Problem:
Person A and Person B each possess a d20 die (a die with 20 sides from 1-20). Person B believes her dice are extra lucky and challenges Person A to a "dice-off".
Person B is so convinced of her luck that in each Event, she sets up the following arrangements:
-In each Event, Person B will roll twice and pick the highest number from those rolls.
-In each Event, Person A will roll thrice, pick the highest number from those rolls and add 1/4 of Person B's highest number, rounded up to the nearest integer, to his own number.
-Whoever has the highest total number at the end of each Event "wins" that Event. If both numbers are equal, it is considered a "tie".
Assuming that Person B is not as lucky as she thinks she is (and isn't cheating in any way), for any given Event, what is the probability that:
a) Person A will "win"?
b) Person B will "win"?
c) The Event will result in a "tie"?
d) If Person A only added 1/5 of Person B's highest number instead of 1/4: how will the probability change for a), b), and c), respectively?
---
I secretly suspect our professor is either a D&D nerd or a sadist. (or maybe even both...)
I considered and tried listing the possibilities to see if I could see a pattern, but it quickly got out of control, and I'm pretty sure there's an easier way to solve this problem; I'm not sure how to approach it or really to start; it seems a bit daunting.
It seems like there's almost too much going on here at the same time. (three rolls+highest fraction of the two rolls??? vs. two rolls???)
Please let me know if there's a way to actually solve this problem like a sane person instead of brute-forcing cracking it by listing every single possibility...
Person A and Person B each possess a d20 die (a die with 20 sides from 1-20). Person B believes her dice are extra lucky and challenges Person A to a "dice-off".
Person B is so convinced of her luck that in each Event, she sets up the following arrangements:
-In each Event, Person B will roll twice and pick the highest number from those rolls.
-In each Event, Person A will roll thrice, pick the highest number from those rolls and add 1/4 of Person B's highest number, rounded up to the nearest integer, to his own number.
-Whoever has the highest total number at the end of each Event "wins" that Event. If both numbers are equal, it is considered a "tie".
Assuming that Person B is not as lucky as she thinks she is (and isn't cheating in any way), for any given Event, what is the probability that:
a) Person A will "win"?
b) Person B will "win"?
c) The Event will result in a "tie"?
d) If Person A only added 1/5 of Person B's highest number instead of 1/4: how will the probability change for a), b), and c), respectively?
---
I secretly suspect our professor is either a D&D nerd or a sadist. (or maybe even both...)
I considered and tried listing the possibilities to see if I could see a pattern, but it quickly got out of control, and I'm pretty sure there's an easier way to solve this problem; I'm not sure how to approach it or really to start; it seems a bit daunting.
It seems like there's almost too much going on here at the same time. (three rolls+highest fraction of the two rolls??? vs. two rolls???)
Please let me know if there's a way to actually solve this problem like a sane person instead of brute-forcing cracking it by listing every single possibility...