Coin Tossing Time Travelers

Question

In the future when Time Travel (abbreviated as TT) will be common, coin tossing will become a serious mind-sport. To prepare for the future we create a competition for programs where time traveling will be really happening from the viewpoints of the entries.

The competition is a round-robin style King of the Hill consisting of coin tossing matches between Java classes.

Rules of the coin tossing match

• There are two players and 100 rounds.
• In every round a coin is tossed and based on the result one of the players scores 1 point. Each player has 50% chance to score a point.
• After the tossing both players have a chance to control the time by pulling levers.
• If you pull a blue lever (revert stopper) no TT is possible to the round the lever was used or any earlier round anymore. TT's attempting to go to these rounds will have no effect.
• If you pull a red lever (reverter) you try to revert the time back to a former round. If succeeded the opponent's memory will be reverted to its memory before the chosen round and the coin toss results starting from the chosen round will also be deleted. The only possible sign for your opponent about the TT will be the number of its unused levers which will not be reverted back.
• Each player has 5 blue and 20 red unused levers at the start of the match. These levers are not affected by TT's.
• If no TT happens at the end of a 100th round the game ends and the player with the higher score wins.

Details

• Rounds have a 1-based indexing (form 1 to 100).
• Before round x you are provided the number of available blue and red levers, the coin toss results until turn x (inclusive) and the memory of your (last) x-1th round.
• Pulling a blue lever in round x stops any TT's that have a destination at round x or before (it blocks a TT if it happens on that same exact round too).
• Reverting to round x means that the next round will be round x.
• If both players choose to revert at the end of a round the time is reverted to the earlier destination which is not blocked. The player(s) who tried to revert to this time will keep their memory.

Technical details

• You should write a Java class implementing the provided Bot interface.
• Add your bot to the project.
• Add an instance of your Bot to the Bot in the file Controller.java.
• Your class should not keep information between calls. (In most cases having only final variables outside of functions satisfies this requirement.)
• You can give information to the controller in the memory field of your returned Action object. This will be given back to you in the next turn if no TT happened. If a TT happens, you will receive the corresponding earlier memory of yours.
• You can use the totalScore() method of the Game class to get the score of a history string.

Protocol

• At every turn your takeTurn(...) method is called with 5 arguments:

  • the number of unused blue levers
  • the number of unused red levers
  • the coin tossing history, a string consisting of 1's and 0's marking your wins and losses in the previous rounds. The first character corresponds to the first coin tossing. (In the first round the length of the string will be 1.)
  • a string, your stored memory from the previous round
  • the 1-based index of this round

• At every turn your method returns an Action object containing

  • an integer in the move field describing your action:

    • 0 for no action
    • -1 to pull a blue lever and block TT's going through this round
    • a positive integer x, not larger than the current round, to pull a red lever and try to revert back to round x
    • Invalid integers are treated as 0.

  • a string containing your memory from this round which you want to preserve. Note that storing memory is not a crucial part of the challenge. You can make good entries without storing any useful data in the string. At the first round the string will be an empty string.

• Your method should take no more time than 10 ms per round on average in a match.

• Regularly failing the time-limit results in disqualification.

Scoring

• Winning a match earns 2 points and a draw earns 1 point for both players. Loss earns no points.
• A bot's score will be the total number of points it collected.
• The number of matches played between each pair of contestants will depend on the number of entries and their speed.

Two simple example bots are posted as answers.

The controller and the first couple Bots are available here.

Test results with bots submitted until November 3.:

Total Scores:

Oldschool: 3163
Random: 5871
RegretBot: 5269
Nostalgia: 8601
Little Ten: 8772
Analyzer: 17746
NoRegretsBot: 5833
Oracle: 15539
Deja Vu: 5491
Bad Loser: 13715

^{(The controller is based on the Cat catcher challenge's controller. Thanks for @flawr providing it as a base for this one.)}

Bonus: a nice 6-minute film based on a similar concept.

Answer 1

Analyzer

This analyzes the past to make the best predictions for the future.

EDIT: Avoids blue levered times. Uses blue levers effectively. Uses red levers more effectively. Added scariness for Halloween season.

EDIT: Fixed off by 1 error.

EDIT: Improved computeWinningProbability function. Now uses red levers and blue lever more aggressively.

