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?"

Play paper 50% of the time.

[Anonymous Coward]

Expect them to play scissors a lot to beat your paper. Play rock as often as they play scissors.

put a spin on it

[ihtoit]

Rock, paper, scissors, lizard, Spock!

Scissors cut paper
Paper covers rock
Rock crushes lizard
Lizard poisons Spock
Spock smashes scissors
Scissors decapitate lizard
Lizard eats paper
Paper disproves Spock
Spock vaporizes rock
Rock crushes scissors

Programming Course Topic

[NeuroBoy]

I've been having students in my introductory programming courses work on this class of problem for a few years.. They all seem to really enjoy it. I code up bots to play RPS with certain biases just like the OP and they have to program a single player that identifies the bias in an opponent and adjusts its play to give it an advantage. They all routinely can generate solutions that perform far better than random against predictable, dumb bots, but things get very interesting when I throw the students' bots against each other in a throwdown tournament. :)

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;
}