It's probably not a big deal for JD, but I think that can be potentially harmful. Once the bankroll is "big enough" (which JD's clearly is) a new investor's investment isn't going to make the site any more attractive or bring in any volume (i.e. investor gains are going to be zero-sum). When investors see that the max-bets the site accept are a tiny fraction of the kelly, they'll be incentivized to increase their leverage -- effectively taking (expected) money from conservative investors (which will push them into doing the same thing).

And now you end up with a potentially pretty unstable bankroll, as the best strategy for the highly-leveraged investors it to divest their position when ever they see a whale (which ironically is what a big bankroll is for) or have a very significant risk of a whale busting them.

But as I said, probably not a big deal for JD as your bankroll is sufficiently big that even with instability (or a big margin call) it'll have no problem supporting the players you have.

Now that I think I understand what 01010100b is saying, if I understand correctly he was saying if people abuse the offsite feature and put themselves into leveraging, it can cause them to be in negative expected bankroll growth when a whale is betting (true enough) and if enough people do it, it'll put the overall bankroll in negative during a whale betting (true enough, even though it'll only affect the people who have leveraged themselves that way). However I think he made the same mistake I struggled with too, which was thinking that if the bankroll is -EBG that would allow a player to be +EBG.  Fortunately (for investors) this isn't the case, so there's no real abuse avenue.

So there's actually no real issue, just investors need to be aware if they're going to use the offsite feature (especially if they aren't using it as intended) it can easily backfire and the variance will take them out.

But as always, it's really great people verifying and double checking things. Especially valuable when people like Luxo42 find mistakes, which is something I always appreciate (as honestly, my math skills are a lot weaker than 01010100b's and Luxo42's, I've just been working on this problem domain for quite a while)  

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 %)

I don't think so. DarkStar's reply makes perfect sense, maybe re-read it again =)

Taking your example: "Suppose there are two investors, A and B, and each have 50 btc onsite and 50 btc offsite. A is lying about it but B isn't."

A 50 BTC loss to A is 100% loss of their bankroll, but a 50 BTC loss to B is only a 50% loss. This drastically changes things as a margin call to A is fatal, while B would just be looking at replenishing their onsite investment.

Touché, I checked again and you do indeed seem right. I'm both pretty embarrassed about my math and impressed by yours. Well done

You sure about that? It looks to me that the worst case is for the casino is low-value betting on high multipliers from the casinos perspective, but this is generated by a player betting a large amount on a low multiplier. (i.e. if a player is betting 1 BTC to try win 10 BTC,  from the casinos perspective this is a 10 BTC bet trying to win 1 BTC)

Oh wow, brilliant work. I always thought 2x kelly = 0 EBG on a binary bet, but your formula looks correct and it shows that 2x kelly = 0EBG only for the specific case of 2x bet. This actually seems like it's rather good news for investors.

So currently bustabit restricts the per-game limit to 1.5x kelly, but let's assume it used 2x -- the worst behavior could be triggered by a whale max-betting on 200 accounts which would set the forced-point to 1.01x (and stop the game server accepting any new bets). In this kind of insane case, it would only be very slightly negative EBG. But in a more common case of people aiming at higher multiples (especially lottery-style bets), a 2x kelly still leads to very healthy +EBG.

What would be a really cool solution, is that that you dynamically adjusted the limits based on the persons bet multiple. However, I can't really see how to do that cleanly in bustabit without removing the manual-cashout, which would totally suck.

Probably the best thing for bustabit would to never go above 1.99x at the most extreme. That should guarantee that all games are +EBG. Although honestly, I'm not entirely sure that's the best idea. As EBG is only one of the many things that bustabit needs to control for, another thing for instance is controlling variance. Because investing isn't provably fair, if a whale came and won 80% of the bankroll it would look pretty bad even though the site is doing everything correctly.

