https://docs.google.com/spreadsheets/d/1xOG9vG3a_USQX4_H3H3Gyc-ThIKpVk7KhB-Xa7A5Hy4/edit?usp=sharing
I was bored and threw together some formulas in Excel. I don't know if this is useful to anyone when doing encounter design?
I made something similar; it's useful for calculating expected values but so far my experience has been that each party will have wildly different abilities so a formula doesn't really help as much as you'd think.
There’s also the issue that the average damage for any of the dice used (d4, d6, d8, d10, d12) will NOT be an integer.
Expected tries to kill [table] [tr][td]AtkDie↓ Lt Die→[/td][td]d4[/td][td]d6[/td][td]d8[/td][td]d10[/td][td]d12[/td][/tr] [tr][td]d4[/td][td]2.67[/td][td]6.67[/td][td]12.00[/td][td]18.67[/td][td]26.67[/td][/tr] [tr][td]d6[/td][td]4.80[/td][td]12.00[/td][td]21.60[/td][td]33.60[/td][td]48.00[/td][/tr] [tr][td]d8[/td][td]4.57[/td][td]11.43[/td][td]20.57[/td][td]32.00[/td][td]45.71[/td][/tr] [tr][td]d10[/td][td]2.67[/td][td]6.00[/td][td]10.44[/td][td]16.00[/td][td]22.67[/td][/tr] [tr][td]d12[/td][td]2.09[/td][td]4.49[/td][td]7.40[/td][td]11.03[/td][td]15.40[/td][/tr][/table]
I worked this out by count-table rather than pure formula. (makes it easier to replicate the rules - damage die ≤ lieutenant die is no drop).
The OP’s data looks closer to expected tries to step-down…
[table] Expected tries to stepdown [tr][td]AtkDie↓ Lt Die→[/td][td]d4[/td][td]d6[/td][td]d8[/td][td]d10[/td][td]d12[/td][/tr] [tr][td]d4[/td][td]2.67[/td][td]4.00[/td][td]5.33[/td][td]6.67[/td][td]8.00[/td][/tr] [tr][td]d6[/td][td]4.80[/td][td]7.20[/td][td]9.60[/td][td]12.00[/td][td]14.40[/td][/tr] [tr][td]d8[/td][td]4.57[/td][td]6.86[/td][td]9.14[/td][td]11.43[/td][td]13.71[/td][/tr] [tr][td]d10[/td][td]2.67[/td][td]3.33[/td][td]4.44[/td][td]5.56[/td][td]6.67[/td][/tr] [tr][td]d12[/td][td]2.09[/td][td]2.40[/td][td]2.91[/td][td]3.64[/td][td]4.36[/td][/tr][/table]
Worksheet: Sentinel Comics Lieutenants - Google Sheets