Quote from: devans on March 04, 2018, 07:27:21 PM

Quote from: 01010100b on March 04, 2018, 06:49:31 PM

Well yes, but as B moves coins from his offsite to his onsite then his L (as per post above) changes. Let's consider the simplified situation where A and B have the same investment (say 50 btc onsite and 50 btc offsite), A is lying and B isn't, and B will move his offsite to his onsite when he gets margin called (ie when his onsite reaches 0) and not before. While it is true that B will be able to recover whereas A won't, the probability of their onsite going to 0 is the same since they have the same investment, up until the point where B actually starts moving his offsite to his onsite both A and B will evolve in tandem. So if A has the expectation of negative bankroll growth and going bust then B has the same expectation of his onsite going down too.

Sure, the moment B actually moves some coins from his offsite to his onsite the analysis changes since A and B won't have the same investment anymore, but as long as that doesn't happen B has the same (short-term) expectation of losing his onsite as A does. If A can expect to go bust then B can expect to lose his onsite as well, irrespective of whether B will be able to recover again afterwards or not.

You are correct: If an investor is not prepared to move his offsite investment onsite, then he potentially faces negative EBGlike A does in your example.

Consider this scenario: All investors initially set their offsite to be as high as permitted. The overwhelming majority of the bankroll is provided by investors who are not prepared to move their offsite investment onsite if necessary, e.g. because they don't actually own the coins. Only a single investor will move his offsite investment onsite before he is margin called. In this example, the majority of investors are overleveraged and can expect to be eventually margin called. The bankroll as a whole clearly has a negative EBG.

However, this risk is borne solely by the overleveraged investors. Each round, our "compliant" investor is risking 1.125 % of his total investment, which is 1.5x his expected value of 0.75 %. Therefore, he has a positive EBG for all bets, regardless of whether his fellow investors end up being margin called or not.

Eventually, the other investors will be margin called. As the total bankroll shrinks, the compliant investor's stake will increase until he is the only investor, but the risk to his bankroll will stay the same.

Since the investor will move his offsite investment onsite before he is margin called, it makes no difference whether he uses the offsite investment system or not. Not even being margin called and letting time pass before moving his offsite investment back onsite will cause him to have a negative EBG. There is an opportunity cost of being margin called, but he will continue to have a positive EBG, assuming that any sequence of EBG+ bets is also EBG+.

Yes you are right. What is -EBG for A is really just variance for B but B keeps being at long-term +EBG as long as B actually moves his offsite to his onsite as needed. That's where my analysis went wrong, and it is hence probably not exploitable after all.