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)

Your definition of "expected bankroll growth" isn't quite accurate. Have you seen this explanation:
http://www.therxforum.com/showthread.php?t=479974

?

It comes with some worked examples, so it makes it clear. In there he shows an example of betting 1% of your bankroll leading to +EBG and then betting 25% of your bankroll leading to -EGB  (even though your EV just goes up 25x).


So to answer your question, it's the actual expected bankroll growth that goes negative if the house risks over 2x kelly  (and obviously only for those specific bets). The original paper goes into some detail of why optimizing for expected bankroll growth rather than EV is the correct thing to do. Although it's worth noting that the assumptions the kelly makes are pretty unrealistic for a casino (players have a finite bankroll, will only play a finite amount of games and are attracted by higher limits)

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.

But the statement (with the word "positive" added) is totally correct.


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 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)

Just so you know, this doesn't really make a difference. Let's say I sent my bitcoin to someone who lived in a country with capital gains tax, and they sold them -- they wouldn't need to pay capital gains tax either, because they haven't made any capital gains.

So really, the service you are offering is pretty generic money laundering (you obfuscate the source of someones money, so they can get away without paying tax). Which I won't judge on it's ethics, but you should be aware it puts both you and your customers at massive risk (with penalties that frequently involve prison).

But besides, I also think this is a pretty foolish way to do tax evasion. Let's say I have a small amount of capital gains tax I want to brazenly avoid paying, I think it'd be a lot better to just find someone on localbitcoin and do an OTC trade. If the tax office ever found out and believed you didn't do it intentionally, you would probably just have to pay back taxes and penalties. But if someone used a service that is marketed explicitly for tax-evasion, then ... ouch.

And for larger amounts of money, it would be crazy to take all that risk to just avoid tax. If it's pure capital gains you're talking about, seems like it would be pretty straight forward and legal to just relocate to a country without such tax.

 

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.

So the reality is, investors were exposed to exactly what was promised: a lot of variance, a lot of EV and a lot of expected bankroll growth (even if there was an occasional bet that didn't improve it).

I think the ideal would be that every investor can pick their own max kelly (e.g. 0.5x, 1x or 2x) and the max-profit becomes a reflection of that. For me personally as an investor, I would rather high risk (e.g. max of 2x kelly) because for me the greatest risk is simply the counter-party risk (you basically send someone your coins, and hope they're honest with them) but I've talked to some other investors who have said they would prefer a 0.5x kelly as they find the swings disconcerting.

In the end though, everyone needs to look at the risks and decide if it's something they want to partake in. But honestly, this whole discussion is a waste of time: bustabit did exactly what was promised and investor are now sitting on $3.1 million dollars in profit (which they are free to withdraw at any time) after merely weeks.  My understanding from talking to some of the larger investors is that everyone is very happy with the way it is being operated (although there admittedly were some grumblings about the commissions back when the site was deep in the red).

--

Also to clarify, I am strictly speaking as just a normal user/investor -- I do not have an ongoing role in bustabit. I am just trying to clarify the nonsense being posted. Do not take anything I say as an official statement or position

Without knowing the house edge in this scenario, it's not possible to compute.

If you are referring to bustabit, I believe it launched such that the worst case for investors (assuming multiple account aiming for max-profit) was a ~2x kelly. After the update, it was changed such that the worst case would be ~1.5x kelly.  All of these risks were clearly documented


That doesn't impact the kelly at all, as the site is risking based on your post-dilution fee bankroll.

I think the way that makes most sense for me, is that the house needs to sort of assume a whale has infinite money. Like if you imagine dragonmaster2's "100% risk" scenario, it's just a matter of time before the infinite angry whale is guaranteed his win.

But if you invert the scenario, it doesn't really make sense to assume you can be a gambler with an infinite bankroll. And with any finite bankroll, all you can achieve is having a very large chance of busting the house -- but you can never turn that into a "profitable" scenario.


