Thursday, 17 March 2016

"In my experience there's no such thing as luck" - Variance, TIE Interceptors & Novak Djokovic

While X-Wing is definitely my current obsession t'was not always so, and in the past I've blogged and written about several other games, most notably Magic: The Gathering and Android: Netrunner.  Perhaps one of my very best blogs combined those two games to look at how Variance could be understood and tamed in card games, where 'luck of the draw' is a very real random factor.

Miniatures games like X-Wing have their own random factor in the form of dice and so today I want to look at how variance affects X-Wing, what you can do about it, and when you should be trying to add or remove luck from the game.

My revisiting the theme of variance, now with a dicey spin, was inspired by reading a recent frustrated post on Reddit from a player who had reached their wits end with the green dice...

Reddit user rubsnick rolled a bunch of green dice but got no Evades and lost the game.  Understandably frustrating but also, as I'm going to try and show, frustratingly understandable.

Variance 101

First off, I'm going to spend very very little time talking about 'luck' because we're better than that.  I don't turn up to my X-Wing tournament trailing a rabbit's foot and four-leafed clover after walking a half block around any black cats I see.  Hopefully you don't either, because we're all adults and we understand that luck is out of our control.

I'm not going to talk about luck at all, instead I'm going to talk about variance because to a certain degree variance is within our control.  Even though variance in X-Wing is almost always in the form of raw dice roll we have a say in how much variance we invite into our games, when we invite it and how we prepare for the positive/negative outcomes of that variance.

Let's start with a really simple example (that, handily, rlates to rubsnick's case): the survivability of a Tie Interceptor vs a B-Wing

If you shoot at a focused B-Wing with 3 red focused dice, with their 1 Agility but 8 Hull/Shields then you're going to destroy them in 4.9 shots.  If you shoot at a focused TIE Interceptor with the same 3 red dice, with their 3 Agility but only 3 Hull then you're going to destroy them in 4.7 shots.  Although the two ships you're shooting at are VERY different in terms of how they defend themselves they're actually very similar overall in how long it will take you to kill them.  On average.

They key there is the 'on average' part.  What's actually happening is that Variance plays a large part in how that 'average' of 4.7/4.9 turns actually works out in reality.

A TIE Interceptor's defense is based heavily on its ability to roll Evades with the 3 green dice it has at its disposal, because in a worst case scenario the measly 3 Hull it has can be wiped out in a single shot!  Fortunately the green dice mean that on any single shot the TIE Interceptor is actually odds-on to avoid taking any damage at all, with a 54% chance to dodge all incoming hits!

The B-Wing rolls fewer green dice in its defense and so much less Variance is introduced into the equation of how long the B-Wing is going to stay on the table.  Unable to throw many Evades in its defense the damage piles up at a very steady 1 to 2 per shot until the B-Wing is finally put out of its misery.

If you look at the shot-by-shot survivability of the two ships then the impact of variance is made very clear.  Right from the very first round of shooting there's a chance that the flimsy TIE Interceptor could roll a bunch of blank green dice against a bunch of hits and explode immediately.  Yes, it's only a 2% chance but it's a chance that the B-Wing isn't taking.  With 8 Hull/Shields and only 3 red dice against it then the B-Wing knows with utter certainty that it can ride out at least two shots with 0% chance of exploding.

If that sounds bad for the TIE Interceptor then it gets worse, because by the third shot there's a whopping 32% chance that the Interceptor will be toast, while the B-Wing is still rumbling along with only a 4% chance that it's taken 8 damage from the 9 red dice thrown its way.

4% vs 32%  

It's a huge difference in the performance of these two ships who are, on the face of it, taking the same number of shots 'on average'!

So far the increased Variance of the TIE Interceptor's defences have been working against it but over the next three turns the situation flips on its head.  The steady rate of damage that's accumulated by the low Agility ship starts to catch up to the B-Wing, and in fact 83% of all B-Wings will be destroyed in 4 to 6 shots!  Meanwhile any TIE Interceptors still standing after the first few turns still have a 54% chance of dodging all damage from incoming shots.

After 6 rounds of shooting only 13% of B-Wings are left on the table, while you've a 26% chance that your TIE Interceptor is still flying.  Virtually no B-Wing will survive 8 shots, while even out at 10,11,12 shots there are TIE Interceptors that are still refusing to die and rolling multiple Evades every turn.

And that, in a nutshell, is how variance affects X-Wing.  'Slow & steady' won't necessarily win the race, but it at least guarantees that you're in the race for a decent amount of time.  u/rubsnick, however, was running TIE Interceptors whose performance, as we've seen, is less reliable - they can be superstar dodgers one game and little more than shiny pinatas in the next.  He'd built his squad to try and minimise this risk by playing Stealth Device to add an extra defense, and by stacking Evade tokens whenever possible, but underlying all that was a dependence on the green dice to keep his ship on the board.

