bustabit – The original crash game

[Timetwister]

As both sites are yours now, you could offer some way to invest in both places at the same time (shared bankroll). I'd prefer that way more than the "offsite" option, as I may not notice that a casino is losing money (I don't want to have to monitor it constantly), and it's possible that both casinos go bad, which would mean increasing the leverage on both of them, something very risky.

[1713966826]

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[Timetwister]

Some more questions:

1. What's the probability of bust at 1?
2. What's the formula to know the probability of bust before a round reaches X?

Without leverage, the maximum risk per player and round is 0.75% of the bankroll (1x Kelly). If a player were to exceed that he is forced to cash out, but other players aren't. The maximum risk for the entire round is 1.125% (at worst 1.5x Kelly).

If you don't leverage, you will always be guaranteed a positive expected bankroll growth. But if you leverage by 2x you are risking 3x Kelly in the worst case scenario of a super whale use multiple accounts, so your expected bankroll growth may be negative in the worst case scenario.

3. So, if I understand it correctly, assuming players were hitting the maximum bet per round every round (we wish), we'd get 0 expected bankroll growth with a "leverage" of (2*0.75)/1.125=4/3

Is that true?

4. I insist on please checking a way to share Bustadice and Bustabit bankrolls for those of us interested, it would in practice make both bankrolls bigger, maximum bets bigger, and expected returns from investing higher. Good for everyone.

[RHavar]

4. I insist on please checking a way to share Bustadice and Bustabit bankrolls for those of us interested, it would in practice make both bankrolls bigger, maximum bets bigger, and expected returns from investing higher. Good for everyone.

I don't think this is a good idea. Bustadice uses a pretty unique provably fair system that gives investors and Daniel himself much better assurances than any normal provably fair site (including bustabit). Even should the bustadice server and database get hacked, the hacker would still not be able to predict rolls. This means that if a whale comes on bustadice and wins a lot of money, Daniel has very strong assurances the wins are legitimate (or me being also hacked or the hacker). Likewise this ends up extending considerable protections to investors (assuming they believe me and Daniel to be independent).

 And unfortunately these same guarantees can't be extended to bustabit itself, due to the real-time nature of bustabit. And you can't really combine the bankrolls without inheriting the security aspect of the weakest. And I think in practice these are extremely useful guarantees, and should not dismissed lightly. But also taking a step backward, the bustabit/bustadice bankroll both already allow >30 BTC wins which is already higher than any non-busta casino out there. My intuition is that there's probably not much advantage for having a much bigger bankroll anyway, and Daniel's time would be a lot better spent on improving player-facing issues.

[RHavar]

2. What's the formula to know the probability of bust before a round reaches X?

Well bustabit has a 1% house edge, so the chance of getting to >= X is simply 0.99/X.


 And the chance of not getting to X, would be 1 minus that.

Some more questions:

1. What's the probability of bust at 1?

1x bust is kind of a special case. You can't bet at 1x, because there's a 1% house edge it means that 99% of the time you win (nothing) and 1% you lose (everything). This is a bit retarded, so it doesn't even make sense to let people bet at 1x.

So any time a result that comes up that would cause someone betting >= 1.01x  ... it is called a 1x. So to figure out the probability of that, would be:

chance of >= 1.01   is ....   0.99/1.01   ...  or 98.02%
so the chance of not getting it is  1-that. Or 1.98%



...i think

[Timetwister]

4. I insist on please checking a way to share Bustadice and Bustabit bankrolls for those of us interested, it would in practice make both bankrolls bigger, maximum bets bigger, and expected returns from investing higher. Good for everyone.

I don't think this is a good idea. Bustadice uses a pretty unique provably fair system that gives investors and Daniel himself much better assurances than any normal provably fair site (including bustabit). Even should the bustadice server and database get hacked, the hacker would still not be able to predict rolls. This means that if a whale comes on bustadice and wins a lot of money, Daniel has very strong assurances the wins are legitimate (or me being also hacked or the hacker). Likewise this ends up extending considerable protections to investors (assuming they believe me and Daniel to be independent).

