Tuesday, 16 February 2016

"Never Tell Me The Odds" - X-Wing Dice for Beginners

Back in my first blog about X-Wing I launched right into sharing a bunch of things that I'd learned about how ships maneuvered and some common tips and tricks that I thought were worth knowing.  X-Wing is a game of two halves, though, and what happens in the Combat Phase is just as important as what happens in the Planning & Activation Phases, so this time around I want to look at the dice of X-Wing, and some of the wonderful maths that spins off it.


Now, if you're a serious maths-head then the internet is full of great places where people have already crunched a lot of the X-Wing numbers.  I'm going to try and boil some of that hardcore number crunching into something more digestible for those who aren't in the mind to drill everything to three decimal places.

That said, if you ARE the type of person who wants to know the maths properly then for some extra-curricular reading you can check out some of these place:

Mathwing (an opus of X-Wing Math)



And also: right before I sat down to write this blog there was another great dice-related blog at Not Such A Bad Pilot that I recommend reading as we cover a lot of the same ground.




The Basics

Ok, so now that the egg-heads are gone we can really get into it... and I'm going to start right at the start because I think a fair number of X-Wing players have probably never even picked up the dice they're rolling to see what's on the eight sides.


Hands up if you though the dice were going to be balanced - that the same number of hits on the red dice as there are evades on the green dice?  A few of you, I bet.  Yeah, initially I would have assumed the same as well, but in fact the game is weighted towards ships being able to deal damage (and it's a good job, or you'd be playing forever with pristine untouched ships!).

When you roll a red dice you've got a 50% chance of rolling a hit/critical, rising to 75% chance if you have a Focus token to spend.

When you roll a green dice you've only got a 38% chance of rolling a Evade, rising to 63% if you have a Focus token to spend

So in the scenario where you've got 1 red dice against 1 green dice, and no Focus tokens, 50% of the time you're going to roll a hit, and then 62% of the time they're going to roll something other than an Evade.  Combine those two facts and you've got a 31% chance of dealing damage.

50% x 62% = 31%

If you add Focus tokens into the mix then it gets slightly harder to hit the target, as the hits out number the evades by only 6 to 5, instead of 4 to 3.

75% x 38% =28%

Those numbers aren't hugely different, though, so it's easier to just remember ~30% chance of a hit with/without a Focus.  The trouble is... how often do you ever roll just one red dice? (HWK-290 owners, you have my sympathy)


1 plus 1 does not equal 2

So if you're normally dealing 0.31 damage with 1 red dice vs 1 green dice, then that doubles when you roll 2 red dice vs 2 green dice, right?  So now you're dealing an average of 0.62 damage with each shot, right?

Wrong.

What we also need to take into account is that we've been looking at the 50%/75% of times when you rolled a Hit, because if you got a Blank on your red dice then we don't care what the defender would get with his dice.  In reality you DO care when you start rolling multiple dice, though, because the defender might have rolled an Evade against your Blank red dice and can use that Evade against your other red dice that you've rolled at the same time.

In fact the average damage you deal with with 2 red vs 2 green dice isn't 0.62 (assuming nobody has a Focus), it's only 0.51.

I could go on with umpteen examples of dice vs dice, but it's just easier to show you the tables.



Right, before you go crossed-eyed trying to work that out in every possible scenario let me cut that right down to the chase for you and tell you what it really means.

You need to be rolling more dice than your opponent.

Period.  Full stop.  Drop the mic.  We're done.  

If you want an "X-Wing Dice Strategy 101" boiled down to three words then those three words would be "Roll", "more" and "dice", used exclusively in that order.


Overload Dice

When you roll a red dice against a green dice you've got about a 25% chance of dealing damage  The exact % depends on how many red dice are being thrown against how many green dice and whether you're focussed etc, but it stays in that ballpark.  When you roll an extra red dice that isn't opposed by a green dice (what I call 'Overload Dice') then your odds of dealing damage with that dice improve HUGELY - to 40% without a Focus token to burn, and 60% with a Focus.


That's the benefit of the Overload Dice - a huge jump in your chance of actually dealing a damage, from 25% with an opposed dice to 60% with that Overload dice!  And in fact if you roll a second or third Overload Dice then the odds on those dice get even better (as there's less chance that your opponent rolled enough 'spare' Evades to cancel out yet more red dice).

You may think that going from 2 red dice to 3 red at Range 1 is a 50% increase in your damage output (rolling 3 dice is 50% more then 2 red dice), but if the target has two agility then you're adding an 'Overload' Dice and it's more like a 100%+ increase in damage!

Oh, and finally, a quick word about what Focus is doing in those tables.  The difference between neither player having a Focus and both players having one is that Focus accentuates the advantage for the player with the most dice.  This makes sense - Focus affects all the dice you roll so the more dice you roll the more chance you have for Focus to lend you an edge.



Implications of Overload Dice


NOTE: When originally published this section of the blog contained material errors.  I've rewritten this section to provide a more accurate view.

We can step away from theory for a moment and talk about some real ways that this drive for 'Overload Dice' will impact how people fly their ships to create a positive mismatch and, more importantly, how they build their squads.

