For what it's worth, come-from-beyond has a point when he says that the situation is exaggerated by an artificial situation with just two accounts.
I decided to try a broader simulation, and see what the effects are.
So, I set this up with 26 accounts, each having a different balance from 1000 to 26000, and bumped it up to a million trials to get consistent results despite statistical noise having a greater impact on a more complex situation.
Here's the code:
#include
#include
// takes a balance; returns an interval to block forging time.
double rollem(double balance){
double roll = 0.0;
while (roll == 0.0) roll = ((double) rand())/RAND_MAX;
return 1000 * roll / balance;
}
main(){
double balances[26], times[26];
double min, totalmoney = 0.0;
int wins[26];
int winner, count, trial, TRIALS = 1000000;
for (count = 0; count < 26; count++){
balances[count] = (count+1) * 1000;
totalmoney += balances[count];
wins[count] = 0;
}
for (trial = 0; trial < TRIALS; trial++){
for (count = 0; count < 26; count++){
times[count] = rollem(balances[count]);
}
min = times[0];
winner = 0;
for (count = 1; count < 26; count++)
if (min > times[count]){
min = times[count];
winner = count;
}
wins[winner]++;
}
for (count = 0; count < 26; count++){
printf("%c got %f%% of the wins with %f%% of the money.\n", count+'A',
100*(double)wins[count]/TRIALS,
100*(double)balances[count]/totalmoney);
}
}
The effect is still present, in that the accounts with larger than median balances get more than their share of blocks, but it's considerably less important given the number of accounts and range of account values under consideration. I deliberately let the smaller account win the block in every tie, just to ensure that the bias demonstrated was not due to a systematic error going the other direction.
In this broader simulation, people do not get three times the number of blocks relative to someone with half their balance; Instead they get only a tiny fraction more than double. (note, these pairs are AB, BD, CF, DH, EJ, and so on).
Here are the results:
A got 0.269800% of the wins with 0.284900% of the money.
B got 0.545100% of the wins with 0.569801% of the money.
C got 0.832000% of the wins with 0.854701% of the money.
D got 1.076900% of the wins with 1.139601% of the money.
E got 1.364900% of the wins with 1.424501% of the money.
F got 1.627700% of the wins with 1.709402% of the money.
G got 1.925300% of the wins with 1.994302% of the money.
H got 2.226500% of the wins with 2.279202% of the money.
I got 2.473800% of the wins with 2.564103% of the money.
J got 2.812900% of the wins with 2.849003% of the money.
K got 3.108000% of the wins with 3.133903% of the money.
L got 3.333500% of the wins with 3.418803% of the money.
M got 3.667000% of the wins with 3.703704% of the money.
N got 3.954400% of the wins with 3.988604% of the money.
O got 4.229700% of the wins with 4.273504% of the money.
P got 4.554900% of the wins with 4.558405% of the money.
Q got 4.813100% of the wins with 4.843305% of the money.
R got 5.146400% of the wins with 5.128205% of the money.
S got 5.400300% of the wins with 5.413105% of the money.
T got 5.720200% of the wins with 5.698006% of the money.
U got 6.039900% of the wins with 5.982906% of the money.
V got 6.336200% of the wins with 6.267806% of the money.
W got 6.610200% of the wins with 6.552707% of the money.
X got 7.018400% of the wins with 6.837607% of the money.
Y got 7.296000% of the wins with 7.122507% of the money.
Z got 7.616900% of the wins with 7.407407% of the money.