//Boo!
package bots;

import main.Action;
import main.Game;

import java.util.*;
import java.util.stream.Collectors;

/**
 * Created 10/24/15
 *
 * @author TheNumberOne
 */
public class Analyzer implements Bot{

    @Override
    public String getName(){
        return "Analyzer";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
                           String memory, int roundNumber) {
        /*System.out.println(Game.totalScore(history) + " : " + history);
        try {
            Thread.sleep(100);
        } catch (InterruptedException e) {
        }*/
        int roundsLeft = 100 - roundNumber;
        int myScore = (Game.totalScore(history) + roundNumber) / 2; //My number of wins.
        int enemyScore = roundNumber - myScore;                     //Enemy's number of wins.
        Map<Integer, Double> bestRounds = new HashMap<>();
        int timeLimit = 0;

        Scanner scanner = new Scanner(memory);
        if (scanner.hasNext()){     //No memory, first turn.
            boolean triedTimeTravel = scanner.nextBoolean();
            if (triedTimeTravel){
                int time = scanner.nextInt();
                if (roundNumber > time) {     //Failed.
                    timeLimit = time;
                }
            }
            timeLimit = Math.max(timeLimit, scanner.nextInt());
            int size = scanner.nextInt();
            for (int i = 0; i < size; i++) {
                bestRounds.put(scanner.nextInt(), scanner.nextDouble());
            }
        } else {
            bestRounds.put(1, 0.5);
        }

        clean(bestRounds, roundNumber, timeLimit);
        double winningProb = computeWinningProbability(myScore, enemyScore, roundsLeft);
        String newMemory = computeMemory(bestRounds, roundNumber, winningProb);

        if (winningProb >= new double[]{1.5, .75, .7, .65, .6, .55}[blue_levers]){ //Ensure success ... slowly.
            return getAction(-1, newMemory, timeLimit, roundNumber);
        }

        int bestRound = bestRound(bestRounds);
        double bestRoundProb = bestRounds.get(bestRound);

        if ((winningProb <= bestRoundProb - .05 || winningProb < .5 && bestRoundProb > winningProb) && red_levers > 0){
            return getAction(bestRound, newMemory, timeLimit, roundNumber);  //Let's find the best past.
        } else {
            return getAction(0, newMemory, timeLimit, roundNumber); //Let's wait it out :)
        }
    }

    //Should be combined with computeMemory.
    private static Action getAction(int actionNum, String newMemory, int timeLimit, int roundNumber){
        if (actionNum == -1){
            timeLimit = Math.max(timeLimit, roundNumber);
            newMemory = "false " + timeLimit + " " + newMemory;
            return new Action(actionNum, newMemory);
        }
        if (actionNum == 0){
            return new Action(actionNum, "false " + timeLimit + " " + newMemory);
        }
        if (actionNum > 0){
            return new Action(actionNum, "true " + actionNum + " " + timeLimit + " " + newMemory);
        }
        return null;
    }

    private static int bestRound(Map<Integer, Double> bestRounds) {
        int best = 0;           //If no previous rounds ... just go forward a round.
        double bestScore = -1;
        for (Map.Entry<Integer, Double> entry : bestRounds.entrySet()){
            if (entry.getValue() > bestScore){
                best = entry.getKey();
                bestScore = entry.getValue();
            }
        }
        return best;
    }

    private static String computeMemory(Map<Integer, Double> map, int roundNumber, double winningProb) {
        StringBuilder builder = new StringBuilder();
        builder.append(map.size() + 1).append(" ");
        for (Map.Entry<Integer, Double> entry : map.entrySet()){
            builder.append(entry.getKey()).append(" ").append(entry.getValue()).append(" ");
        }
        builder.append(roundNumber + 1).append(" ").append(winningProb);
        return builder.toString();
    }

    private static void clean(Map<Integer, Double> data, int round, int timeLimit) {
        data
                .entrySet()
                .stream()
                .filter(entry -> entry.getKey() > round || entry.getKey() <= timeLimit)
                .map(Map.Entry::getKey)
                .collect(Collectors.toList()).forEach(data::remove);
    }

    private static double computeWinningProbability(int myScore, int enemyScore, int roundsLeft){ //Too complex for IntelliJ
        int height = myScore - enemyScore;
        double total = 0.0;
        for (int i = Math.max(height - roundsLeft, 2); i <= height + roundsLeft; i += 2){
            total += prob(roundsLeft, height, i);
        }
        total += prob(roundsLeft, height, 0) / 2;
        return total;
    }

    private static double prob(int roundsLeft, int height, int i){
        double prob = 1;
        int up = i - height + (roundsLeft - Math.abs(i - height))/2;
        int down = roundsLeft - up;
        int r = roundsLeft;
        int p = roundsLeft;
        while (up > 1 || down > 1 || r > 1 || p > 0){  //Weird algorithm to avoid loss of precision.
            //Computes roundsLeft!/(2**roundsLeft*up!*down!)