 And unfortunately these same guarantees can't be extended to bustabit itself, due to the real-time nature of bustabit. And you can't really combine the bankrolls without inheriting the security aspect of the weakest. And I think in practice these are extremely useful guarantees, and should not dismissed lightly. But also taking a step backward, the bustabit/bustadice bankroll both already allow >30 BTC wins which is already higher than any non-busta casino out there. My intuition is that there's probably not much advantage for having a much bigger bankroll anyway, and Daniel's time would be a lot better spent on improving player-facing issues.

I meant offering that option, not that by default investing in one place entails investing in both. I’d personally prefer that my bankroll was used in both places, so I’d have bigger expected returns. If others prefer just one of the sites, they could choose that option too.

[Timetwister]

2. What's the formula to know the probability of bust before a round reaches X?

Well bustabit has a 1% house edge, so the chance of getting to >= X is simply 0.99/X.


 And the chance of not getting to X, would be 1 minus that.

Some more questions:

1. What's the probability of bust at 1?

1x bust is kind of a special case. You can't bet at 1x, because there's a 1% house edge it means that 99% of the time you win (nothing) and 1% you lose (everything). This is a bit retarded, so it doesn't even make sense to let people bet at 1x.

So any time a result that comes up that would cause someone betting >= 1.01x  ... it is called a 1x. So to figure out the probability of that, would be:

chance of >= 1.01   is ....   0.99/1.01   ...  or 98.02%
so the chance of not getting it is  1-that. Or 1.98%



...i think

I see. Wouldn’t the probability of 1 be 1% then?
1-0.99/1=0.01

[devans]

I meant offering that option, not that by default investing in one place entails investing in both. I’d personally prefer that my bankroll was used in both places, so I’d have bigger expected returns. If others prefer just one of the sites, they could choose that option too.

I understand the use case, but I don't think it's worth providing. In order to safely risk the optimal amount, bets against the bankroll need to be processed sequentially. Synchronizing bets across both games isn't feasible, e.g. you wouldn't want to wait for the round on bustabit to end before you're able to place a bet on bustadice. bustabit could pessimistically reserve part of the bankroll while bets on bustadice continue, but then bustadice investors would no longer be risking the optimal amount.

Regardless, the solution is overly complex without providing any benefit to either casino. At more than 4,000 BTC each, both bustabit and bustadice already have the largest bankrolls of any Bitcoin casinos that I'm aware of.

You can still invest in both bankrolls at the same time by using the offsite investment feature. Of course that means you'll need to be slightly more active in managing your investment than if you had only invested in one bankroll.

[Timetwister]

I meant offering that option, not that by default investing in one place entails investing in both. I’d personally prefer that my bankroll was used in both places, so I’d have bigger expected returns. If others prefer just one of the sites, they could choose that option too.

I understand the use case, but I don't think it's worth providing. In order to safely risk the optimal amount, bets against the bankroll need to be processed sequentially. Synchronizing bets across both games isn't feasible, e.g. you wouldn't want to wait for the round on bustabit to end before you're able to place a bet on bustadice. bustabit could pessimistically reserve part of the bankroll while bets on bustadice continue, but then bustadice investors would no longer be risking the optimal amount.

Regardless, the solution is overly complex without providing any benefit to either casino. At more than 4,000 BTC each, both bustabit and bustadice already have the largest bankrolls of any Bitcoin casinos that I'm aware of.

You can still invest in both bankrolls at the same time by using the offsite investment feature. Of course that means you'll need to be slightly more active in managing your investment than if you had only invested in one bankroll.

I see, I didn't think about that, it makes sense to keep them separate then.

