4 ms·
And I'm saying that you're wrong there - the chance of getting more than half of the blocks approaches 1 as the number of blocks increases, given that you have
by laverya 8y ago
And I'm saying that you're wrong there - the chance of getting more than half of the blocks approaches 1 as the number of blocks increases, given that you have 51% of the hashing power.
You're focused on the chance of getting 6 in a row. But what you should be looking at is the chance of getting at least 7 in 13, which is given by this equation:
P(K>=N) = sum(nCr(M, k) * p^k * (1-p)^(M-k)) from k=N to M
With M=13, N=7 and p=.51 - which works out to about 53%. But 8 in 15 also works, 9 in 17, etc. The limit of that probability (n+1 in 2n+1 as n -> inf) is 1.
Also, a casino is not likely to have many days in the red, just like it won't have many years in the red. (for bets only, ignoring everything else) This is because while the chance on any one bet may only be 51%, the chance of 10,000 bets, or 1,000,000 bets having a majority go south starts to get very, very small. (~27.5% for 1000 bets, ~2.5% for 10,000 bets at 51%, etc)