Embracing Variance

The root of rubsnick frustration isn't just that the TIE Interceptors were bringing variance into his games, it appears.  Rather it seems like it was bringing variance that he wasn't really psychologically prepared for, and when it went against him he felt betrayed by his dice and the game.

Firstly, this isn't a particular failing of his because it's human nature that we will often ignore the moments where luck went our way but we'll remember the times when it went against us.  This is how memories are formed, ultimately: bad memories stick better than good memories (it's known as Negativity Bias, and its a pretty well-researched psychological effect).  

When rubsnick rolled his blank green dice he suffered a very strong negative emotional response to watching Soontir Fel explode, but if you asked him I doubt he could clearly recall any detailed incidences where the opposite had happened and he had rolled nothing but Evades against several incoming shots.  Statistically speaking it must have happened at some point, but it won't have stuck in rubsnick's memory in the same way.  

This is entirely human.  We tend to class the moments of good variance as 'business as usual' or attribute the success to our own good judgement - "of course I rolled 4 Evades, I picked a ship with high Agility and used a Focus token".  But when that same variance that we invited into the game goes against us we will usually externalise the blame so that it's not our fault "the dice were terrible for me today, I'm so unlucky".  

When we win it's because we were good, when we lose it's because we were unlucky... if we're honest with ourselves then we've probably all been there and thought that way.  It's just our ego playing tricks on us, though, and when you go with a high variance strategy you need to be more phlegmatic and adopt a win some/lose some attitude.

You need this attitude because playing a high variance strategy, when you're not ready for the consequences of that, is only going to piss you off.  This is what happened to rubsnick.

A Magical Anecdote

In my past life as a Coverage writer for Magic: The Gathering I was privileged to get to know many of the best Magic players to have ever played the game, and one of the first things that struck me was how well they handled defeat.  The best players trusted their ability and understood that in the long run they'd still come out ahead, so on the days when variance had gone against them and they'd gone 0-3 and dropped out of the tournament they would just shrug their shoulders and get ready for the next one.  Eventual success was almost guaranteed, they just couldn't predict when that success would come because variance would always play a part.

This attitude came in sharp contrast to the attitude that I'd seen in players a level or two below the best players, and in sharp contrast to my own attitude when I was playing.  For many players like that the desire to prove that you are good enough to win something can remove that healthy perspective on the impact of variance.  When a day lost to variance that should be "oh well, maybe next time" becomes "it should have been last time" then you are on the path to the dark side.

At the same Grand Prix that Raphael Levy (one of the all-time Magic greats) had done terribly but dropped out with a smile on his face I interviewed a Belgian player called Geoffrey Siron.  He looked me right in the eye and said that his recent Pro Tour win had vindicated him, and now that he knew he was good enough he entered every tournament expecting to win it.  There was no room for variance in Geoffrey's worldview - he took victory personally, and he took defeat personally too.  Geoffrey Siron was finished with the game a year later, chewed up by not being able to replicate his success, while a decade later Raphael Levy is still losing in major tournaments... and winning in others.

Why Variance Can Be Your Friend

So if playing a high variance strategy is frequently a one-way ticket to bitterness and bad times then why would you ever do it?

The answer is because high variance strategies, when the variance goes your way, will enable you to overperform the low variance strategies who are sticking closer to the average outcomes.  Yes, there will be a bunch of times when variance is either against you or roughly evens out to neither good or bad, but sometimes it's going to be overwhelmingly in your favour.  It's those overperforming occasions that you're really in the high variance pool for, and that you would choose to play this way then comes down to a meta decision with a number of other factors:

What does success look like to you?
What is the prize structure (if any)?
How good are you?
How many chances do you have?

I've put these questions in roughly the order that I think you would approach them, so let's go through one by one.

1) What does success look like to you?

This one is multifaceted and is really asking what you want to get out of playing X-Wing at this particular time.  If you're playing casually and just want to have a good entertaining game where the best pilot wins then variance is not your friend because both extremes of variance will destroy this casual gaming experience.  The game where your opponent flies very well but simply can't beat your dice rolling is not an enjoyable game for him, and neither is the game where your ships explode at the first touch.  Sure, a lot of the time variance won't be working to those extremes, but some of the time it will and those games will suck.

To my mind the high variance strategies are often about embracing a very cold-blooded mindset that you really care most about winning, and not just winning more than they lose but winning EVERYTHING.  It works best for players who understand that they've taken a gamble of poor performance in a trade-off to try and achieve a strong performance, either that or you're so casual in your approach that you're happy to play X-Wing even if your ships die right away!

2) What is the prize structure (if any)?