Is this correct? Assuming players were hitting the maximum bet per round every round (we wish), we'd get 0 expected bankroll growth with a "leverage" of (2*0.75)/1.125=4/3

[devans]

I see. Wouldn’t the probability of 1 be 1% then?
1-0.99/1=0.01

Not quite. 1 - 0.99 / m is the probability of losing a bet at m. So 0.01 is actually the probability of losing a bet at 1.00x if such a bet were possible.

This might seem impossible since 1.00x is the lowest multiplier you can roll, so you would expect the probability of losing that bet to be 0%. But if we look at the formula we can see that it's actually possible to "roll" a 0.99 before a floor of 1.00x is applied:

Code:

// 4. X = 99 / (1-X)
X = 99 / (1 - X)

// 5. return max(trunc(X), 100)
const result = Math.floor(X)
return Math.max(1, result / 100)

[devans]

Is this correct? Assuming players were hitting the maximum bet per round every round (we wish), we'd get 0 expected bankroll growth with a "leverage" of (2*0.75)/1.125=4/3

I think that's what you mean, but it's worth clarifying: Only your risk affects your expected bankroll growth, not the bet size. That's why bustadice could safely accept 3,000+ BTC bets as long as they don't try to win more than the maximum profit.

Your expected bankroll growth becomes 0 at 2x Kelly and at worst bustabit risks 1.5x Kelly, so your calculation looks correct to me.

[Samarkand]

Has anybody an idea why Bustadice currently has
a higher bankroll than Bustabit?

A rational investor would put their money in Bustabit, because of the higher
betting volume (roughly 215k BTC wagered at Bustabit vs
72k BTC wagered at Bustadice). Of course the historical
data might not be a good predictor for the future betting
volume, but still it is at least an indication for a higher
potential profit.

[RHavar]

Has anybody an idea why Bustadice currently has
a higher bankroll than Bustabit?

My guess is its due to bustadice having a multi-party provably fair system, which gives investor there some guarantees that are not offered on any other casino. And not only does the multi-party provably fair system offer some protection for investors against the house playing on the site, it also offers good protection against the casino being compromised (i.e. even if the site was fully compromised, an attacker couldn't predict rolls to make it look like he's a lucky person. So he'd be more restricted to robbing the hot funds)

[Timetwister]

Is this correct? Assuming players were hitting the maximum bet per round every round (we wish), we'd get 0 expected bankroll growth with a "leverage" of (2*0.75)/1.125=4/3

I think that's what you mean, but it's worth clarifying: Only your risk affects your expected bankroll growth, not the bet size. That's why bustadice could safely accept 3,000+ BTC bets as long as they don't try to win more than the maximum profit.

Your expected bankroll growth becomes 0 at 2x Kelly and at worst bustabit risks 1.5x Kelly, so your calculation looks correct to me.

I was thinking about something that is needed to make the "offsite" bankroll option really safe. Instead of investors manually adjusting their offsite bankroll, it would automatically change if things go wrong, to keep the same "leverage" as the last time the offsite amount was modified.

For example, you invest 1 BTC onsite and 0.5 offsite. If at any point your onsite part drops from 1, then your offsite amount would automatically adjust to keep that 1:0.5 ratio. So if the casino is losing, your bankroll could drop to 0.9 onsite and offsite would be adjusted to 0.45. That way your "leverage" doesn't increase when things go wrong. If the casino is doing well, you may end up with 1.1 onsite and 0.5 offsite. So if you notice it and you still desire to keep the same "leverage", you'd manually adjust your offsite amount to 0.55 to keep the same 1:0.5 ratio.

You could also offer another option, which would be to keep adjusting the onsite/offsite ratio even after winning bets (this is basically better for everyone except people that really are keeping a specific amount of BTC outside ready to be deposited if things go wrong).

Basically unless something like this is implemented, you are forced to keep adjusting your offsite amount/depositing. And therefore you have to keep monitoring how your investment is doing. That obviously isn't possible in practice. So it's not safe to keep any amount of BTC offsite with the current system.