Let's think of a Rebel player who is trying to decide how to round out his squad.  With his last 24 points he could bring in either two basic Z-95 Headhunters or he could play a single T-70 X-Wing instead, and the deciding factor is which ship will do the most damage?.

The most obvious way to look at this is that the two Z-95 Headhunters bring a combined four red dice to the table, while the X-Wing only has three red dice, so if you take the two TIE Fighters you get to deal more damage.

Except that's not necessarily true, and in fact in many scenarios the single X-Wing is more dangerous, even though fewer red dice are rolled.  

Why?

When you roll your red dice twice, you're also allowing your opponent to roll his green dice twice!

It's really obviou when somebody explains it to you, but a lot of people don't think that far ahead and just assume "4 dice is better than 3 dice".

What you get is a more nuanced picture where you need to consider what you're likely to fly against.  When your opponent doesn't have many green dice to roll in his defense then the Z-95 Headhunters pay off in more damage output, but when you're up against ships with high Agility, or with Evade actions, then the two red dice of the Z-95s are going to really struggle to 'punch through' without any chance of getting an Overload dice.


I can actually get very topical here, because in the last week FFG have spoiled the upcoming Jumpmaster-5000 ship with the option of spending a whopping 12 (twelve!) points on a Title called Punishing One (the ship belonging to the bounty hunter, Dengar) that adds an extra dice to all your Primary Weapon attacks.  This title pushes the Jumpmaster from 2 red dice to 3 dice - adding exactly that critical 'Overload Dice'.  

So is that 12 points well-spent?  Well the simple answer is 'almost certainly, yes'.  And in fact because it's 12 points exactly it makes it very easy to see this because it's basically exactly the example I just showed above with the two Z-95s vs the X-Wing.  How much better is it to spend that second 12 points on turning a Z-95 Headhunter's 2 red dice into an X-Wing's 3 red dice, rather than as a second Z-95?  Well, up to 15% better against high Agility ships.

So does that mean 12 points is the fair cost of an extra red dice?

Well, that depends.  If the 12 points were going onto a HWK-290 to give it a second red dice then the answer would be "hell, no", as that second red dice is unlikely to be an Overload - trying to turn the HWK-290 into a damage dealing machine is throwing good money after bad.  If the 12 points were going onto a TIE Phantom to give it a base of 5 red dice then I'd tear your arms off to fit that for just 12 points, because it would almost always be an Overload and add almost a full point of damage every single time I fired.  Get into Range 1 with that theoretical overcharged TIE Phantom and you'd be one-shotting Soontir Fel with ease, Evade token or not!

Away from the specific example of the Punishing One, the huge importance of having an extra red dice explains why so many more people are willing to pay 7 points for a Heavy Laser Cannon that cannot shoot at Range 1 than they are to pay less for a Mangler Cannon that fires at any range and is more likely to deal a Critical damage.  That 4th red dice of the Heavy Laser Cannon is often going to be the extra dice that gets around a TIE Fighter's three green dice and pushes through the damage, which is well worth paying a little extra for.  

It also makes you re-evaluate pilots like Miranda Doni, who can add an extra red dice at the expense of a shield, or the Scum Y-Wing ace Kavil.  Adding a red dice is phenomenally important for the amount of damage you deal out - it's not just "+50% damage" to go from two red dice to three, it's often "+100% or more".




TL,DR

"Roll more dice."

Hell, I'll go even better, because this pretty much exactly sums up the Z-95 Headhunters vs X-Wing Interceptor question...

"Roll More Dice > Roll Dice More"

Yeah, there you go.  I should stick that on a T-Shirt, I'd make millions.


Hopefully this has given you some simple things to take away and think about, without working your noggin too hard!  

I'm going to be following up with a second part where I look at how a basic bit of X-Wing maths can really help you make the right decisions, both in building squads and in making actions and flying your ships.

6 comments:

  1. This isn't anywhere close to accurate. Look at your math wing chart. expected damage 3 reds vs 3 greens is correct at 0.67 (which you gracefully round up to 0.7 to help your point).

    But 2 attacks from 2 reds vs 3 greens is the expected damage of 2 reds vs 3 greens (0.35) TIMES TWO ATTACKS.

    Two ties out dps an interceptor as well as having double the hull.

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    1. 2 v 3 = 0.35 TIMES TWO ATTACKS isn't how it works.

      2 v 3 (x2) = 4 v 6 = 0.48
      If your attacking twice, you defender is defending twice, and thus increases his chances to defend.

      That is why "3 v 3 = 0.67" from the interceptor is better

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    2. lets step through it real slow. lets pretend its different turns instead of the same turn with two different ships.

      The first turn you have an expected damage of 0.35. next turn, regardless of whether you shot before, or hit before, or anything... you have another shot.... that has an expected damage of 0.35. the first 0.35 + the 2nd 0.35 equals.... 0.7


      It's most definitely not 4v6 as if you score 3 evades on the first strike they don't carry over to the 2nd strike. you have to treat it as two separate

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    3. It looks to me as if, in the "Implications of Overload Dice" section, the author is assuming the attacker and defender have focus for every attack.

      Delete
  2. This comment has been removed by the author.

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  3. Can you explain this a little more: "When you roll a red dice against a green dice you've got about a 25% chance of dealing damage."

    ReplyDelete