Legends WR Calculator

%Sweep over win rates

%Win rate
wr = 0.2:0.01:1;
E = zeros(size(wr));

%Number of stars to advance, assume 2 serpent stars
nAdv = 6;

for wri = 1:length(wr)
%Create the absorbing markov chain. This step isn't strictly necessary, but is
%good for being able to check that things came out correctly

M = zeros(nAdv+3); %Matrix is mostly zeros. Need three extra states for two serpent and one rank up state
M(1,1) = 1; %Once rank up is reached that state is final

%Fill in the common elements
for i = 2:nAdv+2
  M(i,i-1) = wr(wri);
  M(i,i+1) = 1-wr(wri);
end

%Fill in the last row
M(nAdv+3,nAdv+2:nAdv+3) = [wr(wri),1-wr(wri)];

%Display what M is
%disp(M)

%Take the non-absorbing submatrix
Q = M(2:nAdv+3,2:nAdv+3);

%Figure out the N matrix
N = inv(eye(nAdv+2)-Q);

%Take the expected number of games
E(wri) = sum(N(nAdv,:));

end

figure('Position',[100,100,1000,750])
semilogy(wr*100,E,'LineWidth',2)
xlabel('Deck Win Percentage')
ylabel('Expected Number of Games to Rank Up')
grid on
title('Ranking Up at Rank 4-2')
set(gca,'xtick',[20:10:100])

figure('Position',[100,100,1000,750])
plot(wr*100,E,'LineWidth',2)
xlabel('Deck Win Percentage')
ylabel('Expected Number of Games to Rank Up')
grid on
title('Ranking Up at Rank 4-2')
set(gca,'xtick',[20:10:100])