[Samarkand]

...
My guess is its due to bustadice having a multi-party provably fair system, which gives investor there some guarantees that are not offered on any other casino.
...

I didn´t think of that explanation, thank you. Maybe investors are indeed valuing
this multi-party provably fair system more than I thought.

...
You could also offer another option, which would be to keep adjusting the onsite/offsite ratio even after winning bets (this is basically better for everyone except people that really are keeping a specific amount of BTC outside ready to be deposited if things go wrong).

Basically unless something like this is implemented, you are forced to keep adjusting your offsite amount/depositing. And therefore you have keep monitoring. So it's not safe to keep any amount of BTC offsite with the current system.

Your feature request seems unnecessarily complicated and I don´t really see
why devans would implement something like this. If you are worried about this,
you can just adjust your investment manually from time to time. Most
investors are clearly not worried about this as I have never seen anybody ask
for a feature like this.

I´d also disagree with the bolded statements. Investing at 5:1 leverage and then not
monitoring your investment at all may be risky, but if you choose a more conservative leverage
and check your investments every once in a while I don´t really see a problem.

Where I actually agree with you is the fact that having an onsite/offsite system at all
ends up forcing investors to use leverage in order to not get diluted. I know that the
system is designed for something different, but in reality people just use it to invest
with leverage without even having the offsite coins in most cases (this has been
the case at every single dice site that allows leveraged investments in my experience).

[Timetwister]

Your feature request seems unnecessary complicated and I don´t really see
why devans would implement something like this. If you are worried about this,
you can just adjust your investment manually from time to time. Most
investors are clearly not worried about this as I have never seen anybody ask
for a feature like this.

I´d also disagree with the bolded statements. Investing at 5:1 leverage and then not
monitoring your investment at all may be risky, but if you choose a more conservative leverage
and check your investments every once in a while I don´t really see a problem.

Where I actually agree with you is the fact that having an onsite/offsite system at all
ends up forcing investors to use leverage in order to not get diluted. I know that the
system is designed for something different, but in reality people just use it to invest
with leverage without even having the offsite coins in most cases (this has been
the case at every single dice site that allows leveraged investments in my experience).

Just because others may not have mentioned it before doesn't mean they don't agree with me (maybe they didn't think about it or didn't care to post here, this thread is very small considering how big is Bustabit nowadays).

I think the onsite/offsite system is useful not only to people that really are keeping coins outside for counterparty risk (personally I think that's a minority) but also to allow people to leverage, because they are less risk adverse (although I'd limit the leverage, the 1:1 ratio used here is reasonable, not like those casinos allowing 1:24...). However, unless something like what I explained before is implemented, everyone using any offsite amount is required to keep monitoring, and changing their offsite amount (if they are leveraging) or depositing (if they are keeping coins outside because of counterparty risk). That's not really possible.

You say to check "from time to time", but that wouldn't prevent you from the scenario you are trying to avoid, the casino losing lots of money and therefore either your leverage raising more that you would like, or not having time to deposit your offsite amount. If big losses happen, it would probably be in a short time span, so you are required to monitor all the time your investment. Just because that scenario hasn't happened yet (or maybe it already did, I don't know), it doesn't mean it can't happen in the future.

I'm slightly "leveraged" (not really, I have those coins outside) and after considering this, I regret my decision. For now I'm not changing anything as it sucks to remove the offsite amount after having paid the dilution fee, but I wouldn't use any offsite amount from now on unless this is changed.

[RHavar]

I'm slightly "leveraged" (not really, I have those coins outside) and after considering this, I regret my decision. For now I'm not changing anything as it sucks to remove the offsite amount after having paid the dilution fee, but I wouldn't use any offsite amount from now on unless this is changed.

You can adjust your offsite without paying dilution fee. You only pay dilution fee when your (onsite+offsite) goes up. So if you decrease your offsite at the same time as increasing your onsite, you pay nothing (by design)

[devans]

Has anybody an idea why Bustadice currently has
a higher bankroll than Bustabit?

