The math is all wrong - or, rather, irrelevant.
The volume the site has had of large bets is nowhere near millions. The millions of tiny bets become pretty much irrevelant compared to the much smaller number of large bets when looking at variance.
No, if you look at the variance for a number of smaller bets totaling the same wagered amount the variance will go down. When you compare the error from this to the error we were looking for (0.9% to 1.1%) you have numbers x and y such that 0.9% < x < profit < y < 1.1%. The math isn't wrong, it's just less precise. However it restrains the profit just as well. The fact is that if we used many smaller sized bets we would actually be closer to 1% profit than if we used fewer larger bets.
Try looking at what happens if you have 3 million bets at 1 satoshi and 1 bet at 500 BTC. How likely is it that profits would be anywhere near expectation? It's not just unlikely, it's impossible.
You are off by four orders of magnitude. 3 million one satoshi bets is 0.03 bitcoins. What my example represents is fifty thousand million (50,000,000,000) one satoshi bets compared to one bet of 500:
0 < 4.95 < profit in btc < 5.05 < 500
(where 0 is the loss from 500, 4.95 is -1% from house odds, 5.05 is +1% from house odds, and 500 is the profit from a single lost bet @ 500).
Point being precisely correct math is a waste of time, it is easier to calculate looser bounds which restrain the profit in the desired fashion and are just as mathematically sound.
As there's no way to get hundreds of people playing at high stakes then the choices are either:
1. Allow large max bets - getting the most possible expected profit but also taking on huge variance.
2. Don't allow large bets - the smaller you reduce the max bet the lower variance becomes (as the max bet becomes progressively nearer to the mean bet and the long-term arrives faster).
I'm fine with #1 - as it currently is. If you reduce max bets not only do you lose the few players who use them but also those who come to the site to watch them and one of the biggest factors differentiating J-D from other sites.
This isn't what I had in mind, I wouldn't make this kind of offer unless I felt I had something worthwhile to share tho. To answer elm, given that dooglus should have site profits of ten million btc by now but is struggling to hold 2000, I think what I have to say is worthwhile to him.