Was not able to watch this thread, and checked it just know. I don't see your point why you commented this on my post. I only commended dooglus on how he explained how house edge and casino investments work, since I really never had the time to research how it truly ticks. But hey, you are entitled to your opinion, but I just don't see any point why you were so hostile to it.

It's at least definitely possible for a player to be +EBG yet -EV, the edge case is simple. Suppose the casino bets 100% of its bankroll on each bet, then even though it may have +EV, at some point it's going to lose. So the player will have, with probability one, gained money and hence is at +EBG - though he may require a deep bankroll.

Fair enough. I guess I'm not overleveraged then. But what would happen if there's a margin call? Granted it may be unlikely that all investors would get margin-called at once and/or that they would actually attempt to convert BTC to CLAMs but still. I'm surprised nobody has called JD "dishonest and shameful"... or maybe they have and I just missed the drama.

And I guess I'm not leveraged on BAB either because I can get BTC by selling those JD CLAMs

Hi Everyone,

You may have noticed Primedice just went down and has been redirected. Our registrar where we registered the domain years ago (anonymous speech) which was the same registrar originally used by bitcointalk.org has been compromised. Right now the version of primedice being served is a phishing website. You might have noticed the certificate is gone, DO NOT LOGIN OR DEPOSIT until we officially say things are ok and you will be safe. We noticed this instantly and are working with that registrar to restore access to the domain.

Your balances and passwords on the real version of primedice are safe. To be clear just our domain has been redirected to a phishing site, our servers are not compromised.

In case somebody already loged into the fake primedice

IF YOU HAD SAME PASSWORD ANYWHERE ELSE AS ON PRIMEDICE, CHANGE THAT PASSWORD ASAP!

I don't know about removing that feature - seems useful for those who don't fully trust BaB - lets them limit the risk of BaB absconding with their entire investment. It would seem to create some risk (to the owners of BaB) regarding investors who state large but non-existent off-site holdings

Not sure what the argument is here? Investors who cannot or are not willing to make capital calls are essentially just gambling that variance will swing their way

You are correct: If an investor is not prepared to move his offsite investment onsite, then he potentially faces negative EBG–like 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+.

Your argument does indeed seem pretty reasonable under this assumption, but I don't think the assumption itself holds. For instance in my investment in bustabit, I am using some offsite -- and when the whale was winning, I started moving money from offsite to onsite (by depositing). I didn't even want to risk the possibility of a margin call (as it would suck to be an investor during all the downfall and then potentially miss out on a recovery). And now the site has (more than) recovered, I have taken that money back out of the site (to lower my CP risk, and keep bitcoin where I feel they are most secure).

Further more, that's exactly what the offsite system is designed to do. You can (mis)use it as a leverage system, but it's going to have ugly properties.  I think in a perfect world bustabit would have both an offsite system (like it does) as well as a leverage system (where you can state your max risk %)

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.

The assumption that B will replenish his onsite with his offsite as he takes losses doesn't hold in real life, there will be a delay before B logs in and makes those changes, and the bankroll can change by a lot very fast - before B might be able to react by moving coins from offsite to onsite. My argument above applies to a constant offsite.

inb4 "dishonest and shameful"...

2x kelly is not 0-ebg for any binary (two-option) bet. It's only for 50% bet.
For bets with low probability 0-EBG point is very slightly less than 2x kelly. Wolfram alpha
Something like up to 1.9933 Kelly
For bets with high probability 0-EBG point is more than 2x kelly. Wolfram alpha

Yup, great explanation btw. I think your summary is a lot clearer than the original.

So now that we have a way of calculating the expected bankroll growth, we can introduce another term "the kelly".

If you plot the expected bankroll growth (EBG) against how much you are risking -- you will see the chart is sort of parabolic. And the point in which  EBG is maximized is known as the kelly.

