Another question. Considering the current onsite and offsite bankroll, what percentage of the onsite bankroll would have the casino to lose so that a player with 1:3 leverage (1 onsite, 2 offsite) would lose everything she deposited?
Would it be 1/(investor's leverage/average leverage) ?
So in this example: 1/(3/(5243/2978)=1/(3/1.76)=1/1.7=0.59; 59% drop; 2978*0.59=1757 BTC lost by the casino
I think it's like this:
The investor has 1/3rd of his investment onsite, and 2/3rd offsite. Wins and losses are added and subtracted from his onsite investment. If the total bankroll decreases with 1%, his total investment decreases with 1% (fees are not included in this example). Since the offsite investment profits are also added to the onsite investment, the offsite investment decreases with 3%.
We can conclude that if the total bankroll loses 33.3%, the onsite investment would be 'used up', and therefore will be gone. With the current total bankroll that would be (.33333 * 5050BTC =) 1683 BTC
Actually what you are saying is the same, but easier. You lose everything when the total bankroll (the number you use, 5050, which was 5243 in my example) drops 1/(your leverage). It's the same as when the real, onsite, bankroll drops your leverage/the average leverage.
So the more leveraged other users are, the bigger the drop has to be based on the onsite number. In the extreme case that everybody was 1:3, the onsite bankroll would have to drop 100%, which is equivalent to the total bankroll dropping 1/3.