            if ((prob >= 1.0 || r <= 1) && (up > 1 || down > 1 || p > 1)){
                if (p > 0){
                    p--;
                    prob /= 2;
                    continue;
                } else if (up > 1){
                    prob /= up--;
                    continue;
                } else if (down > 1){
                    prob /= down--;
                    continue;
                } else {
                    break;
                }
            }
            if (r > 1) {
                prob *= r--;
                continue;
            }
            break;
        }
        return prob;
    }

}

Score (since Nov 2):

Total Scores:
Oldschool: 3096
Random: 5756
RegretBot: 5362
Nostalgia: 8843
Little Ten: 8929
Analyzer: 17764
NoRegretsBot: 5621
Oracle: 15528
Deja Vu: 5281
Bad Loser: 13820

Answer 2

Nostalgia

package bots;

import main.Action;
import main.Game;

public class Nostalgia implements Bot {

    @Override
    public String getName() {
        return "Nostalgia";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
            String memory, int roundNumber) {

        int current_score = Game.totalScore(history);

        // wait until the end to use blue levers
        if (current_score > 0 && blue_levers >= (100 - roundNumber)) {
            return new Action(-1, memory);
        }

        // become increasingly likely to go back as the gap between the good old days
        // and the horrible present increases
        if (current_score < 0 && red_levers > 0) {
            //identify the best time to travel back to
            int best_score = -100;
            int good_old_days = 1;
            int past_score = 0;

            int unreachable_past = 0;
            if(memory != "") {
              unreachable_past = Integer.parseInt(memory, 10);
            }

            for(int i = unreachable_past; i<roundNumber ; i++) {
              if(history.charAt(i) == '1') {
                past_score += 1;
                if(past_score > best_score) {
                  best_score = past_score;
                  good_old_days = i + 1;
                }
              }
              else {
                past_score -= 1;
              }
            }
            if(roundNumber >= 95 || Math.random() < (best_score - current_score) / 100.0) {
              return new Action(good_old_days, Integer.toString(good_old_days));
            }
        }

        // if neither action was needed do nothing
        return new Action(0, memory);
    }
}

Not tested, just a quick stab at trying to make a bot that's difficult to block (because it decides when to pull the red lever mostly randomly) but that makes decent decisions.

Edit: I missed this rule:

If you pull a blue lever (revert stopper) no TT is possible through that round anymore

That seems like a good reason to use memory -- if you remember trying to TT to a given round, you may have failed, so you shouldn't try to TT to that round again. Edited my bot to try to avoid this.

Answer 3

Oracle

I shamelessly copied some code from Analyzer (for parsing the memory). This submission tries to pull a blue lever early and then slowly builds up his lead. I think the performance of this bot makes up for the ugly code :)

package bots;

import java.util.*;
import java.util.Map.Entry;
import main.*;

public class Oracle implements Bot {

    @Override
    public String getName() {
        return "Oracle";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        int roundsLeft = 100 - roundNumber;
        Map<Integer, Integer> rounds = new HashMap<>();
        int myScore = (Game.totalScore(history) + roundNumber) / 2;
        int difference = myScore*2 - roundNumber;
        int highestBlockedRound = -1;
        int bestScore = 0;
        boolean hasUsedBlueLever = false;

        Scanner scanner = new Scanner(memory);
        if (scanner.hasNext()) {
            //timeTravel toRound highestBlockedRound hasUsedBlueLever bestScore rounds round1 percent1 round2 percent2 round3 percent3...
            boolean triedTravel = scanner.nextBoolean();
            int time = scanner.nextInt();
            if (triedTravel){
                if (roundNumber > time) {
                    highestBlockedRound = time;
                }
            }
            highestBlockedRound = Math.max(highestBlockedRound, scanner.nextInt());

            hasUsedBlueLever = scanner.nextBoolean();
            bestScore = scanner.nextInt();

            int size = scanner.nextInt();
            for (int i = 0; i < size && i < roundNumber; i++) {
                int number = scanner.nextInt();
                int diff = scanner.nextInt();
                if (number < roundNumber) {
                    rounds.put(number, diff);
                }
            }
        }
        rounds.put(roundNumber, difference);
        final int blockedRound = highestBlockedRound;

        int roundToRevert = 0;
        if (rounds.size() > 2) {
            Optional<Entry<Integer, Integer>> bestRound = rounds.entrySet()
                    .stream()
                    .filter(x -> x.getKey() >= blockedRound && x.getKey() <= roundNumber)
                    .sorted(Comparator
                        .comparingInt((Entry<Integer, Integer> x) -> x.getValue()*-1)
                        .thenComparingInt(x -> x.getKey()))
                    .findFirst();
            if (bestRound.isPresent()) {
                roundToRevert = bestRound.get().getKey();
            }
        }

