Just rolled double sixes 5 times in 8 rolls in backgammon… AI says the odds of that happening are:
1,175,463 to 1
We live in a world of black swans
Discussion
Saw 46 come up on roulette 6 times in a row, don't even know the odds but it was insane
A low probability event is not a black swan, which after all were abundant and long-standing where known. In your example you demonstrate our knowledge of the event and how likely the known event is to occur, in the long run.
Love your work, great to see you here!
Good point
Won’t see another one !!
saw a post on r/sipstea that reminded me of this. A guy who was declared dead for 14 min …. then revived, bought a lotto card to celebrate and won a car, then bought another one and won a six figure amt.
there’s a low probability or black swan event.
An absolutely diabolical result for your poor opponent!
I don’t agree:
This is a binomial probability problem. Each roll of a fair six-sided die is an independent trial with success probability \(p = \frac{1}{6}\) (rolling a 6) and failure probability \(1 - p = \frac{5}{6}\) (rolling anything else). We want the probability of exactly \(k = 5\) successes in \(n = 8\) trials.
The binomial probability formula is:
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]
First, compute the binomial coefficient:
\[
\binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!} = 56
\]
Substitute into the formula:
\[
P(X = 5) = 56 \left( \frac{1}{6} \right)^5 \left( \frac{5}{6} \right)^3 = 56 \cdot \frac{1^5 \cdot 5^3}{6^8} = 56 \cdot \frac{125}{1,679,616} = \frac{7,000}{1,679,616}
\]
Simplify the fraction by dividing numerator and denominator by their greatest common divisor (which is 8):
\[
\frac{7,000 \div 8}{1,679,616 \div 8} = \frac{875}{209,952}
\]
This fraction is in lowest terms. As a decimal approximation, this is about 0.00417 (or 0.417%).
The math is beyond me, I will admit
I'd ask AI to write simple-to-understand code to virtually replicate how you rolled the dice a few billions of times and then calculate how many of the results matched what you saw. Then review the code to see if it seems to match what you expect and run it.
Even when I calculate odds myself, I often write a quick script to brute force an approximation for assurance. CPU cycles are cheap.
Pretty sure that formula is for rolling 6, 5 out of 8 times. nostr:npub1trr5r2nrpsk6xkjk5a7p6pfcryyt6yzsflwjmz6r7uj7lfkjxxtq78hdpu mentioned rollings 6s (two dices of 6), 5 out of 8 times.
Start solo mining
So many things are happening at once that 1 in a billion things are happening all the time.
That of course doesn't solve the challenge of predicting which 1 in a billion thing will happen.
Ai is bad at math tho
Plug in a bitaxe ASAP!
While certain outcomes are more special than others, every specific outcome is rare. Therefore don't restrain yourself simply because an outcome is unlikely, but rather maximize what you do in your life and you will see many amazing events.