Some thoughts on the whale's win today (conclusion: he had a 67% chance of pulling it off).
The whale can STOP betting when he chooses, so the probability of what happened today is not as low as it seems. I haven't dug up the exact numbers, but let's assume:
1. He wanted to win 2500 BTC (after which point he would stop gambling)
2. He was willing to go down as much as 10,000 BTC before giving up
3. He was betting 200 BTC each time and always attempting to 2X his bet (this just simplifies the simulation).
I ran the following Mathematica code:
In[6]=
bankroll := 10000;
target := 2500;
n := 10000;
bet := If[Random[] > .505, 1, -1]
outcomes = Table[profit = 0;
While[profit < target && bankroll > -profit, profit += 200 * bet ];
If[profit > 0, 1., 0], {n}];
100 * (Plus @@ outcomes)/ n
Out[6]= 67.23
So, 67% of the times that he applies this strategy he would earn his 2500BTC target before going bust.
This is a very interesting take.
Unrelated fun fact:
while I don't think he's cheating, it is worth noticing that if he
was cheating, then pretending to be victim of a gambler's fallacy (like he is doing) is actually a great tactic to go unnoticed.