Topic: bustabit – The original crash game - page 112. (Read 61394 times)

who will  finally bring the Provably Fair option for investors?

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.

"In general, all investors have only been exposed to +EV and positive expected bankroll growth."

RHavar

HE=1% (look at ev - it's 0.99)

please dont forget the HE of a casino or the edge a player could have in case he uses KC

2x kelly is not 0-ebg for any binary (two-option) bet. It's only for 50% bet. ADDED later: and one of multipliers is 0.
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

You would think with millions of dollars at stake, you would take it more serious and actually make sure you have all the facts stated clearly and run the proper models so that what you claim is true.

You did not do this.  There were much simpler solutions to keep investors protected, but you both refused to admit to mistakes and greedily kept accepting higher bets while soliciting for a larger bankroll.

You two are dishonest and shameful human beings.

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)

Let's use Dooglus as the judge on the matter.

If I can convince Dooglus that you deceived investors, you agree to be red-tagged by everyone.
If I can convince Dooglus that any of you lied, you agree to be red-tagged by everyone.
If I can convince Dooglus that investors were not on the same playing level as RHavar, RHavar agrees to be red-tagged by everyone.

If I can convince Dooglus that your lies and deceit led to negative consequences for investors, you agree to publicly acknowledge this in a written statement.

"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.