So I got curious about how the probability works for Ironsworn, and wrote a python script to simulate the outcome of...
So I got curious about how the probability works for Ironsworn, and wrote a python script to simulate the outcome of some rolls with different modifiers. (I was inspired by the discussion on taking the +1 from Secure an Advantage over the momentum). The big takeaway that I found from the data is that the odds of getting a weak hit are nearly stagnant regardless of modifier (clocking in between 40-45%), what really moves are the odds of Strong hits and Misses. Each +1 to the modifier increases the odds of a Strong hit and decreases the odds of a miss by about 10%. Thus, taking a +1 forward on your next roll is generally going to net you a 10% increased chance of success overall, with a 10% higher chance that it's going to be a Strong hit. That is, of course, if I did this code right. It seems correct in the samples that I checked though, so here's hoping!
Your math looks correct to me, Justin Gordon! Here's the full odds table.
ReplyDeleteAs you noted, a +1 has averages out to roughly a 10% impact. This is less than PtBA 2d6 rolls (which are more on the order of a 15% step, give or take).
The curve is nicely centered on weak hits until you get to +4, and has a shallow drop-off that makes it worthwhile to gather up a couple of bonuses via moves/assets. Unlike 2d6, a decent chance at a miss will haunt you all the way up to +5/+6 range (a reason to save up some momentum, just in case).
The math actually worked out pretty nicely for what I was trying to do. It was a long struggle to get there.
You can also see why stats start at 1 rather than 0.
https://lh3.googleusercontent.com/lKzas23uT2DI8uT5_FJqs8SVw-e27TH8A_QBSc85tn-hqnGxiNPVLOjXLVoHmFbl45-MKzQK96TBs2kGsXQFosDUw0X2is7ib9g=s0
The momentum breakdown also has some really interesting data to share! Especially as you get to higher momentum, you start to see some real gains (7 - 8 momentum increases the odds of a strong hit by 15%!)
ReplyDeleteI've got to say what I find really interesting about both of these charts is the way that a weak hit kind of settles in to the 40-45% bracket, ensuring that you'll always have enough complications to push the story forward.
I've got to be honest, when I did this breakdown I expected to find the math a lot swingier under the hood than it ended up being (the interaction between 2d10 and 1d6 was giving me heck on the probabilities).
Very cool stuff!
https://lh3.googleusercontent.com/yMdMUsHwWp31UoT_BWJQOV3CpSJjRiodugZKHt8GvZClk11m5aP50nU16ZkJFkQsbsxZxYfUIPhGlIkMi5pk6TRjFguRPPdNVnU=s0
Shawn Tomkin thanks for sharing that! I definitely agree that the numbers flow really nicely with this mechanic. The one fact I pulled from this data is that my dice definitely hate me.
ReplyDeleteThanks for diving into the math, Justin Gordon. And, yeah, it is a surprisingly nice little curve.
ReplyDeleteThe other thing that I thought was worth pointing out is that if you consider the Strong Hit to be equivalent to a Critical Hit in d20 that even with only a +1 on your roll you have triple the chance of rolling it (15%) than you would in D&D (1/20 or 5%)!
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ReplyDeleteJustin Gordon You min/maxer! LOL, inside joke 😉
ReplyDeleteJohn Risus haha, who needs story when I've got these stats!
ReplyDeleteShawn Tomkin , your odds table has me wondering if I'm doing something wrong. I came up with-
ReplyDeleteAction Roll: Miss/Weak Hit/Strong Hit
1: 100/0/0
2: 81/18/1
3: 64/32/4
4: 49/42/9
5: 36/48/16
6: 25/50/25
7: 16/48/36
8: 9/42/49
9: 4/32/64
ronald v if the number on the left is the modifier then you definitely have an error. 1d6+1has a minimum roll of 2, which means you have at least some chance of both weak and strong hit (where one or both challenge dice come up 1)
ReplyDeleteronald v ... Looks like you are only accounting for the stat, and not the D6?
ReplyDeleteThose numbers appear to be an accurate representation of the odds on a progress move (i.e. End the Fight), however, using the amount of progress boxes filled. If that was your intent, you've got it right.
Shawn Tomkin that's the odds I forgot to account for, now we've got a full set!
ReplyDeleteThanks! Yep, forgot to remove the "1" result.
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