A Rock Paper Scissors Brainteaser

New submitter arsheive (609065) writes with a link to this interesting RPS brainteaser: "How do you play against an opponent who _must_ throw Rock 50% of the time, and how much would you be willing to pay to play against them?"

Comments

Re:Simple.... Odds are even

[narcc]

Actually now that I think about it more

... you realize that you're doing the submitter's homework?

Re:Simple.... Odds are even

[ShanghaiBill]

The Nash Equilibrium is for you to play paper 2/3rds of the time, and rock 1/3rd. His best counter strategy is to play rock 50% (he cannot go lower) and scissors 50%. He cannot do better. If you deviate from 2/3 paper and 1/3 rock, he can adjust his strategy to do better. With the optimal strategy, you will win 1/2, lose 1/3, and tie 1/6.

Here is my search for the Nash Equilibrium:

#include

struct rps {
    double rock;
    double paper;
    double scissors;
};

static double
eval(struct rps *a, struct rps *b)
{
    return
        (a->rock * (b->scissors - b->paper)) +
        (a->paper * (b->rock - b->scissors)) +
        (a->scissors * (b->paper - b->rock));
}

int
main(void)
{
    struct rps you;
    struct rps him;

    him.rock = 0.5;
    double worst_best_eval_for_him = 1.0;
    double best_rock_for_you = 0;
    double best_paper_for_you = 0;
    double worst_best_paper_for_him = 0;
    double dx = 0.001;
    for (you.rock = 0; you.rock best_eval_for_him) {
                    best_eval_for_him = p;
                    best_paper_for_him = him.paper;
                }
            }
            if (worst_best_eval_for_him > best_eval_for_him) {
                worst_best_eval_for_him = best_eval_for_him;
                best_rock_for_you = you.rock;
                best_paper_for_you = you.paper;
                worst_best_paper_for_him = best_paper_for_him;
            }
        }
    }
    printf("worst_best_eval_for_him = %f\n", worst_best_eval_for_him);
    printf("best_rock_for_you = %f\n", best_rock_for_you);
    printf("best_paper_for_you = %f\n", best_paper_for_you);
    printf("worst_best_paper_for_him = %f\n", worst_best_paper_for_him);
    return 0;
}

Re:Simple.... Odds are even

[ShanghaiBill]

Sorry, but Slashdot mangled that code badly because of the angle brackets.

Let me try again:

#include <stdio.h>

struct rps {
    double rock;
    double paper;
    double scissors;
};

static double
eval(struct rps *a, struct rps *b)
{
    return
        (a->rock * (b->scissors - b->paper)) +
        (a->paper * (b->rock - b->scissors)) +
        (a->scissors * (b->paper - b->rock));
}

int
main(void)
{
    struct rps you;
    struct rps him;

    him.rock = 0.5;
    double worst_best_eval_for_him = 1.0;
    double best_rock_for_you = 0;
    double best_paper_for_you = 0;
    double worst_best_paper_for_him = 0;
    double dx = 0.001;
    for (you.rock = 0; you.rock < 1.0; you.rock += dx) {
        for (you.paper= 0; (you.paper + you.rock) < 1.0; you.paper+= dx) {
            you.scissors = 1.0 - you.rock - you.paper;
            double best_paper_for_him = 0.0;
            double best_eval_for_him = -1.0;
            for (him.paper = 0; him.paper < 0.5; him.paper += dx) {
                him.scissors = 1.0 - him.rock - him.paper;
                double p = eval(&him, &you);
                if (p > best_eval_for_him) {
                    best_eval_for_him = p;
                    best_paper_for_him = him.paper;
                }
            }
            if (worst_best_eval_for_him > best_eval_for_him) {
                worst_best_eval_for_him = best_eval_for_him;
                best_rock_for_you = you.rock;
                best_paper_for_you = you.paper;
                worst_best_paper_for_him = best_paper_for_him;
            }
        }
    }
    printf("worst_best_eval_for_him = %f\n", worst_best_eval_for_him);
    printf("best_rock_for_you = %f\n", best_rock_for_you);
    printf("best_paper_for_you = %f\n", best_paper_for_you);
    printf("worst_best_paper_for_him = %f\n", worst_best_paper_for_him);
    return 0;
}

Re:Always do rock.

[ArcadeMan]

Of course. You use the rock to smash him in the head while he tries to stab you with the scissors. Your friend then uses the paper to write a letter to your parents about how you died in a stupid fight about statistics.