Pursuing a high variance strategy is usually about attempting to maximise your chances of being 'lucky' because the rewards are distributed most heavily towards the top few (or top one!) positions.  

If you're in a 10-man tournament with some cool token prizes for the Top 8 and nothing else then there's virtually zero incentive to play high variance - all you're doing is increasing your chances of bad variance making you one of the two people who miss out on the Top 8 prize!  If, however, you're in a Nationals tournament with 200 players and the winner gets a flight to the World Championships while second place gets little more than a hearty handshake... then variance starts to look a lot more attractive.  

If you're really committed to winning, and winning means finishing 1st out of 200 people then an attitude of "if you ain't first, you're last" makes it sound like time to line that variance up and go for broke. 

3) How good are you?

This may require some real soul-searching but it's an important factor.  Choosing high variance is about trying to OVERperform for your skill level.  If you're already one of the best players in the room then you may not need to overperform, you just need to avoid UNDERperforming.  At that point the addition of variance is indesirable.

When I try and explain variance to non-gamers I often use a Tennis example.  It's great at illustrating how the difference skill between you and your opponent will change your decision so I'm going to wheel it out again...

You're a pretty good tennis player.  You're a member of a club and you've played in a few local competitions.  You're never going to turn pro, but you know your way around the court.  Although you're pretty average overall you've got one great weapon up your sleeve - god damn, but you've one hell of a serve! 

You smash that thing down the court so fast that the other guy has almost no chance of even getting a racquet on it!  The only trouble is that your big serve is also pretty wild, and like half the time you're double-faulting like crazy, then other matches you're lasering it down the line like an unbeatable end of level boss.  The rest of your tennis game is actually pretty average, but that big serve has dragged you through some games you know you should have lost.

There's a tennis competition in town, and it's big money.  You play just one point against your opponent and if you win the point then you get $10,000!  For just one point!  That's crazy.  So you go along and, lucky you, you're get picked to go up and play and take your shot at that $10,000.  

Now you're on the baseline and about to serve.  Win this one point and it's $10,000 in the bank, lose and you get nothing.  

So... do you serve big, or you do you play it safe?

The correct answer is that I've not given you all the information that you need to decide, because I've not told you who you have to score a point against for the $10,000.  And who that is will decide what you do.

Scenario A: it's a big Nike endorsement event and they've got Novak Djokovic on court.  You need to score a point against the best player in the world.

Scenario B: it's a TV show where they're trying to give money away for publicity, and all you have to do is score a point against sometime comic Jack Black.

So let's try it again... do you serve big, or do you play it safe?

Well by now it's hopefully obvious that your big serve is a high variance option - when you slam that ball you've no idea if it's going to be in or out, but you know they can't return it so skill is almost entirely removed from the equation.  

The answer is that in Scenario A you hit that ball as hard as you possibly can.  Yeah it could go wide but if you connect with it right then even Novak Djokovic has no chance of returning it and you can sleep on a pile of money that night.  A safe serve would definitely be in, but then Djokovic will almost certainly tear you apart if you actually have a rally with him so that's not an option.

In Scenario B the chances are that you're a better tennis player than Jack Black so you don't need the big serve, and in fact it represents an unnecessary risk.  Just get the ball onto the court and even if he manages to return it over the net you should be able to beat him for a point in a rally.

4) How Many Chances Do You Have?

If a high variance approach is 'gambling' on getting a good result, then how many times are you going to get to take that gamble if you only need it to pay off once?  

The current Store Championship season is a good example of this... if you can only make it to one Store Championship then there's a bit more on the line if you choose to play high variance, as if you crap out then it was your one shot.  But if you're going to five Store Championships then you've a good chance that variance will go your way in at least one of those events, which might be a significant helping hand in bringing home a plaque and some bragging rights.

More chances at success mean you've more chances of a high variance strategy delivering an overperformance at least once.  Fewer chances make it more of a risk to put so much to the roll of a dice.

Controlling Variance

So hopefully by now you've got a good idea of what Variance means in X-Wing, and when you should try and use it to your advantage or try and minimise its influence.

What we've not really looked at is how you can actually control the amount of variance either way.  In some games this can be quite hard to work out, but in X-Wing there's a pretty good rule of thumb to remember:
  • If MORE dice are being rolled then you are increasing variance.
  • If LESS dice are being rolled, or you can modify/reroll the results of those dice, then you are reducing variance.

When you look at how players are building their squads it's clear that the cards which reduce variance are valued much more than those that increase it, but I'll have a quick look at both, if only because some of the examples are really interesting examples of why one upgrade is played much more often than the other.

