SMPPS buffer size probability calculator

smpps.m

% SMPPS buffer size probability calculator
%  - bitfoo - 2011-08-27

prob = 0.0000000000000001289400139122594962648449268272088374942;
log_prob = log(prob);
log_1_minus_prob = log1p(-prob);

num_hashes = 500 * 1024^3 * 60 * 60 * 24 * 30; % 30 days @ 500GH/s
num_blocks = num_hashes * prob; % a proxy for PPS

ks = 0:2*num_blocks;
ps = zeros(size(ks));

for k=ks
  log_p = 0.0;
  % n choose k:
  for i=1:k
    log_p = log_p + log((num_hashes - (k-i))/i);
  end
  % p^k * (1-p)^(n-k)
  log_p = log_p + k*log_prob + (num_hashes-k)*log_1_minus_prob;
  ps(k+1) = exp(log_p);
end

figure(2);
plot(50*(ks - num_blocks),cumsum(ps), 'linewidth', 2);
axis([-1500 1500 0 1]);
xlabel('SMPPS buffer size after 30 days at 500GH/s [BTC]');
ylabel('Probability of buffer <= x');
grid on;
print -dpdf smpps.pdf