        if (roundsLeft + Game.totalScore(history) <= 0 && red_levers > 0) {
            roundToRevert = highestBlockedRound+1;
        } else if (blue_levers > 0 && roundToRevert == roundNumber && ((hasUsedBlueLever && difference >= bestScore*1.5) || (!hasUsedBlueLever && difference > 1))) {
            roundToRevert = -1;
            hasUsedBlueLever = true;
            bestScore = difference;
            highestBlockedRound = roundNumber;
        } else if (red_levers > 0 && roundToRevert > 0 && rounds.get(roundToRevert) > difference+2) {
            roundToRevert += 1;
        } else {
            roundToRevert = 0;
        }

        StringBuilder sb = new StringBuilder();
        sb.append(roundToRevert > 0).append(' ');
        sb.append(roundToRevert).append(' ');
        sb.append(highestBlockedRound).append(' ');
        sb.append(hasUsedBlueLever).append(' ');
        sb.append(bestScore).append(' ');
        sb.append(rounds.size()).append(' ');
        rounds.entrySet().stream().forEach((entry) -> {
            sb.append(entry.getKey()).append(' ').append(entry.getValue()).append(' ');
        });
        String mem = sb.toString().trim();
        scanner.close();
        return new Action(roundToRevert, mem);
    }
}

Answer 4

RegretBot

At the end of our life the match, we regret our past failures, and attempt to go back and fix them.

package bots;

import main.Action;
import main.Game;

public final class RegretBot implements Bot {

    @Override
    public String getName() {
        return "RegretBot";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        int actionNum = 0;
        if(roundNumber == 100) {
            // if it's the end of the game and we're losing, go back
            //  in time to the first loss, in hopes of doing better
            if(Game.totalScore(history)<=0 && red_levers > 0) {
                actionNum = history.indexOf("0")+1;
            }
            // if we're winning at the end, pull a blue lever if we can,
            //  to prevent our opponent from undoing our victory
            else if(blue_levers > 0) {
                actionNum = -1;
            }
        }
        // we don't need no stinkin' memory!
        return new Action(actionNum, null);
    }

}

Answer 5

Little Ten

Little Ten does a lot of multiplying and dividing by 10, using numbers that are multiples of 10, and going back to rounds that are multiples of 10.

package bots;

import main.Action;
import main.Game;

public class LittleTen implements Bot {

    @Override
    public String getName() {
        return "Little Ten";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        int score = Game.totalScore(history);
        char c = history.charAt(history.length() - 1);
        if (memory.isEmpty())
            memory = "1";

        if (roundNumber == 100) {
            if (score >= 0)
                // We're tied or ahead by the end of the match. Prevent time
                // travel if we can; otherwise whatever happens happens.
                return new Action(blue_levers > 0 ? -1 : 0, memory);
            else {
                // Travel to earlier rounds the farther behind we are if we can
                // (of course using 10 as a reference)
                if (red_levers > 0) {
                    int i = Integer.parseInt(memory);
                    int round = score <= -10 ? i : 100 - ((100 - i) / (11 + (score <= -10 ? -10 : score)));
                    return new Action(round, memory);
                }
            }
        }
        else if (score >= 7 + roundNumber / 20 && blue_levers > 0) {
            // We're ahead; we don't want to lose our lead, especially if the
            // match is close to ending. But we don't want to use up our blue
            // levers too quickly.
            int choice = (int) (Math.random() * 100),
                bound = (roundNumber / 10 + 1) * 5 - ((6 - blue_levers) * 5 - 2);
            if (choice < bound) {
                memory = String.valueOf(roundNumber);
                return new Action(-1, memory);
            }
        }
        else if (score <= -3) {
            // Possibly use a red lever if we're falling too far behind
            if (red_levers > 0) {
                int choice = (int) (Math.random() * 100),
                    bound = score <= -11 ? 90 : 10 * (-3 - score + 1);
                if (choice < bound) {
                    // Check the first round that is the lower multiple of ten
                    // and decide if we've been successful up to that point; if
                    // so, travel back to that round, otherwise go back 10 more
                    int round = roundNumber / 10 * 10;
                    if (round < 10)
                        return new Action(1, memory);
                    String seq = history.substring(0, round-1);
                    int minRound = Integer.parseInt(memory);
                    while (Game.totalScore(seq) <= 0 && round > 10 && round > minRound) {
                        round -= 10;
                        seq = history.substring(0, round-1);
                    }
                    if (round == 0)
                        round = 1;
                    return new Action(round, memory);
                }
            }
        }
        return new Action(0, memory);
    }
}

Edit: Changed the mechanics a little now that the explanation of what happens when a blue lever is pulled is clearer. Also did a bit of rebalancing.

