charts the various types of save (and combinations) showing the odds of taking no casualties for up to 6 saves (I cut it off at 6 as about half of them approach zero at this point).  The legend on the right shows the ranking from best to worst with a 2+ rerollable save being the best, and a regular 6+ save being the worst.  The sharper eyed in the audience may notice that some of the save types listed in the legend don’t show up in the graph – namely “5+ FNP” and “3+ FNP”.  Rest assured this isn’t an error, it is simply that they are coincidentally covered by other save types that perform identically.  So a 5+ with Feel No Pain save works out the same as a regular 3+ save, and a 3+ with Feel No Pain save works out the same as a regular 2+ save.

Or do they?

The calculations are correct, but you need to interpret the data in the context if the game itself.  So saving on a 5+ followed by a 4+ for FNP is statistically the same as a 3+, until you get hit by an AP5 or AP4 weapon, at which point all you get is the FNP, which is just a 4+ save (as you can see from the chart is a lot worse than a 3+).  The FNP could also be blocked by a high strength AP- weapon, leaving you with just a 5+.

In a similar vein, the 3+ with FNP is the same as a 2+, but what if they got hit by a battle cannon? the 3+ is negated by AP3, and (assuming we’re talking about T4 units) the FNP is negated by the instant death rule.  So no saves of any kind!  But a squad of terminators would still get their 2+ and (assuming that 5 are wounded by the blast) they have a 40% chance of taking no casualties at all!

So what about those opening questions?  Well Altmann was interested in the effect of FNP on terminators, and to show the difference I’ve scaled the number of saves taken up to 30, and dropped the weaker save types.

The effect is actually pretty strong, if we take say 20 saves, a regular terminator squad has only a 3% chance of being unharmed while the FNP terminators have an 18% chance (again assuming that they aren’t hit by something that negates FNP!)

Joe’s suggestion of the Wolf Tail Talisman (WTT) is charted below. Assuming the squad has power armour, then it works out quite close to (but slightly better than) a 4+ reroll, and worse than a 2+ save.

This should let you compare the various save types available to you, but don’t forget the context of how saves and FNP get negated! If there are any other save types you want to see included, then please do leave a comment.

2 Comments   |  tags: , , , , , , , , , , , , , , , , | posted in Probability

30 March 2011

Undo! Undo!

By WarHamSandwich

Sometimes things just don’t go your way.  We’ve all had that situation where you really wish you could do that roll again.  Thanks to wonders such as twin-linking, or lightning claws, sometimes we can.  Today we are talking about re-rolls, and (as is my habit) here’s a question:

A bolter shot hits and wounds a Warlock on a Jetbike, he needs to make a 3+ armour save to survive.  If the farseer had cast Fortune to give him a reroll on that save, how much more likely would he be to survive? and would he have been better off in Terminator armour instead?

Rerolls don’t change the range of possible results (i.e. 1-6) but they do change odds of a particular result.  I’m following the usual format for the percentage odds here so I won’t labour the discussion with what each row means.

1 2 3 4 5 6
= 2.78% 8.33% 13.89% 19.44% 25.00% 30.56%
< 0.00% 2.78% 11.11% 25.00% 44.44% 69.44%
> 97.22% 88.89% 75.00% 55.56% 30.56% 0.00%
<= 2.78% 11.11% 25.00% 44.44% 69.44% 100.00%
>= 100.00% 97.22% 88.89% 75.00% 55.56% 30.56%

Well actually … it is a little different this time so perhaps I should give some explanation to the more interesting bits.

  • The ‘equals’ row gives the odds of a particular result if you were to roll two dice and pick the highest.
  • The ‘less than’ row shows the odds of failing a particular result, e.g. theres a 25% probability of failing a 4+ (rerollable).
  • The ‘greater than or equal to’ row shows the odds of succeeding on a particular result, e.g. the odds of succeeding in a 5+ (rerollable) is 55.56%

“So what?” says you.  In isolation it’s not that insightful, but if we compare it to the odds of a ‘normal’ (i.e. not re-rollable) outcome it gets very interesting.  The odds for a normal roll are covered here, but I’ve graphed the odds of success for normal vs rerollable to really show the difference.

Ok so the odds of getting a 1 or better is 100% in both cases … duh.  But what about that Warlock from the beginning?

The jetbike Warlock has a 33.33% chance of failing that save (with no reroll).  If the Farseer has done his job and put Fortune on that Warlock, then the reroll brings the probability of failure down to 11.11%.  The reroll makes him three times less likely to fail! and what about that terminator armour? it has a 16.67% chance of failing that save – that’s twice as good as the basic Warlock, but one and a half times worse than the Fortuned Warlock!

A fortuned jetbike Warlock has significantly better saving throws than a Terminator with a Stormshield – think about that before you try gunning down a Seer Council.

Take a moment to really look at the chart.  The rerollable 6+ is almost as good as a basic 5+, and is about twice as likely as a normal 6+.  The 5+ reroll is better than a basic 4+, and so on until they converge at 1.  Also notice those trendlines I’ve added, the basic rolls get linearly less likely, but the rerolls stay high and then gradually fall off as you hit 6.

Of course, not all re-rolls are there to mitigate failure – sometimes you can be forced to reroll a success, but that analysis will have to wait for next time…

6 Comments   |  tags: , , , , , , , , | posted in Probability

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