Now a casino isn't really able to make every bet "a kelly" because that would require telling players how to bet, but what it can do is limit bets that get too risky. I'm not really sure there's a good robust way to do this, at it totally depends on the context.

For instance it's my unconfirmed belief that physical casinos employ very strict limits on the general tables because they know if someone wins "big" they will just walk, instead of turning over the money. (i.e. last casino I was in, had a $50 limit on a number in roulette, unless you were a high roller in which case they were happy taking over x10 that).

Bustabit also has some pretty unique constraints, as the limits can everyone. So it really needs to balance the idea of having a "hard cap" risk amount it accepts per game, while also being able to accept as much from a single player as possible. The system it uses of having a 1x kelly per-player and a hard-cap of a 2x kelly (or currently 1.5x) per-game seems pretty reasonable.

The other interesting thing about 2x kelly, is that for a binary bet (win all, or lose all) there is 0-EBG (but positive +EV). But actually bustabit (from the houses perspective) isn't a binary bet, it can lose some and win some. So assuming I calculated everything right (which very well might not be the case, as I can't come up with an analytical solution) it's actually quite common for a 2x kelly to be positive expected bankroll growth! (and the worst case is a 2x kelly is 0 EBG)

I like how dooglus explained what he learned from his reading, made it a lot clearer to me too how things are actually computed mathematically in terms of how much investors really can profit from each bet depending on the parameters of the casino investment and the house edge. Would say that I've always just trusted that my money will grow in casino bankrolls bu never knew the science of how things really worked.

It used to be required for all users, but currently the minimum required is 1.5x (due to the 25% commission having been temporarily suspended). You can leverage that up to 3x if you want to. That is the optional part.

It's the bankroll that goes negative. The casino starts losing money if the allowed bet is too high, it's a statistical certainty long term.

Here's a simple script I made that may help you wrap your head around it:
https://jsfiddle.net/089vv8wh/

It's set to 50% max profit so you can see how quickly it goes down.
Try setting it to 1x kelly or lower (and ramping up the loop count) to see positive growth.

No, it was 2x Kelly with the commission and is now 1.5x Kelly without it.

Without the commission, investors' EV for each bet is 1 % (the house edge) and the risk per round is 1.5 % of the bankroll.

Yeah, I meant to write "and positive expected bankroll growth" but forgot the word "positive". If you take a bunch of bets with +EV and +EBG  and add another bet with +EV and 0EBG .. the result is still +EV and +EBG. But then I realized, I shouldn't even feed the troll.


Yes, so you've said. How about you open a scam accusation against me in the proper forum, and I'm happy to defend anything I've said or done without derailing this thread.

The "no expected bankroll growth" refers to the worst case (2x) and for a specific game (when the whale(s?) were aiming at the forced cashout point). In general, all investors have only been exposed to +EV and expected bankroll growth.

And devans commission seems very well deserved, his job is to run the site and bring in volume. He has been doing a good job of that. And even though his investors are up >3M dollars in a few short weeks, how lucky or unlucky players are, is out of his control. It's not unreasonable to charge a fixed volume-based commission, especially considering investors are expected to earn 75% of the site's profit. But if you disagree with the model, that's fine, you shouldn't invest.

The highest the max profit (per game) has ever been is 1.5% of the bankroll. It actually was not ever changed it's just that because the commissions were no longer charged, that went from a ~2x kelly to a 1.5x  (as kelly is effectively a measure of your risk/reward)

At 2x kelly, an investor simply has 0 expected bankroll growth. That isn't inherently bad or anything (consider that it is still massively +EV), and the risks were well published. It's also worth noting that even when the whale was playing (with multiple accounts) it seemed most of the time he cashed out before the "forced cash out". Which means those bets were all < 2x kelly.

To protect investors, the most a single player can win in one game is 1 % of the bankroll, in line with the Kelly criterion.

if RHavar confirmed 2x KC so please lets hear his opinion why he did use a 2x KC as he knows very good the risk of 2x KC