Is it worth rolling 3d8 instead of 1d20 in Dungeons & Dragons?
Hello all! I have this problem that I tried to solve but confused at some point.
For some context, I am playing Dungeons & Dragons with some friends. In D&D, whenever you want to do some actions, you roll a 20-sided die. Rolling 1 means absolute fail while rolling 20 means absolute succes in most cases. Various success levels changes based on the rest of the numbers, but unrelated to my problem.
Sometimes you can have advantage on those rolls, which means you roll the die twice and take the higher one.
I have this gambling themed item that allows me to roll 3d8 instead of a 1d20, whenever I have an advantage. Which is 3 8-sided die.
While rolling this 3d8 item, I have severeal possibilities:
- Rolling 3 uneven rolls
- Rolling 3 even rolls
- Rolling sequential numbers (ex: 1,2,3)
- Rolling 3 identical rolls
- Rolling 3 7s
- Rolling 3 8s
- Additionally if the total of the rolls equals to 13, I can roll any one of the dice and possibly get a better roll
Rolling any of the above set of rolls automatically makes my attempt absolute success, with additional effects that are unrelated.
I tried to calculate my possibilities of winning compared to regular 1d20. Please let me know if I calculated wrong (It's been a while since highschool)
For the regular d20, my probability of absolute success with advantage is (1/20+1/20)= 1/10 or 0.1
With this item, my possibilities are
3 uneven rolls, 4/8 x 4/8 x 4/8
3 even rolls, 4/8 x 4/8 x 4/8
sequential roll, 6/8 x 5/8 x 4/8 (I can roll 6 as highest to have increasing sequantial)
3 identical rolls, 1/8 x 1/8 x 1/8
3 sevens, 1/8 x 1/8 x 1/8
3 eights, 1/8 x 1/8 x 1/8
If I did math correct, the outcome is 251/512, or roughly 0,4.
Now here where it gets complicated:
- I couldn't calculate reverse-sequential,
- I think I calculated the regular d20 calculations wrong.
- having an option to reroll on of the die, if the total 13 should affect the final outcome but I don't know how to calculate that.
In the end, I am almost sure that rolling 3d8 is always better than rolling 2d20 bu I want to understand exactly how and have a better understanding of maths!
Thanks for everyone for help!