Topic: bustabit – The original crash game - page 109. (Read 61394 times)

Yes, the expected value of the bankroll growth in absolute numbers. BG and PG are random variables.

No. That is for expected value only. EVcasino + EVplayer = 0.

Try EBG * EPG = 1
For example, EBG = 1.05 (+5%)
So, EPG = 1/1.05 = 0.952 (-4.76%)
But i'm not sure it would work.

Investment with fixed offsite bankrolls looks very bad unlike with fixed multiplier / leverage

It is not clear for me how such investment system will behave in some cases. I would like to see the source code or investment math of BaB and JD (if that's possible and appropriate for dooglus and devans)

And here is a case.
Two investors - A is onsite and B is offsite. 1xKK.
Very bad day for casino. Investor B is in pre-margin-call position.
Investor A: 8 onsite, 0 offsite
Investor B: 1 onsite,  991 offsite
Bankroll: 1000, max profit: 10. Player bet and win.
And thas is disaster. Max profit more than onsite bankroll. It's more than casino's "cash"! Casino can not pay to player. What EBG are you talking about?
Of course, this is rare case. But math should works always everywhere. if it is not, then the whole investement system is working incorrectly.

Looks like there is no such problems at leverage investment system.

Maybe, would be better to create separate topic?

Can you check where I'm going wrong with this? Here's how I looked at it:

Let BG and PG be two random variables, BG is the house's bankroll growth and PG is the player's bankroll growth (in absolute numbers). Then:

BG + PG = 0 (money only moves back and forth between the house and the player, so a loss for one is a gain for the other and vice versa)
E[BG + PG] = E[0] (taking the expected value of both sides)
E[BG + PG] = 0 (expected value of a constant is that constant)
E[BG] + E[PG] = 0 (by linearity of expected value)
E[BG] = -E[PG]

Which leads to the player's EBG being the opposite of the house's EBG, so if the house is at -EBG then the player is at +EBG and vice versa. Perhaps by EBG is meant the median bankroll growth and not the mean bankroll growth? In which case the linearity condition above wouldn't apply.

Yes, that's exactly why I'm saying that it would be best if they just stopped referring to it as leverage, because the system doesn't function as one.

Makes sense, thanks.


Shouldn't "real leverage" still do better in that scenario if the players lose slightly more than they win as expected due to house edge?

Or more realistically betting 10k CLAM at 10%, and hitting 8 times more than expected.


I designed it to allow investors to reduce their counterparty risk. The amount of value they have offsite that they are holding back is closer to a constant than a multiple of their onsite amount. When their onsite amount doubles due to a whale losing, that doesn't change how much they own that isn't deposited.

And BAB pretty much copied JD's design for the 'offsite' stuff.

Another reason is purely practical. If all the investors have the same leverage, we don't need to calculate each investor's bankroll size after every bet. All we need to store is what percentage of the bankroll is theirs. If you have 10% of the bankroll before someone bets, you still have 10% of the bankroll after they bet. All I need to update is the size of the bankroll. If you are using 2x leverage and I'm using 3x, my share of the bankroll will increase and yours will decrease each time a player loses a bet. That adds additional complexity that I didn't want to deal with.

Following on from my post earlier about "real leverage" vs. the fixed offsite investment, maybe it's interesting to compare how going 10x using offsite investment compares with using an actual 10x leverage:

Suppose A uses offsite investment, starts with 10 BTC and declares 90 BTC "offsite". We can call this "10x offsite". He has an effective bankroll of 100 BTC and risks 1% of it per bet. So he's risking 1 BTC on the first bet.

And suppose C uses actual 10x leverage (not currently possible on bustabit, but let's assume). He starts with 10 BTC, and risks 10% of it per bet. So he's also risking 1 BTC on the first bet.

The first bet has the same effect on both investors. They win or lose 1 BTC.

If the house wins:
  * A now has an effective bankroll of 11 BTC onsite + 90 BTC offsite for a total of 101 BTC, and risks 1.01 BTC on the next bet.
  * C now has a bankroll of 11 BTC and risks 10% of it, or 1.1 BTC on the next bet.

We can see that C (using actual 10x leverage) has increased his risk per bet by 10%, while A (using 10x offsite) has only increased his risk per bet by 1%.

If the house wins again:
  * A wins 1.01 BTC, has 12.01 + 90 = 102.01 effective, and risks 1.0201 BTC on the next bet.
  * C wins 1.1 BTC, has 12.1 BTC, and risks 1.21 BTC on the next bet.

