riskSimulationSingleBattleFlex.m

% Main Function associated with risk simulator GUI
% flexibility in changing number of dice that is rolled

function probabilities = riskSimulationSingleBattleFlex...
    (num_attack, num_defense, num_trials, diceMax, attackDiceLim, ...
    defenseDiceLim, numConsideredLim)

% Attack and defense always roll as many dice as they can, but bounded by
% the number of dice that are specified for both sides.
% For the attack, the greatest number of dice it can roll is one less than
% the total number of remaining troops. The greatest number of dice the
% defense can roll, however, is the number of defending troops.

% We are always considering the greatest number of troops possible,
% bounded by the specified number considered parameter. The number of
% troops is the smallest of either the parameter itself, one less than the
% number of attack dice, or the number of defense dice. 


ATTACK = num_attack;    % number of attacking troops
DEFENSE = num_defense;  % number of defending troops
probabilities = zeros(num_attack, 1);

for k = 1 : num_trials

    num_attack = ATTACK;
    num_defense = DEFENSE;
    
    while num_attack > 1 && num_defense > 0
        % figuring out the number of dice
        
        if attackDiceLim == 0
            num_diceAttack = num_attack - 1;
        elseif num_attack - 1 > attackDiceLim
            num_diceAttack = attackDiceLim;
        else
            num_diceAttack = num_attack - 1;
        end

        if defenseDiceLim == 0
            num_diceDefense = num_defense;
        elseif num_defense > defenseDiceLim
            num_diceDefense = defenseDiceLim;
        else
            num_diceDefense = num_defense;
        end
        
        % figuring out number of considered:
        if num_diceAttack >= numConsideredLim && num_diceDefense >= numConsideredLim
            num_considered = numConsideredLim;
        elseif num_diceAttack <= num_diceDefense
            num_considered = num_diceAttack;
        else
            num_considered = num_diceDefense;
        end
            

        rollsA = [];
        % roll and sort dice
        for j = 1 : num_diceAttack
            rollsA(j) = floor(rand()*diceMax) + 1;
        end
        rollsA = sort(rollsA, 'descend');

        rollsD = [];
        for j = 1 : num_diceDefense
            rollsD(j) = floor(rand()*diceMax) + 1;
        end
        rollsD = sort(rollsD, 'descend');


        % decide number of lost troops
        countA = 0;  % this counts how many dice the attack loses
        countD = 0;  % this counts how many dice the defense loses
        for j = 1 : num_considered
            if rollsD(j) >= rollsA(j)
                countA = countA + 1;
            else
                countD = countD + 1;
            end
        end

        num_attack = num_attack - countA;
        num_defense = num_defense - countD;

    end

    probabilities(num_attack) = probabilities(num_attack) + 1;

end

probabilities = probabilities / num_trials * 100;