So when the house is risking more than a 2x kelly, you have a sort of weird scenario where it's bad for the house (it'll probably go broke) but also bad for the player (it'll still have an expectation to lose)

Well it completely depends on how you expect people to bet. If you are assuming the "worst case" of high-profit bets then Daniel is right. If there's more modest bets that aren't fully utilizing the bankroll, then the investor who decided to leverage will probably end up doing better (as their leverage will be closer to the kelly).

Probably Daniel should've added said: "Assuming an angry whale ..." to make it more correct, but honestly I think very few people really appreciate the harm in over-leveraging so I think the site has a duty to err on the side of pushing people into not using offsite for the purpose of leverage.


I remember after I sold MoneyPot to the current owners, they did a few little changes that resulted in the bankrollers risk being a worst-case going from a 1x kelly to a worst case 3.33x -- no matter how hard I tried (including even writing a simulator, that showed an angry whale would consistently bust them) they never listened. It's just not intuitive for people to realize that despite being +EV you can still expect to keep busting due to over-leverage (and funnily enough, even after they should've learnt the hard way and lost most of their bankroll they just resorted to hacks like limiting max-bet instead of addressing the core issue)

And to be honest, the whole idea of negative expected bankroll growth while having positive expected profit really screwed with my head. It took a lot of creating simulations to get a grasp on it. And the part that I found the most counter-intuitive is that if the casino is over-risking to the point that it expects to lose money, shouldn't it be profitable for a whale to play there?

Nope. It's just your reading comprehension sucks.


Devans said "the most a single player can win"  ... he is talking about max profit, and I said "the max bet" referring to the most you can bet at once.

That's why bustadice only restricts the max profit because each bet is "single player", while bustabit needs to restrict both to protect both investors and not ruin the playing experience for other players.

Anyway, I really don't want to waste more energy on this. I'll let someone else waste their time with you

I would have thought the answer is pretty obvious. Based on the betting, I assume it was a single person (although I have no insider knowledge that would allow me to verify that) who was consistently betting more than 1% of the bankroll amount. It's just that site never promised to stop it, and that it's irrelevant for the reasons I explained.

I really don't understand what your problem is, especially considering how well investors have been done (and currently have totally commission free earnings)



Forgot to switch accounts?

Just to be clear, I didn't allow anything. I am just a passive investor there, it's Daniel who is the owner.

And secondly, if you read the FAQ and terms you would see that the site never deviated from what it promised. I guess there's some ambiguity on the term "player" as you could interpret it to mean "person" or you could interpret it to be "bustabit account". However, bustabit has had a long standing policy of allowing multiple accounts for a single person (doing anything differently would imho be kind of crazy, as it's a policy that's impossible to enforce and results in a lot of false-positives like when people from the same house hold are players)

But the reality is it doesn't matter. Take a look at bustadice.com for instance, which operates in virtually the same way with a similar size bankroll and players are free to bet up to like 2000 BTC if they want. It would actually be advantageous to bustabit and investors if bustabit allowed the same thing (after all, if someone bets 1000 BTC in a single game, that's 10 BTC of EV) but the entire reason that bustabit doesn't allow it is to protect other players. Whales that bet a lot of money are able to drive the "forced cashout point" down really low, which can really negatively impact other people who were hoping to aim at higher multiples.

tldr; the max bet restriction exists to protect the experience of other players, not investors/the house

The guy is just an idiot, I am investing on the same terms as everyone else. Ironically the whale just busted and everyone (including me) in the bankroll should now be at a considerable profit. People like quickmaffs take the term "the house always wins" too literally, invest and then start crying at the slightest down turn in profit.

Some thing I used to always tell players was "the casino isn't a charity" when they thought there was free money to be had from gambling, but the same really can be said for investors. The site isn't giving money to investors as some act of kindness, it is paying them in +EV to accept a lot of risk and eat a lot of variance.

Anyway, as of now investors are up 280 BTC, I doubt anyone has cause for complaint