After 10 wins:
  * A has profited by 100 * 1.01**10 - 100 = 10.4622 BTC (104.62% profit)
  * B has profited by 10 * 1.1**10 - 10 = 15.9374 BTC (159.37% profit)

After 50 wins:
  * A has 7.4x'ed his 10 BTC (((100 * 1.01**50) - 90) / 10 = 7.4)
  * B has 117.4x'ed his 10 BTC ((10 * 1.1**50) / 10 = 117.39085287969579)

So in the best case, the 'real leverage' investor does a lot better than the fixed 'offsite' investor.

In the worse case, where the player wins all his max bets, the 'real leverage' investor also clearly does a lot better than the fixed 'offsite' investor. The fixed 'offsite' investor always (until he goes bust) has at least 90 BTC invested (his offsite amount), and so risks at least 0.9 BTC every bet. Since he started with 10 BTC, he will be bust after just 11 or 12 winning max bets, whereas the 'real leverage' investor will still have 0.515 BTC left even if the player wins 50 max bets in a row.

This likely means that the "real leverage" player does worse than the fixed offsite investor in the much more common case where the player wins and loses more equally.

All it takes is a whale betting 9 million CLAM at 99%

Slightly different question - is there a reason why "leverage" or "offsite" on BAB and JD is not percentage-based but a fixed amount? I.e. if I have 5 coins onsite, I might want to set offsite to 100% of onsite instead of 5 coins and that way offsite could go up or down. This would make the whole EBG- theory of the last few pages more in line with reality.

I think it's confusion between the most a single account can bet in one round, and the most all the accounts together can profit by in one round.

So two confusions: one account vs. all of them, and the amount staked vs. the amount profited.

Fun fact: not a single person has ever been "margin called" on JD. Probably because the bankroll is so large compared to the size of bets that happen that there's never a significant percentage downturn in the bankroll.

Even if you're at 25x offsite, the bankroll needs to draw down 4% before anyone is margin called. The current bankroll is 19.6 million, so the site would need to lose 784,000 CLAMs to cause the riskiest investor to get margin called. That's 8 max-profit bets. (JD max profit is 0.5% of the bankroll).

It's not impossible, but it does seem pretty unlikely.

That doesn't sound right. How can the chance of bankruptcy ever be zero?

Can you quote where they stated this?

I personally do not understand why RHavar stated this if devans's statement is true:


The only explanation I am able to see is that devans is only a front man on the papers and in reality RHavar pulls the strings.

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.

I guess the big "/s" matching the color of your trust wasn't big enough for you? Sorry if I gave you any wrong ideas. Please focus on your BAB crusade instead, preferably in an appropriate Scam Accusations thread.

There's no reason to call dooglus these things.  If dooglus announced 1% of house bankroll as max profit and then allowed 2% of house bankroll as max profit instead, all while taking a direct commission from the higher wagers, then yes, it would be the same.

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

Kelly is the same for both, but the chance to go bankrupt goes from 0 to X% depending on the amount of leverage. At high enough leverage, going bankrupt is almost a certainty because of variance.

I've been attempting to find a good answer to your question, and came up with a surprising realization. Your "A" guy would appear to be running a 2x kelly risk, and so we would say he has zero expected bankroll growth. We know that if the percentage you risk is twice the house edge then your expected growth is zero.

BUT... he is only risking 2x on the first bet. After that his offsite stays constant. If the house loses money, A starts risking more than 2x kelly, and if the house wins money, A finds himself risking less than 2x kelly. A isn't really using "leverage" at all. Leverage would be where he is constantly risking 2%. But this "offsite" feature means he is always risking 1% of (onsite + 50) - which is quite a different thing.

In conclusion, we can't accurately say that if you go 2x using offsite investment then you can expect 0 bankroll growth. That's not true, because kelly only talks about what happens if you are risking the same percentage of your actual bankroll on every bet, and A isn't...

That doesn't necessarily follow. If you have a billion dollars worth of BTC, you could calculate what that's worth in CLAM and declare that as your "offsite" investment. It doesn't matter that there aren't enough CLAMs in the world to actually convert it to CLAMs, it's still part of your effective bankroll, which you want to risk 1% of. The "offsite investment" feature allows you to effectively use your BTC in the JD bankroll without having to even convert it to CLAM.

There isn't a problem with the offsite investment feature.  The feature itself is fine.  It's just that RHavar and devans deceived investors by stating a kelly criterion that was 1/2 of what it really was while profiting greatly at their expense.