“Just Double 1 it” part 1 – People suck at guessing odds

Part one of two. In these articles I’m going to explore the common refrain of “Just double 1 it” in Kings of War and why people shouldn’t offer this. I’m rushing to get this posted before Elliot arrives for our Friday gaming session (in accordance with support bubble lockdown rules) and cut this part out of the larger article, so it might seem a bit disjointed. Here we go though.

Intro

A really common thing to hear in Kings of War is the phrase “just double 1 it”. A unit is so comprehensively fucked by multiple rear chargers that the only conceivable way it’ll survive is if the attacker rolls a double 1 on the nerve test.

Stop it.

Bad Kings of War players. Bad.

People often cite “just get on with it” or “I’m not making someone waste time rolling dice when we know the outcome”, but there are plenty of reasons why you should not skip straight to “just double 1 it”

People Suck At Guessing Odds

Baiting headline is a clickbaity headline. We’re humans. We’re not great at calculating big numbers in our heads.

Many players are often far too quick to offer double 1s, thinking that it’s the only realistic chance of survival when the chances of surviving through a fluffed attack roll are significant and often higher than double 1s.

The really common example is a charge against a war engine. Players have it in their head that a charged war engine is a dead war engine, so will offer an anything-but far more readily than anywhere else. I’ve seen plenty of double 1 offers where even rolling the average amount of damage wouldn’t get it to a double 1 situation, let alone fluffing the attack roll and rolling under-average.

I’ve had an Abyssal Champion (5 attacks, Me3, CS1) charge a KoM War Engine (De4, Ne 9/11) and had the offer to skip to double 1s. The Champ will average just 7 damage and need a 4 to break. If it fluffs the roll then I could even find myself needing a 7+ to break.

Sometimes the amount of attacks are overwhelming and there’s effectively no chance that anything but a double 1 will save the unit, but other times it’s surprisingly likely that a 3 or 4 (or even higher) on the resulting nerve test will not rout. We know where the absolute extremes are, but honestly, working out whether something is in the fuzzy middle ground takes longer than just rolling the dice out in the first place.

I did a little bit of a test to see how well people judge the likelihood of only snake eyes saving a unit.

I posed three situations to Kings of War Fanatics and asked them whether they would skip straight to “just double 1 it”:

1. A dragon (Me3, 10 Attacks, CS3) rear charges an Ironclad Regiment (De5 Ne 14/16)
2. A vampire (Me3, 7 Attacks, CS2) charges a KoM war engine (De4, Ne 9/11)
3. An ogre regiment (Me3, 9 Attacks, CS1) charges a Dwarf war engine (De5, Ne 10/12)

I should have thought a bit more about this before just posting polls in Fanatics. Seeing the results and the discussion could influence how people answer, especially in the cases where some people calculated the odds and posted the “correct” answer in the comments. Regardless, I think the results still demonstrate what I’m talking about.

Note: I “worked out the odds” by brute forcing 100,000 simulated dice rolls for each situation. I’m still very wobbly on Bayesian Probability and trust my python/macro scripts much than my maths.

Dragon in the rear

Here’s the damage output bellcurve of a dragon charging into the rear of an Ironclad Regiment.

Green bars indicate situations that only a the snake eyes rule will save a unit – i.e. total damage plus 2 exceeds the rout limit of 16. The yellow bar is the result where it’s still a snake eyes to save the unit, but that’s only because it reaches 15 altogether – 1 short of the rout limit. Red are the situations where the dragon will deal less than 12 damage – and a roll of a 3 will not be enough to rout.

That’s a lot of red. A lot.

6.2% of the time when a dragon charges into the rear of a unit of knights, it will not be an anything-but situation. You need at least a 4 to rout the knights, probably higher. 5.9% of the time a snake eyes roll will save the knight regiment, but because you didn’t hit the rout limit rather than the double 1 rule.

Now, granted, for the red situations the dragon not only has to roll massively under average but also again on the nerve test. However, if you feel that snake-eyes is enough of a chance that you’re going to make someone carry out a dice roll (2.8%), then surely carrying out a dice roll for an event that’s twice as likely to occur should be done?

Let’s see what Fanatics said. Would they allow a player to skip to “just double 1 it”?

Only 70% of respondents would make their opponent roll it out. 30% either wouldn’t be sure or would jump straight to the nerve test. While it’s great to see the majority rolling it out, that’s still a lot of people who perhaps don’t realise how likely it is that you don’t get it to a double 1 situation.

A few people in the Double1/Not Sure qualified their response by saying that if the Nerve roll was low then they would subsequently make their opponent roll out the attacks. However, the highest number stated before this option was taken was a nerve roll of 4. There’s still a 1.1% chance that the required nerve roll will be 5+.

Vampire vs War Engine

Significantly lower chance of needing a 4+ to rout, but not insignificant. Again the chances of snake eyes on 2D6 is just 2.8%, so it’s still more likely that you need a 4 or more anyway. There’s still a 5.1% of getting 8 damage, so a snake eyes result will fail to meet the rout limit of 11.

Here’s how Fanatics voted:

47% would make their opponents roll it out. 5 people said to roll nerve first and if it’s “high”, take off the war engine (I didn’t want people to add options to the poll – Doh!). I put them in the Not Sure category.

A large number would make their opponent just roll a nerve test though. While the chances of it being a 4+ to rout are low, they’re not nothing. It could also cause undue frustration if the double 1 comes up and rolling out would have needed a 3+ regardless of the double 1 rule.

Ogre Regiment vs Dwarf War Engine

This is a situation I’ve personally witnessed. A regiment of Ogre Warriors charging a Dwarf War Engine. I was offered an “Anything but a double 1”. Here’s the bellcurve:

27.6% of the time, a 3 will fail to break the Dwarf War Engine. That’s insane.

Thankfully, most voters said that they wouldn’t skip straight to the nerve test, however:

15% said they would skip to the double 1. 15%. When there is a 28% chance that it won’t be a double 1 situation.

People suck at recognising odds

In each situation, the majority did say that they would make their opponent roll out the attacks, however a significant number would jump straight to the double 1. Even those who said that they would skip to nerve and then go back to the attacks seemed to underestimate the likelihood of the charger really fluffing their roles. The most extreme example where 28% of the time it would not be a double 1 situation, a significant number said they would skip.

Does the number of dice really matter?

Each of these situations had relatively low numbers of dice. Increase the dice and I’m sure the people going for the “just skip to the nerve” answer would jump up more, even if the odds were similar to the Ogre Warrior example. I’d had enough of posting the polls though, and I’m sure Fanatics was sick of me, so I didn’t want to push it further.

I think the point has been proven even with these relatively low dice situations.

A note on the Double 1 Rule

I have a suspicion that people overestimating the likelihood of an anything-but situation happening contributes to the complaints about the snake eyes rule. I see people frustrated at the rule sometimes after they rolled a double 1, but they needed a 3+ to rout the unit anyway, so it’s not the double 1 rule that saved it.

If you skipped a roll to “just double 1 it” because you think it’s dead obvious that it’s the only way to save the unit, and the dreaded snake eyes came up, then that contributes to your view on the rule.

Except, if you had rolled it out then there was only a 90% chance that it would be a double 1 situation anyway. A 4 or 5 on the nerve test might have failed to break as well, but you have it in your mind that it was purely the double 1 rule itself that meant you failed to break.

Part Two

We know that people aren’t great at realising just how likely it is that it won’t be an anything-but situation. Part two coming soon where I examine things such as clocks and sportsmanship and beat you down with the message “Stop skipping attack rolls. Roll everything out FFS.”