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| 1 | from matplotlib.pyplot import gcf, legend, plot, savefig, show, title, xlabel, ylabel | |
| 2 | import numpy | |
| 3 | from numpy import arange, array, average, cumsum, std, zeros_like | |
| 4 | from numpy.random import random | |
| 5 | ||
| 6 | BLOCK_REWARD = 25 | |
| 7 | ||
| 8 | def difficulties(diff_increase, epochs, length): | |
| 9 | exps = numpy.floor(numpy.linspace(0, epochs, epochs * length, endpoint=False)) | |
| 10 | return diff_increase ** exps | |
| 11 | ||
| 12 | def payouts(diffs, hashrate, pool_hashrate): | |
| 13 | - | pool_rewards = random(len(diffs)) < pool_hashrate / diffs |
| 13 | + | pool_rewards = BLOCK_REWARD * (random(len(diffs)) < pool_hashrate / diffs) |
| 14 | return hashrate / pool_hashrate * pool_rewards | |
| 15 | ||
| 16 | def accumulate(times, hashrate, pool_hashrate, diff_increase, epochs, epoch_length): | |
| 17 | diffs = difficulties(diff_increase, epochs, epoch_length) | |
| 18 | pays = zeros_like(diffs) | |
| 19 | for _ in xrange(times): | |
| 20 | pays += payouts(diffs, hashrate, pool_hashrate) | |
| 21 | return pays / times | |
| 22 | ||
| 23 | def plot_cum_payouts(times, hashrate, pool_hashrate, diff_increase, epochs, epoch_length, linetype, label, **plot_kwargs): | |
| 24 | pays = accumulate(times, hashrate, pool_hashrate, diff_increase, epochs, epoch_length) | |
| 25 | cum_pays = cumsum(pays) | |
| 26 | ticks = arange(len(pays)) | |
| 27 | plot(ticks, cum_pays, linetype, label=label, **plot_kwargs) | |
| 28 | ||
| 29 | def plot_times_cum_payouts(times, hashrate, pool_hashrate, diff_increase, epochs, epoch_length, linetype, label): | |
| 30 | for i in xrange(times): | |
| 31 | label_i = label if i == 0 else None | |
| 32 | plot_cum_payouts(1, hashrate, pool_hashrate, diff_increase, epochs, epoch_length, linetype, label_i) | |
| 33 | ||
| 34 | def plot_cloud(): | |
| 35 | times = 100 | |
| 36 | inverse_hashrate = 1000 | |
| 37 | red_pool_percent = 50 | |
| 38 | blue_pool_percent = 20 | |
| 39 | difficulty_inc_percent = 15 | |
| 40 | epochs = 4*2 | |
| 41 | epoch_length = 2016 | |
| 42 | plot_times_cum_payouts(times, 1.0/inverse_hashrate, blue_pool_percent/100.0, (1 + difficulty_inc_percent/100.0), epochs, epoch_length, 'b-', "%d%% pool" % blue_pool_percent) | |
| 43 | plot_times_cum_payouts(times, 1.0/inverse_hashrate, red_pool_percent/100.0, (1 + difficulty_inc_percent/100.0), epochs, epoch_length, 'r-', "%d%% pool" % red_pool_percent) | |
| 44 | legend(loc='upper left') | |
| 45 | title("{times} earnings simulations: {difficulty_inc_percent}% difficulty increase every {epoch_length} blocks, {block_reward} btc block reward, miner hash rate = 1/{inverse_hashrate} initial network hash rate".format(
| |
| 46 | times=times, | |
| 47 | difficulty_inc_percent=difficulty_inc_percent, | |
| 48 | epoch_length=epoch_length, | |
| 49 | block_reward=BLOCK_REWARD, | |
| 50 | inverse_hashrate=inverse_hashrate)) | |
| 51 | xlabel('block')
| |
| 52 | ylabel('cumulative earnings')
| |
| 53 | gcf().set_size_inches(16,12) | |
| 54 | savefig('simulated_pool_variance.png', dpi=50)
| |
| 55 | show() | |
| 56 | ||
| 57 | def plot_average(): | |
| 58 | times = 10000 | |
| 59 | inverse_hashrate = 1000 | |
| 60 | red_pool_percent = 50 | |
| 61 | blue_pool_percent = 20 | |
| 62 | difficulty_inc_percent = 15 | |
| 63 | epochs = 4*2 | |
| 64 | epoch_length = 2016 | |
| 65 | plot_cum_payouts(times, 1.0/inverse_hashrate, red_pool_percent/100.0, (1 + difficulty_inc_percent/100.0), epochs, epoch_length, 'r-', "%d%% pool" % red_pool_percent, linewidth=10) | |
| 66 | plot_cum_payouts(times, 1.0/inverse_hashrate, blue_pool_percent/100.0, (1 + difficulty_inc_percent/100.0), epochs, epoch_length, 'b--', "%d%% pool" % blue_pool_percent, linewidth=10) | |
| 67 | legend(loc='upper left') | |
| 68 | title("average earnings from {times} simulations: {difficulty_inc_percent}% difficulty increase every {epoch_length} blocks, {block_reward} btc block reward, miner hash rate = 1/{inverse_hashrate} initial network hash rate".format(
| |
| 69 | times=times, | |
| 70 | difficulty_inc_percent=difficulty_inc_percent, | |
| 71 | epoch_length=epoch_length, | |
| 72 | block_reward=BLOCK_REWARD, | |
| 73 | inverse_hashrate=inverse_hashrate)) | |
| 74 | xlabel('block')
| |
| 75 | ylabel('cumulative earnings')
| |
| 76 | gcf().set_size_inches(16,12) | |
| 77 | savefig('simulated_pool_average.png', dpi=50)
| |
| 78 | show() | |
| 79 | ||
| 80 | ||
| 81 | def stdev(times, hashrate, pool_hashrate, diff_increase, epochs, epoch_length): | |
| 82 | diffs = difficulties(diff_increase, epochs, epoch_length) | |
| 83 | earnings = [] | |
| 84 | for _ in xrange(times): | |
| 85 | cum_pays = cumsum(payouts(diffs, hashrate, pool_hashrate)) | |
| 86 | earnings.append(cum_pays[-1]) | |
| 87 | return average(earnings), std(earnings), round(100.0 * std(earnings)/average(earnings), 2) | |
| 88 | ||
| 89 | ||
| 90 | print "pool 0.5 inc 1.15:", stdev(100000, 1/1000.0, 0.5, 1.15, 2*4, 2016) | |
| 91 | print "pool 0.2 inc 1.15:", stdev(100000, 1/1000.0, 0.2, 1.15, 2*4, 2016) | |
| 92 | ||
| 93 | plot_cloud() | |
| 94 | plot_average() |
