Topic: bustabit – The original crash game - page 112. (Read 61162 times)

"To protect investors, the most a single player can win in one game is 0.75 % of the bankroll, in line with the Kelly criterion."




You guys definitely defrauded investors, lied, and abused your powers.  Full scam accusation coming soon.

Stop asking me to leave to try and hide.  We had the opportunity to handle this in a civil manner, but RHavar, being the scumbag he is, tried to discredit me by calling me an idiot and encouraged everyone to look away.

When millions of dollars are at stake and you are both profiting off of it, the details need to be fully investigated and combed through, not just swept under the rug like you guys have attempted to do.

You are both dishonest and shameful human beings.

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.

I thought you had already lost all your money on just-dice!

dooglus, you seem to know alot about bustabit. next step is to make offer and buy bustabit.


i would gamble there. thus, you would become very very rich

Well, the bankroll can never go negative - the house only ever risks a percentage of it, so at worst it approaches zero. Maybe you mean the site profit goes negative, but that's not necessarily the case either. It's possible for the house to over-leverage and still make a profit by getting lucky.

Thanks to Ryan's linked article I think I understand it now. The point I wasn't understanding is that "expected value" isn't the same as "expected bankroll growth".

Specifically, the expected value of each bet is 1% of the amount wagered, whether the house is over-leveraged or not. It's always positive so long as the house edge is positive.

Whereas the expected bankroll growth is more to do with the factor by which the bankroll grows with each bet.

For instance, suppose the house is risking 50% of its bankroll with every bet, that the payout is 2x, and the chance of the player winning is 49.5%. That's a standard 1% house edge bet, but massively over-leveraged.

Each time the house wins a bet like that, it adds 50% to its bankroll, or in other words it multiplies the bankroll by 1.5
Each time the house loses a bet like that, it loses 50% of its bankroll, or in other words it multiplies the bankroll by 0.5

In the long run, the house wins 0.505 times per bet, and loses 0.495 times per bet.

We can calculate the expected bankroll growth factor per bet as (growth when winning)^(probability of winning) * (growth when losing)^(probability of losing).

In this case, that's:

  1.5^0.505 * 0.5^0.495 = 0.8708

In other words, when the house is risking 50% of its bankroll every roll with a 1% house edge on a 49.5% bet, the house expects to multiply its bankroll by 0.8708 each roll, on average.

If we change the maximum bet to allow players to only win 2% of the house bankroll each bet, the multiplies change to 1.02 for a win and 0.98 for a loss, and so the expected bankroll growth factor changes to:

  1.02^0.505 * 0.98^0.495 = 1

In other words risking 2% of the bankroll with a 1% edge leads to a static bankroll.


What really made me see it, is imagine the case whether the house risks 50% of its bankroll each time, and starts with 100 units.

If the player wins their first bet, the bankroll is down to 50 units. Then if the player loses a bet, the bankroll only goes up to 75.
On the other hand, if the player loses their first bet, the bankroll goes up to 150 untis, but then if the player wins, the bankroll again goes down to 75.

So each time the player makes two bets where one wins and one loses, the bankroll drops 25%. In the long run, the number of wins and losses is going to be about the same (assuming 50% betting, and no house edge, let's say). We can pair each winning bet with a losing bet, and see that the house is going to lose 25% about n/2 times, where n is the number of bets that were made. There's a tiny chance that the player does exceptionally badly and ends up massively down, but by far the most likely outcome is that the house loses almost all of its bankroll.

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. Thanks for sharing.

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)

Sorry to derail the scam accusations, but I'm still not happy with this.

What is it that actually goes negative when the house risks over 2x Kelly? It can't be the expected profit per bet, since that is always 1%, hence positive. And it can't be the expected bankroll growth, since that's simply the expected profit per bet summed (or averaged) over all the bets, which therefore is also a constant 1%. So what is it? I can't find a good Kelly resource. They're either too basic, and simply say "expected bankroll growth goes negative" (which I don't think is accurate) or they go far too deep into the math and confuse me.

Oh, I see what you mean! Yeah, that's correct.

ok, i understand. i meant zero-growth bankroll point for investors was at 1.5% of bankroll, and now it's at 2% of bankroll.

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.

I think the worst-case risk growthed from 1.5x Kelly to 2x Kelly after comissions' suspend, but not dropped?

2x Kelly was the risk in the worst-case scenario, where all bets in a round target the same multiplier and would reach the round's profit limit. The intention behind that is to provide high rollers with a good experience on bustabit when several of them are playing at the same time, even if it means accepting suboptimal bets.

Even so, investors were never exposed to risk that carries an expectation of negative bankroll growth. When I suspended the commission, the worst-case risk dropped to 1.5x Kelly, ensuring that their expected bankroll growth was exclusively positive.



That is only the case for an individual investor that (ab)uses the offsite investment system to risk more than he actually has.

The offsite system is meant to allow investors to lower their counterparty risk and free up liquidity by not depositing their entire investment. I strongly recommend to only use it for that purpose. If you use the offsite system properly or don't use it at all, you never have an expectation of negative growth.

If you honestly believe that I have defrauded someone, open a scam accusation and let the community be the judge.

Feel free to link to that scam accusation in this thread as well, but please stop hijacking it. Even though you keep moving the goalposts, all of your accusations have been addressed and this is getting repetitive.

now I am confused. if 2x is leading to 0 bank toll growth then 3x is even worse and should lead to bank roll = investors losses. I dont see a reason to allow 3x then. please correct me if I am wrong

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.

I'm confused and can't really tell from looking at the site (never even deposited bits on v2) -  Is the 2x Kelly required for all investors or is it by choice?

Bullshit. More lies.  You expect me to be formal after you tried to hide all of this and dismiss me by abusing your trust and insulting me?  I will be both keeping this thread active and be opening up a full scam accusation on you and your partner.

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.