Basic probability in Ironsworn

Ironsworn RPG has an interesting dice mechanic: The action score, which is a d6 plus attribute plus bonuses, is compared to two d10s (the challenge dice).

To get a strong hit, with no negative outcomes, the action score has to be greater than both the challenge dice. To get a weak hit, with positive outcomes but probable penalties, the action score must be greater than just one challenge die. And to get a miss, which has almost entirely negative outcomes, the action score must be less than or equal to both challenge dice.

You can build this up into overall probability calculations: You can calculate the probability that a specific action score will be a strong or weak hit, or a miss, then work out the range of action scores that a d6 could give you given a set total of attribute+bonuses. The probability for a strong, weak or no hit is then analogous to the average probability for an outcome for the given action scores across the range.

As far as I can tell, the attribute plus bonuses must always be at least 1 – I haven’t come across a situation yet where this isn’t true (I suppose you could try to make a Progress Move with no Progress, but that’s a stupid example). And I haven’t seen a case for any total attribute plus bonuses to exceed 5 (attribute of +3 with an asset granting you a +2 add). On page 8, it also says that your action score cannot exceed 10; anything higher should just be dropped back to 10. That means that the range of possible action scores is 2-10, although I’ll go 1-11 for reasons that are apparent from the table below.

Action score	1	2	3	4	5	6	7	8	9	10	11
Strong hit	0%	1%	4%	9%	16%	25%	36%	49%	64%	81%	100%
Weak hit	0%	18%	32%	42%	48%	50%	48%	42%	32%	18%	0%
Miss	100%	81%	64%	49%	36%	25%	16%	9%	4%	1%	0%

That’s to say, the a strong hit increases by a square law, and the miss probability decreases in the same manner. The weak hit probability increases to a peak of 50%, then drops off again at the same rate.

Because of the action score upper limit of 10, the final column for ’11’ should just match that for ’10’ – that’s the easiest way to handle that. That’ll be assumed from now on.

Given a set combination of attribute and adds, which is determined by the fiction (and hence not mechanically), you get a range of values which you can achieve with a single d6. So, for a total of +2, you can get between 3 and 8, each having equal likelihood (1/6). Because this is “you roll this action die and your challenge dice are this”, you multiply this by the probability of that particular action score getting, for example, a strong hit. So, for the example of +2:

Action score	3	4	5	6	7	8
Strong hit	0.7%	1.5%	2.7%	4.2%	6.0%	8.2%
Weak hit	5.3%	7.0%	8.0%	8.3%	8.0%	7.0%
Miss	10.7%	8.2%	6.0%	4.2%	2.7%	1.5%

No surprises there – this just takes the values across a set range, from the previous table, and multiplies them by the probability of rolling that specific number on a d6 – 1/6, or 16.7%.

The last piece of the puzzle is that, for each total attribute+bonus, you can roll any one of six different action scores. For +2, it could be 3, 4, 5, 6, 7 or 8. This “or” logic means you add all of these probabilities to determine what the likelihood of rolling a strong, weak or no hit actually is. For the example of +2:

Attribute + adds	+2
Strong hit	9.2%
Weak hit	31.7%
Miss	59.2%
A hit (strong or weak)	40.8%

“A hit” here is just “strong hit or weak hit”, i.e. the sum of these two values.

This kind of table can then be calculated for all possible combinations of attribute + adds – i.e. 0-5 (again, I’ve not yet found a case for +0, but it might exist). The only complication would have been for the 11=10 end of the column, but copying the 10 column into the 11 removes that problem (effectively, the likelihood of getting ’11’ becomes 0, and the likelihood of getting ’10’ becomes 1/3 – it’s achieved on a 5 or a 6, i.e. 1/6+1/6=1/3). In the table below, I summarise what I’ve found, highlighting the maximum likelihood for a given total addition.

Attribute + adds	+0	+1	+2	+3	+4	+5
Strong hit	9%	15%	23%	33%	45%	56%
Weak hit	32%	40%	44%	44%	40%	35%
Miss	59%	45%	33%	23%	15%	9%
A hit	41%	55%	67%	77%	85%	91%
A cost	91%	85%	77%	67%	55%	44%

In this table, “a cost” is an outcome where some kind of penalty is incurred – either narrative (you fail), mechanical (you suffer) or both (you fail and you suffer).

There are interesting results here. The first is that you always have a better than average chance of scoring at least a weak hit: for +1, your chance for “a hit” is 55%. 11 times out of 20, you won’t fail. So regardless of your statistics, you can always gamble, and more times than not (literally), you will succeed at what you set out to do.

Look also how your most likely outcome increases through the table. If you use your best stats, you’re most likely to get a strong hit; if you use your middling stats, you’ll get a weak hit; and if you use your weakest stats, you’ll most likely miss.

Another thing to note is that strong hits are the most likely outcome only at the extreme end of the table. This means that if you have only weak stats that apply to the fiction, it’s better to drive the narrative towards preparation and planning, i.e. moves that will build momentum through weak hits. If failure is not an option, then be proactive only with moves that are going to give you bonuses of +4 or +5. This works better with characters that have the “planning” stats as their weaker stats – it’s annoying to have to continually build momentum using your best stats, then be faced with hardship and difficulty at moments of high tension.

At some point I’ll do another analysis post about momentum, but now is not the time. It’s fairly hard to analyse it, because it requires decision making.

One final thing that I see is that “hits” and “costs” increase and decrease in the same pattern, but are always a substantial fraction. This is the “fail forward” model that modern narrativist games tend to promote.

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My usual approach to narrativist games is that, in many ways, failure is much more interesting than success (I tried applying this to gamist games as well, which is why I got kicked out of DnD games). In play-by-post FATE, I tell my GMs to assume that I succeed at cost rather than fail. Powered by the Apocalypse games like Blades in the Dark and Ironsworn take this to a new level: succeeding at cost is probably the most likely outcome in most scenarios.

Injury is temporary, but glory is eternal!

“Fail Forward” narrativists

Injury is temporary, but glory is eternal! – or, at least, fiction eternal (also death, but there you go; it’s only a game). We want to fail, because failure drives the narrative more interestingly than outright success. That can be frustrating, but it can also lead your story to more interesting places.

Of course, the real message of a narrativist gamer is this: make the move that the fiction suggests, not the one that your meta-game analysis suggests is most likely to succeed. But every now and again, it’s nice to make a decision that’s based on the certainty of uncertainty.