High Variance
  • High Agility/Low Hull ships
  • 'Swarm' tactics
  • 'Alpha Strike' tactics using a lot of one-shot Ordnance
  • Stealth Device
  • Lando Calrissian
  • R2-D2 (Crew)
  • Ion Projector

Low Variance
  • High Hull/Low Agility ships
  • Emperor Palpatine
  • Predator & Gunner
  • Darth Vader
  • C-3P0
  • Twin Laser Turret
  • Autothrusters

There's some interesting comparisons there that I'd want to highlight, C-3P0 being one of them.

The popular C-3P0 crew card is basically asking you to gamble on a dice roll, which is surely adding variance not taking it away?  Well, yes that's true but what players are actually doing is using C-3P0 to remove variance from ships with 1 Agility by always gambling on 0 Evades being rolled.  So where you'd normally roll your green dice and be uncertain of getting an Evade you now now that you're either going to roll an Evade, or roll 0 Evades, and so get to add an Evade.

Lando Calrissian, on the other hand, will almost never be played despite the fact that in the long run he's going to be more effective than making a Focus action every turn (you've got two 5:8 chances of getting a Focus or Evade, so on average you'll get 1.2 Focus/Evade tokens each turn).  This is because you can't rely on the variance going your way when you need it to and 3pts is a lot to invest on that incertainty... especially when those same 3pts can be invested in the certainty of C-3P0!

And let's look at the specific of rubsnick's situation and his TIE Interceptor.  He didn't just take a blank Soontir Fel into the tournament, he had already tried very hard to reduce variance.
  • Stealth Device - adding Agility doesn't reduce variance, but it stacks the odds in your favour
  • Push The Limit - for either maneuvering to avoid rolling defense dice at all, or for stacking Focus and Evade tokens to reduce variance
  • Autothrusters - for adding free Evade results, reducing variance
  • Emperor Palpatine - nearby on his Lambda Shuttle, the Emperor is the ultimate Variance reducer

In fact rubsnick had worked very hard to reduce the variance involved in keeping Soontir Fel alive.  He'd ensured that he would be ok in pretty much any scenario other than rolling all blank dice.  But that still left a variance window for the odds of rolling all blank dice - a small window, but a window.  The mistake and frustration stems from thinking that shrinking the chances of something bad happening is the same as eliminating the chances of something bad happening.  The real extremes of bad variance are still there, and even with all those tricks added... sometimes a TIE Interceptor is still just a TIE Interceptor and will explode when a B-Wing would not.


I started this by picking out a post by a single person, but really this isn't about rubsnick because I think these are issues that we all face.  X-Wing is a dice-rolling game, and however much you can spec your squad out to fix the odds of that dice-rolling in your favour with Upgrades and Crew and pilot abilities... sometimes the dice will be bad and you'll lose.  It doesn't need to be about green dice, it could be about endless blank red dice.

Variance is ever-present in X-Wing.  So the lessons about being psychologically prepared for when that variance goes against you are valuable for everyone.

But the extent that you rely on variance is something that you can control.  You can play Interceptors or you can play B-Wings, and whichever you choose you'll have to understand the strengths and weaknesses of both approaches.  If you don't appreciate both sides of the decisions that you make then it leads to frustration and anger.  

That's the dark side.  Don't do that.

When you pick Interceptors understand that you'll win 100-0 one match and lose 0-100 the next, and sometimes that will be out of your control.  And when you suffer the 0-100 you have to take a deep breath, count to ten, and remember that it's also part of why you went 100-0 before.  And if you're a weaker player then maybe a run of hot dice will take down a better player.

When you pick B-Wings those 100-0 wins are harder to get because your low-variance ships all have a pretty well-defined lifespan, and some of them aren't going to make it out the other side.  But equally, the 0-100 defeats are less likely, and if you're a better player then there's more chance that you'll be given the chance for superior play to carry the day for you without your dice crapping out from under you.

And me?  Two years ago I played in a Magic tournament where I had no knowledge of ANY of the cards in my deck, let alone the cards in my opponents decks.  I was the least prepared player in the room and by all rights I should have finished dead last, but instead out of nearly 1,500 players I finished in the top 100 and won $250.  Because I embraced Variance.  I asked myself what success looked like and I looked at what the prize structure was, I understood that I was an underdog in the tournament, and even though I only had once chance at the risky play, it was probably my only chance.  Know when variance is right for you and you can reap the rewards.


  1. Wow, what a great article! Not only do you hint at advice on playing the game to your strengths, but you suggest a mindset to help combat that feeling of crushing defeat by which a lot of players get discouraged. Such a good read; thanks David!

  2. This is an excellent article, and I feel like you wrote it in such a way that it works for even non X-Wing players. I am going to share this with my Armada group.

  3. Cool post, being okay with loosing is certainly a learned skill. Your well written pseudo scientific explanation helps my poor competitive N. American mind.. a bit...