Answer 6

Random

Random's strategy is the following:

• block with a 10% chance if in the lead and has blue levers left
• travel back one turn (replaying the last round) with 10% chance if behind in score and has red levers left

package bots;

import main.Action;
import main.Game;

public class RandomBot implements Bot {

    @Override
    public String getName() {
        return "Random";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
            String memory, int roundNumber) {

        // if in the lead and has blocks left, blocks with a 10% chance
        if (Game.totalScore(history) > 0 && blue_levers > 0
                && Math.random() > 0.9) {
            return new Action(-1, null);
        }

        // if behind and has travels left, travel back the current step to
        // replay it with a 10% chance
        if (Game.totalScore(history) < 0 && red_levers > 0
                && Math.random() > 0.9) {
            return new Action(roundNumber, null);
        }

        // if neither action were needed do nothing
        return new Action(0, null);
    }
}

Answer 7

NoRegretsBot

package bots;

import main.Action;
import main.Game;

public final class NoRegretsBot implements Bot {

    @Override
    public String getName() {
        return "NoRegretsBot";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        // every 20 turns, pull a blue lever to lock in the past
        // hopefully this will thwart some of those pesky time-travelers
        return new Action(roundNumber%20==0?-1:0, null);
    }

}

Answer 8

Bad Loser

This bot uses no memory and is surprisingly good (but it doesn't beat Analyzer or Oracle).

package main;

import bots.Bot;

/**
 * Created 11/2/15
 *
 * @author TheNumberOne
 */
public class BadLoser implements Bot{
    @Override
    public String getName() {
        return "Bad Loser";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        if (history.contains("00") && red_levers > 0){       //Subtract a zero for better performance against
            return new Action(history.indexOf("00") + 1, "");// Analyzer and Nostalgia, and worse performance 
                                                             // against everything else.
        }
        int wins = 0;
        for (char c : history.toCharArray()){
            wins += c - '0';
        }
        if (wins >= new int[]{101, 51, 40, 30, 20, 10}[blue_levers]){
            return new Action(-1, "");
        }
        return new Action(0, "");
    }
}

Answer 9

Oldschool

This bot never does any action as Oldschool doesn't believe in time traveling.

package bots;

import main.Action;

public class OldschoolBot implements Bot {

    @Override
    public String getName() {
        return "Oldschool";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
            String memory, int roundNumber) {       
        // never tries to block or travel at all
        return new Action(0, null);
    }
}

Answer 10

Deja Vu Bot

This bot tries to track when it pulls the blue to avoid red pulls into that region. Will only pull red levers when significantly behind in the score.

package bots;

import main.*;

public class Dejavu implements Bot
{
    @Override
    public String getName()
    {
        return "Deja Vu";
    }

@Override
public Action takeTurn(int blue_levers, int red_levers, String history,
                       String memory, int roundNumber) {

    if(roundNumber == 1)
    {
        memory = "-1";
    }
    int[] blevers = getBlueLevers(memory);
    char[] hist = history.toCharArray();
    int ms = 0;
    int ts = 0;
    int rl = -1;
    boolean bl = false;
    boolean url = false;

    for(int i = 0; i < hist.length; i++)
    {
        switch(hist[i])
        {
            case '1':
            ms++;
            break;
            case '0':
            ts++;
            break;
        }
    }

    if(ts - ms >= 10)
    {   
        for(rl = hist.length - 1; ts - ms <= 5 && rl >= 0; rl--)
        {
            switch(hist[rl])
            {
                case '1':
                ms--;
                break;
                case '0':
                ts--;
                break;
            }
        }
        url = true;
    }

    if(ms - ts >= 7)
    {
        bl = true;
        url = false;
        memory += "," + roundNumber;
    }

    for(int i = 0; i < blevers.length; i++)
    {
        if(rl <= blevers[i])
        {
            rl = blevers[i] + 1;
        }
    }

    if(url)
    {
        return new Action(rl, memory);
    }
    else if(bl)
    {
        return new Action(-1, memory);
    }
    else
    {
        return new Action(0, memory);
    }              
}

private int[] getBlueLevers(String s)
{
    String[] b = s.split(",");

    int[] bl = new int[b.length];
    for(int i = 0; i < b.length; i++)
    {
        bl[i] = Integer.parseInt(b[i]);
    }

    return bl;
}

}