Failure track analysis

The Delve expansion for Ironsworn describes an optional mechanic that rewards players for their rolls that result in a miss. Every time they miss, they add 1 tick (or 3 ticks if the roll was a progress roll, but I'll completely ignore these for this analysis) to a failure track. Every 4 ticks constitute a full mark and the failure track can have up to 10 marks. Once the track has 6 marks (in other words after 24 miss-rolls) the player can choose to "learn from their mistakes". This move is resolved by a roll and resets the fail track to zero ticks again. The resolution is a simple progress roll against the fail track where a strong hit awards 3 XP, a weak hit awards 2XP and a fail rewards 1XP. Additionally a strong hit will let the player discard an asset for more XP (which I will ignore for this analysis) and a weak hit will narratively force the player to learn the wrong lesson from their failures which is in my opinion a hefty penalty if role-played correctly.

I did a small analysis of the 5 different points when a player can trigger the "learn from your mistakes" move:

Learn from your mistakes when you have this many marks	Miss-rolls to gain 1XP	Miss-rolls to have to learn the wrong lesson
6	12	96
7	12.73	175
8	13.33	355.6
9	13.85	900
10	14.29	4000

Triggering the "learn from your mistakes" move as frequently as possible gives more XP overall but the difference is minor: less than 20% extra XP compared to waiting for a full failure trackbefore you trigger. At the same time frequent triggers will result in a 4066% increase in how often you'll be learning the wrong lesson compared to waiting for a full failure track before triggering!

If someone wants to verify the code that produced the above table, I wrote it on a casio fx-3650P II just for fun so I can't exactly upload the code but here's a rough dump:

For 6->M To 10:

0->X:

0->Y:

1->A:

Lbl 1:

1->B:

Lbl 2:

(M>A)+(M>B)+1+X->X:

(M<=A)+(M<=B)=2=>Y+1->Y:

B+1->B:

B<=10=>Goto 2:

A+1->A:

A<=10=>Goto 1:

M[output triangle symbol]

M*400/X[output triangle symbol]

M*400*Y[output triangle symbol]

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