Quote from: mberg2007 on September 23, 2013, 09:40:31 AM

Quote from: cdnbcguy on September 23, 2013, 03:58:02 AM

We profit 76 % of the time over 1,000 bets - not 50.8 % of the time like with 1 bet.

THAT'S being an investor, not a gambler.

Also - has anyone noticed that despite the 1 percent edge JD has never made a 1 % profit? It was about half that - before the current fiasco - now we know why.

Variance. Lets lower it by refusing big bets.

I'm sorry, but this is the biggest load of BS I have ever read. Clearly you have not done the math.

If you make 1000 bets with a 1% house edge, you will win 490 times and the house will win 510 times. The house will not win 76% of the time.

Variance means nothing as far as house edge. Playing many tiny bets and playing one huge bet provides precisely the same house income over time. As a gambler, you will have no advantage by placing smaller bets and winning and losing small amounts than by placing a single large bet. Over time it's just a matter of scale.

A casino runs the risk of losing the bankroll only if they don't cap the size of their maximum bets. Because obviously there's only a 51% chance of winning that bet, and thus a 49% chance of going bust from the casino's point of view. But JD does have these limits. Noone is placing bets of 1000 BTC or more. The max win is 1% of the invested capital, which makes good sense. There is no reason to limit that further.

What we have here is a situation where someone appears to be actually beating the house edge over many thousands of bets. And this is intriguing, because from a statistical point of view this should not be possible. You can't win a coin toss came if the coin is balanced towards the house, no matter what system you use.

-Michael

I DID make an error in my posting - it is a binomial distribution and a Bernoulli variable, not a Bernoulli distribution.

Nevertheless, the stats is exactly correct.

I also wrote a small program to simulate what happens when a bettor makes 1,000 bets at a 1 percent disadvantage.

After one million rounds of 1,000 bets each, that is, one billion bets, the results are

Player profits 250,803 times 25.333636363636362 %
Player loses 718,707 times 72.59666666666666 %

Just about exactly as predicted.