My guess is its due to bustadice having a multi-party provably fair system, which gives investor there some guarantees that are not offered on any other casino. And not only does the multi-party provably fair system offer some protection for investors against the house playing on the site, it also offers good protection against the casino being compromised (i.e. even if the site was fully compromised, an attacker couldn't predict rolls to make it look like he's a lucky person. So he'd be more restricted to robbing the hot funds)

bustadice has also been doing really well lately, so that might have attracted some investor interest as well. For instance, in terms of wager volume it has consistently led the weekly top 10 on dicesites.com over the past couple of weeks.

[Timetwister]

Has anybody an idea why Bustadice currently has
a higher bankroll than Bustabit?

My guess is its due to bustadice having a multi-party provably fair system, which gives investor there some guarantees that are not offered on any other casino. And not only does the multi-party provably fair system offer some protection for investors against the house playing on the site, it also offers good protection against the casino being compromised (i.e. even if the site was fully compromised, an attacker couldn't predict rolls to make it look like he's a lucky person. So he'd be more restricted to robbing the hot funds)

bustadice has also been doing really well lately, so that might have attracted some investor interest as well. For instance, in terms of wager volume it has consistently led the weekly top 10 on dicesites.com over the past couple of weeks.

What do you think about my suggestions to make using the offsite option really safe (as monitoring all the time isn't realistic)?

[devans]

What do you think about my suggestions to make using the offsite option really safe (as monitoring all the time isn't realistic)?

It sounds like you may have some misconceptions about the intentions behind bustabit's offsite system. Our system is designed to allow investors to reduce their counterparty risk and increase their liquidity. Leverage is used to accomplish that, but allowing investors to choose a static leverage and maintaining that is not its goal.

Assuming you don't misrepresent your offsite investment, you will always risk 0.75 % of your total investment per bet. Whether that is "safe" is debatable–is investing in a casino's bankroll really ever "safe"?–but it is the optimal risk for maximum bankroll growth (see Kelly criterion). That means that leverage will decrease as your the onsite portion of your investment grows and increase as the onsite portion decreases. This is not a flaw, but the correct behavior and by design.

Regardless, automatically reducing your leverage as your onsite portion decreases has the same risks as being margin-called: In both cases your stake will decrease and you won't be able to benefit from an upswing without manual intervention. So I don't fully understand why you consider static leverage to be safer. If you want to be "really safe" and avoid the risk of being margin called entirely then depositing your entire investment is your only option.

[Timetwister]

What do you think about my suggestions to make using the offsite option really safe (as monitoring all the time isn't realistic)?

It sounds like you may have some misconceptions about the intentions behind bustabit's offsite system. Our system is designed to allow investors to reduce their counterparty risk and increase their liquidity. Leverage is used to accomplish that, but allowing investors to choose a static leverage and maintaining that is not its goal.

Assuming you don't misrepresent your offsite investment, you will always risk 0.75 % of your total investment per bet. Whether that is "safe" is debatable–is investing in a casino's bankroll really ever "safe"?–but it is the optimal risk for maximum bankroll growth (see Kelly criterion). That means that leverage will decrease as your the onsite portion of your investment grows and increase as the onsite portion decreases. This is not a flaw, but the correct behavior and by design.

Regardless, automatically reducing your leverage as your onsite portion decreases has the same risks as being margin-called: In both cases your stake will decrease and you won't be able to benefit from an upswing without manual intervention. So I don't fully understand why you consider static leverage to be safer. If you want to be "really safe" and avoid the risk of being margin called entirely then depositing your entire investment is your only option.

The problem is that it's not realistic to be able to monitor the investment all the time and therefore to deposit that offsite money if needed. So if the casino keeps losing, your "leverage" grows at a higher than the desired rate, so potentially you could lose all your onsite investment (as the casino assumes you still have the same amount offsite which you could deposit). It may be an extremely unlikely event, but eventually it will happen.