Table Thoughts: Arithmophobia-Math, Panic, and ASOIAF: TMG 1.5

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Hello! My name is Guillaume Cloutier and I have been playing ASOIAF: TMG for almost 4 months now.  My faction is Neutrals (because money is everything, right?). I have a Math degree as well as some actuarial studies and I love to use my mathematics knowledge to mess around with games I play.

Version 1.5 is now live, and I wanted to share my thoughts on the new panic system.  I think when people see the numbers, they might panic less about the changes (spoiler alert… I love them!).

I absolutely don’t want this write up to be a math class, but there’s one concept I’d like to review before we go further, the concept of “Average” or “Mean”.  The mean of a random event is, the value you will have if, for example, you take a very large sample of that random event, like throwing dice, sum up the value of each dice throw, and finally divide that sum by the number of dice thrown.  Essentially dice average = (total sum of all throws)/number of dice thrown). The more dice you throw, the more the measure will get closer to the “theoretical mean”. So it’s common knowledge that the “mean” of throwing a die is 3.5. I know there’s no 3.5 face on a die, but the more dice you throw; the closer to 3.5 the average becomes.  And if it was possible to throw an infinite number of dice, then the result would be “exactly” 3.5 per die thrown.

An Era of panic!

Back to the topic, when I saw the new 1.5 panic system and the initial reaction of the community, I automatically wanted to run the numbers.  The first thing I analyzed is the “average number of wounds per panic test,” because it is the most important outcome…wounds! The following charts will illustrate the average number of wounds a unit will take when rolling for panic.

Chart 1
Chart 2
Chart 3

Now tell me, what do you see? Personally, I see many soldiers fleeing my Boltons and it’s warming my heart.  The new panic system will make more soldiers flee on average on almost all the most common panic tests in the game, which is basically column -2,-1,0 and +1 in chart 3.  You can see those 4 columns are almost all green. It’s also a straight-up bonus to the crown tactic zone as the -1/-2 column is almost all green, which is another good thing because it was considered the “worst” tactic zone.  Finally, we can see that 7+ and 8+ Morale units are getting mostly a break, but even they will suffer more wounds from unmodified panic tests.  

Panic on Panic on Panic: Is There a Benefit to Stacking Panic Modifiers in 1.5?

Another interesting calculation we can perform with this table is to analyze the impact of the new system on modifiers.  Let’s use the above data to make another table where we see the average additional number of wounds per panic test that a -2 modifier would add to a specific panic test.  The same can be done for different modifiers but I felt that a -2 modifier is the most common.

Chart 4. Please Note – Column header numbers are existing modifiers before the additional -2 has been added,
Chart 5. Please Note – Column header numbers are existing modifiers before the additional -2 has been added,
Chart 6

Just to be sure, let’s look at an example.  Look at Chart 5, the Morale 6+ row with 0 as the modifier.  You see a 0.92. That 0.92 is what an additional -2 modifier would bring in for the additional average wound.  In that specific case, it would bump the average number of wounds for that test from 0.83 to 1.75.

In 1.4, you can easily see higher damage with more modifiers. Not every time, but most of the time, putting more modifiers on a unit was a legit strategy to make more of their warriors flee.  In 1.5, the pattern resembles more of a “pyramid”, where if you can grab the “top of the pyramid” odds, which peak at 0.92 additional wounds (yellow cells in the table), it would be your best option.  But the more modifiers a unit already has, the less appealing it is to put an additional -2 (like Cersei) on a unit.

For example, if I influence a 7+ morale unit that is already engaged with a vicious unit like Mountain’s Men, and within short range of a corpse pile, then Cersei would bump my average number of wounds by 0.42.  But on the other hand, influencing another unit that has moral 6+ without any modifier at the moment would bump it to 0.92 which would make Cersei more than twice as more effective in that situation.

Snake Eyes: Still a Death Sentence?

Those averages are fun, but didn’t they change the 1.4 system because it was too ‘swingy?’  Interesting…  

Let’s modify the values.  Given that succeeding a panic test in 1.5 is equally likely as in 1.4, let’s see the table if we calculate the mean number of wounds from failing a panic test and you will see a surprising conclusion.

Chart 7
Chart 8
Chart 9

So again, my friends, do you see anything special? 

Look at the 1.5 table?  YES! It’s not a mistake, THEY’RE ALL AT 3!

The reason is, given a failed panic test, the number of wounds you take in 1.5 is no longer based on the value you rolled on the panic test itself, but on a separate D3+1 roll. Therefore when it fails every single unit in the game will have the same outcome of wounds.  It really is, in my opinion, a more ‘fair’ system (though more punishing) because in 1.4 units with poor morale would be penalized because due to having higher odds of failing the test, they would potentially suffer tons of wounds… On the other hand, high morale units had low odds of failing combined with fewer wounds if failed.

In conclusion, more wounds? Oh yes, but a fair system for all unit types.  I hope you enjoyed this write up and I’m looking forward to seeing these numbers at work…. ON THE TABLE!




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